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id="toc-Expressed_aim_and_topics_covered-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Book_1,_De_motu_corporum" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Book_1,_De_motu_corporum"> <div class="vector-toc-text"> 1.2 Book 1, De motu corporum </div> </a> <ul id="toc-Book_1,_De_motu_corporum-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Book_2,_part_2_of_De_motu_corporum" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Book_2,_part_2_of_De_motu_corporum"> <div class="vector-toc-text"> 1.3 Book 2, part 2 of De motu corporum </div> </a> <ul id="toc-Book_2,_part_2_of_De_motu_corporum-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Book_3,_De_mundi_systemate" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Book_3,_De_mundi_systemate"> <div class="vector-toc-text"> 1.4 Book 3, De mundi systemate </div> </a> <ul id="toc-Book_3,_De_mundi_systemate-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Commentary_on_the_Principia" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Commentary_on_the_Principia"> <div class="vector-toc-text"> 1.5 Commentary on the Principia </div> </a> <ul id="toc-Commentary_on_the_Principia-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Rules_of_Reason" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Rules_of_Reason"> <div class="vector-toc-text"> 2 Rules of Reason </div> </a> <button aria-controls="toc-Rules_of_Reason-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Rules of Reason subsection </button> <ul id="toc-Rules_of_Reason-sublist" class="vector-toc-list"> <li id="toc-General_Scholium" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#General_Scholium"> <div class="vector-toc-text"> 2.1 General Scholium </div> </a> <ul id="toc-General_Scholium-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Publishing_the_book" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Publishing_the_book"> <div class="vector-toc-text"> 3 Publishing the book </div> </a> <button aria-controls="toc-Publishing_the_book-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Publishing the book subsection </button> <ul id="toc-Publishing_the_book-sublist" class="vector-toc-list"> <li id="toc-Halley_and_Newton's_initial_stimulus" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Halley_and_Newton's_initial_stimulus"> <div class="vector-toc-text"> 3.1 Halley and Newton's initial stimulus </div> </a> <ul id="toc-Halley_and_Newton's_initial_stimulus-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Preliminary_version" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Preliminary_version"> <div class="vector-toc-text"> 3.2 Preliminary version </div> </a> <ul id="toc-Preliminary_version-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Halley's_role_as_publisher" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Halley's_role_as_publisher"> <div class="vector-toc-text"> 3.3 Halley's role as publisher </div> </a> <ul id="toc-Halley's_role_as_publisher-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Historical_context" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Historical_context"> <div class="vector-toc-text"> 4 Historical context </div> </a> <button aria-controls="toc-Historical_context-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Historical context subsection </button> <ul id="toc-Historical_context-sublist" class="vector-toc-list"> <li id="toc-Beginnings_of_the_Scientific_Revolution" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Beginnings_of_the_Scientific_Revolution"> <div class="vector-toc-text"> 4.1 Beginnings of the Scientific Revolution </div> </a> <ul id="toc-Beginnings_of_the_Scientific_Revolution-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Newton's_role" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Newton's_role"> <div class="vector-toc-text"> 4.2 Newton's role </div> </a> <ul id="toc-Newton's_role-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Newton's_early_work_on_motion" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Newton's_early_work_on_motion"> <div class="vector-toc-text"> 4.3 Newton's early work on motion </div> </a> <ul id="toc-Newton's_early_work_on_motion-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Controversy_with_Hooke" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Controversy_with_Hooke"> <div class="vector-toc-text"> 4.4 Controversy with Hooke </div> </a> <ul id="toc-Controversy_with_Hooke-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Location_of_early_edition_copies" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Location_of_early_edition_copies"> <div class="vector-toc-text"> 5 Location of early edition copies </div> </a> <ul id="toc-Location_of_early_edition_copies-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Later_editions" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Later_editions"> <div class="vector-toc-text"> 6 Later editions </div> </a> <button aria-controls="toc-Later_editions-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle Later editions subsection </button> <ul id="toc-Later_editions-sublist" class="vector-toc-list"> <li id="toc-Second_edition,_1713" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Second_edition,_1713"> <div class="vector-toc-text"> 6.1 Second edition, 1713 </div> </a> <ul id="toc-Second_edition,_1713-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Third_edition,_1726" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Third_edition,_1726"> <div class="vector-toc-text"> 6.2 Third edition, 1726 </div> </a> <ul id="toc-Third_edition,_1726-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Translations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Translations"> <div class="vector-toc-text"> 6.3 Translations </div> </a> <ul id="toc-Translations-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Varia" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Varia"> <div class="vector-toc-text"> 7 Varia </div> </a> <ul id="toc-Varia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> 8 See also </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> 9 References </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> 10 Further reading </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> 11 External links </div> </a> <button aria-controls="toc-External_links-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> Toggle External links subsection </button> <ul id="toc-External_links-sublist" class="vector-toc-list"> <li id="toc-Latin_versions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Latin_versions"> <div class="vector-toc-text"> 11.1 Latin versions </div> </a> <ul id="toc-Latin_versions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-English_translations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#English_translations"> <div class="vector-toc-text"> 11.2 English translations </div> </a> <ul id="toc-English_translations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_links" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_links"> <div class="vector-toc-text"> 11.3 Other links </div> </a> <ul id="toc-Other_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" > Toggle the table of contents </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading">Philosophiæ Naturalis Principia Mathematica</h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 71 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-71" aria-hidden="true" > 71 languages </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Philosophiae_Naturalis_Principia_Mathematica" title="Philosophiae Naturalis Principia Mathematica – Afrikaans" lang="af" hreflang="af" data-title="Philosophiae Naturalis Principia Mathematica" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target">Afrikaans</a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%84%D8%A3%D8%B5%D9%88%D9%84_%D8%A7%D9%84%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A9_%D9%84%D9%84%D9%81%D9%84%D8%B3%D9%81%D8%A9_%D8%A7%D9%84%D8%B7%D8%A8%D9%8A%D8%B9%D9%8A%D8%A9" title="الأصول الرياضية للفلسفة الطبيعية – Arabic" lang="ar" hreflang="ar" data-title="الأصول الرياضية للفلسفة الطبيعية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AB%E0%A6%BF%E0%A6%B2%E0%A7%8B%E0%A6%9B%27%E0%A6%AB%E0%A6%BF%E0%A6%AF%E0%A6%BC%E0%A6%BE_%E0%A6%A8%E0%A7%87%E0%A6%9A%E0%A6%BE%E0%A7%B0%E0%A7%87%E0%A6%B2%E0%A6%BF%E0%A6%9A_%E0%A6%AA%E0%A7%8D%E0%A7%B0%E0%A6%BF%E0%A6%A8%E0%A7%8D%E0%A6%B8%E0%A6%BF%E0%A6%AA%E0%A6%BF%E0%A6%AF%E0%A6%BC%E0%A6%BE_%E0%A6%AE%E0%A7%87%E0%A6%A5%E0%A7%87%E0%A6%AE%E0%A7%87%E0%A6%9F%E0%A6%BF%E0%A6%95%E0%A6%BE" title="ফিলোছ'ফিয়া নেচাৰেলিচ প্ৰিন্সিপিয়া মেথেমেটিকা – Assamese" lang="as" hreflang="as" data-title="ফিলোছ'ফিয়া নেচাৰেলিচ প্ৰিন্সিপিয়া মেথেমেটিকা" data-language-autonym="অসমীয়া" data-language-local-name="Assamese" class="interlanguage-link-target">অসমীয়া</a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Philosophi%C3%A6_naturalis_principia_mathematica" title="Philosophiæ naturalis principia mathematica – Asturian" lang="ast" hreflang="ast" data-title="Philosophiæ naturalis principia mathematica" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target">Asturianu</a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Natural_f%C9%99ls%C9%99f%C9%99nin_riyazi_%C9%99saslar%C4%B1" title="Natural fəlsəfənin riyazi əsasları – Azerbaijani" lang="az" hreflang="az" data-title="Natural fəlsəfənin riyazi əsasları" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target">Azərbaycanca</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AB%E0%A6%BF%E0%A6%B2%E0%A7%8B%E0%A6%B8%E0%A6%AB%E0%A6%BF%E0%A6%AF%E0%A6%BC%E0%A6%BE_%E0%A6%A8%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%9A%E0%A6%BE%E0%A6%B0%E0%A6%BE%E0%A6%B2%E0%A6%BF%E0%A6%B8_%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%BF%E0%A6%A8%E0%A7%8D%E0%A6%B8%E0%A6%BF%E0%A6%AA%E0%A6%BF%E0%A6%AF%E0%A6%BC%E0%A6%BE_%E0%A6%AE%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%A5%E0%A6%BE%E0%A6%AE%E0%A7%87%E0%A6%9F%E0%A6%BF%E0%A6%95%E0%A6%BE" title="ফিলোসফিয়া ন্যাচারালিস প্রিন্সিপিয়া ম্যাথামেটিকা – Bangla" lang="bn" hreflang="bn" data-title="ফিলোসফিয়া ন্যাচারালিস প্রিন্সিপিয়া ম্যাথামেটিকা" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%82%E0%A4%B8%E0%A4%BF%E0%A4%AA%E0%A4%BF%E0%A4%AF%E0%A4%BE_%E0%A4%A8%E0%A5%87%E0%A4%9A%E0%A5%81%E0%A4%B0%E0%A4%BE%E0%A4%B2%E0%A4%BF%E0%A4%B8_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%82%E0%A4%B8%E0%A4%BF%E0%A4%AA%E0%A4%BF%E0%A4%AF%E0%A4%BE_%E0%A4%AE%E0%A5%88%E0%A4%A5%E0%A5%87%E0%A4%AE%E0%A5%87%E0%A4%9F%E0%A4%BF%E0%A4%95%E0%A4%BE" title="प्रिंसिपिया नेचुरालिस प्रिंसिपिया मैथेमेटिका – Bhojpuri" lang="bh" hreflang="bh" data-title="प्रिंसिपिया नेचुरालिस प्रिंसिपिया मैथेमेटिका" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target">भोजपुरी</a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8_%D0%BD%D0%B0%D1%87%D0%B0%D0%BB%D0%B0_%D0%BD%D0%B0_%D0%BD%D0%B0%D1%82%D1%83%D1%80%D1%84%D0%B8%D0%BB%D0%BE%D1%81%D0%BE%D1%84%D0%B8%D1%8F%D1%82%D0%B0" title="Математически начала на натурфилософията – Bulgarian" lang="bg" hreflang="bg" data-title="Математически начала на натурфилософията" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target">Български</a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Matemati%C4%8Dki_principi_prirodne_filozofije" title="Matematički principi prirodne filozofije – Bosnian" lang="bs" hreflang="bs" data-title="Matematički principi prirodne filozofije" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target">Bosanski</a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Philosophiae_Naturalis_Principia_Mathematica" title="Philosophiae Naturalis Principia Mathematica – Catalan" lang="ca" hreflang="ca" data-title="Philosophiae Naturalis Principia Mathematica" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target">Català</a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%C3%87%D1%83%D1%82%C3%A7%D0%B0%D0%BD%D1%82%D0%B0%D0%BB%C4%83%D0%BA_%D1%84%D0%B8%D0%BB%D0%BE%D1%81%D0%BE%D1%84%D0%B8%D0%B9%C4%95%D0%BD_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%C4%83%D0%BB%D0%BB%D0%B0_%D0%BF%D1%83%C3%A7%D0%BB%D0%B0%D0%BC%C4%83%D1%88%C4%95%D1%81%D0%B5%D0%BC" title="Çутçанталăк философийĕн математикăлла пуçламăшĕсем – Chuvash" lang="cv" hreflang="cv" data-title="Çутçанталăк философийĕн математикăлла пуçламăшĕсем" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target">Чӑвашла</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Philosophiae_Naturalis_Principia_Mathematica" title="Philosophiae Naturalis Principia Mathematica – Czech" lang="cs" hreflang="cs" data-title="Philosophiae Naturalis Principia Mathematica" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Philosophiae_Naturalis_Principia_Mathematica" title="Philosophiae Naturalis Principia Mathematica – Welsh" lang="cy" hreflang="cy" data-title="Philosophiae Naturalis Principia Mathematica" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target">Cymraeg</a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Philosophiae_Naturalis_Principia_Mathematica" title="Philosophiae Naturalis Principia Mathematica – Danish" lang="da" hreflang="da" data-title="Philosophiae Naturalis Principia Mathematica" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target">Dansk</a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Philosophiae_Naturalis_Principia_Mathematica" title="Philosophiae Naturalis Principia Mathematica – German" lang="de" hreflang="de" data-title="Philosophiae Naturalis Principia Mathematica" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target">Deutsch</a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Philosophi%C3%A6_Naturalis_Principia_Mathematica" title="Philosophiæ Naturalis Principia Mathematica – Estonian" lang="et" hreflang="et" data-title="Philosophiæ Naturalis Principia Mathematica" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target">Eesti</a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/Philosophi%C3%A6_Naturalis_Principia_Mathematica" title="Philosophiæ Naturalis Principia Mathematica – Greek" lang="el" hreflang="el" data-title="Philosophiæ Naturalis Principia Mathematica" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Philosophi%C3%A6_naturalis_principia_mathematica" title="Philosophiæ naturalis principia mathematica – Spanish" lang="es" hreflang="es" data-title="Philosophiæ naturalis principia mathematica" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Philosophiae_Naturalis_Principia_Mathematica" title="Philosophiae Naturalis Principia Mathematica – Esperanto" lang="eo" hreflang="eo" data-title="Philosophiae Naturalis Principia Mathematica" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Philosophi%C3%A6_Naturalis_Principia_Mathematica" title="Philosophiæ Naturalis Principia Mathematica – Basque" lang="eu" hreflang="eu" data-title="Philosophiæ Naturalis Principia Mathematica" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D8%B5%D9%88%D9%84_%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C_%D9%81%D9%84%D8%B3%D9%81%D9%87_%D8%B7%D8%A8%DB%8C%D8%B9%DB%8C" title="اصول ریاضی فلسفه طبیعی – Persian" lang="fa" hreflang="fa" data-title="اصول ریاضی فلسفه طبیعی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Philosophi%C3%A6_naturalis_principia_mathematica" title="Philosophiæ naturalis principia mathematica – French" lang="fr" hreflang="fr" data-title="Philosophiæ naturalis principia mathematica" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Philosophiae_Naturalis_Principia_Mathematica" title="Philosophiae Naturalis Principia Mathematica – Irish" lang="ga" hreflang="ga" data-title="Philosophiae Naturalis Principia Mathematica" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target">Gaeilge</a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Philosophi%C3%A6_Naturalis_Principia_Mathematica" title="Philosophiæ Naturalis Principia Mathematica – Manx" lang="gv" hreflang="gv" data-title="Philosophiæ Naturalis Principia Mathematica" data-language-autonym="Gaelg" data-language-local-name="Manx" class="interlanguage-link-target">Gaelg</a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Philosophi%C3%A6_Naturalis_Principia_Mathematica" title="Philosophiæ Naturalis Principia Mathematica – Galician" lang="gl" hreflang="gl" data-title="Philosophiæ Naturalis Principia Mathematica" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target">Galego</a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AA%E0%AB%8D%E0%AA%B0%E0%AA%BF%E0%AA%A8%E0%AB%8D%E0%AA%B8%E0%AA%BF%E0%AA%AA%E0%AA%BF%E0%AA%AF%E0%AA%BE" title="પ્રિન્સિપિયા – Gujarati" lang="gu" hreflang="gu" data-title="પ્રિન્સિપિયા" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" class="interlanguage-link-target">ગુજરાતી</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9E%90%EC%97%B0%EC%B2%A0%ED%95%99%EC%9D%98_%EC%88%98%ED%95%99%EC%A0%81_%EC%9B%90%EB%A6%AC" title="자연철학의 수학적 원리 – Korean" lang="ko" hreflang="ko" data-title="자연철학의 수학적 원리" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%82%E0%A4%B8%E0%A4%BF%E0%A4%AA%E0%A4%BF%E0%A4%AF%E0%A4%BE" title="प्रिंसिपिया – Hindi" lang="hi" hreflang="hi" data-title="प्रिंसिपिया" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Philosophiae_Naturalis_Principia_Mathematica" title="Philosophiae Naturalis Principia Mathematica – Croatian" lang="hr" hreflang="hr" data-title="Philosophiae Naturalis Principia Mathematica" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target">Hrvatski</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Philosophi%C3%A6_Naturalis_Principia_Mathematica" title="Philosophiæ Naturalis Principia Mathematica – Indonesian" lang="id" hreflang="id" data-title="Philosophiæ Naturalis Principia Mathematica" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Philosophiae_Naturalis_Principia_Mathematica" title="Philosophiae Naturalis Principia Mathematica – Italian" lang="it" hreflang="it" data-title="Philosophiae Naturalis Principia Mathematica" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A2%D7%A7%D7%A8%D7%95%D7%A0%D7%95%D7%AA_%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%99%D7%9D_%D7%A9%D7%9C_%D7%A4%D7%99%D7%9C%D7%95%D7%A1%D7%95%D7%A4%D7%99%D7%99%D7%AA_%D7%94%D7%98%D7%91%D7%A2" title="עקרונות מתמטיים של פילוסופיית הטבע – Hebrew" lang="he" hreflang="he" data-title="עקרונות מתמטיים של פילוסופיית הטבע" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9C%E1%83%90%E1%83%A2%E1%83%A3%E1%83%A0%E1%83%90%E1%83%9A%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%A4%E1%83%98%E1%83%9A%E1%83%9D%E1%83%A1%E1%83%9D%E1%83%A4%E1%83%98%E1%83%98%E1%83%A1_%E1%83%9B%E1%83%90%E1%83%97%E1%83%94%E1%83%9B%E1%83%90%E1%83%A2%E1%83%98%E1%83%99%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%A1%E1%83%90%E1%83%AC%E1%83%A7%E1%83%98%E1%83%A1%E1%83%94%E1%83%91%E1%83%98" title="ნატურალური ფილოსოფიის მათემატიკური საწყისები – Georgian" lang="ka" hreflang="ka" data-title="ნატურალური ფილოსოფიის მათემატიკური საწყისები" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target">ქართული</a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A2%D0%B0%D0%B1%D0%B8%D2%93%D0%B0%D1%82_%D1%84%D0%B8%D0%BB%D0%BE%D1%81%D0%BE%D1%84%D0%B8%D1%8F%D1%81%D1%8B%D0%BD%D1%8B%D2%A3_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D2%9B_%D2%9B%D0%B0%D2%93%D0%B8%D0%B4%D0%B0%D0%BB%D0%B0%D1%80%D1%8B" title="Табиғат философиясының математикалық қағидалары – Kazakh" lang="kk" hreflang="kk" data-title="Табиғат философиясының математикалық қағидалары" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target">Қазақша</a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Philosophi%C3%A6_naturalis_principia_mathematica" title="Philosophiæ naturalis principia mathematica – Haitian Creole" lang="ht" hreflang="ht" data-title="Philosophiæ naturalis principia mathematica" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target">Kreyòl ayisyen</a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Philosophiae_naturalis_principia_mathematica" title="Philosophiae naturalis principia mathematica – Latin" lang="la" hreflang="la" data-title="Philosophiae naturalis principia mathematica" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target">Latina</a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Dabas_filozofijas_matem%C4%81tiskie_principi" title="Dabas filozofijas matemātiskie principi – Latvian" lang="lv" hreflang="lv" data-title="Dabas filozofijas matemātiskie principi" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target">Latviešu</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Philosophiae_Naturalis_Principia_Mathematica" title="Philosophiae Naturalis Principia Mathematica – Hungarian" lang="hu" hreflang="hu" data-title="Philosophiae Naturalis Principia Mathematica" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AB%E0%B4%BF%E0%B4%B2%E0%B5%8B%E0%B4%B8%E0%B5%8B%E0%B4%AB%E0%B4%BF%E0%B4%AF_%E0%B4%A8%E0%B4%BE%E0%B4%9A%E0%B5%8D%E0%B4%9A%E0%B5%81%E0%B4%B1%E0%B4%BE%E0%B4%B2%E0%B4%BF_%E0%B4%AA%E0%B5%8D%E0%B4%B0%E0%B4%BF%E0%B5%BB%E0%B4%B8%E0%B4%BF%E0%B4%AA%E0%B5%8D%E0%B4%AA%E0%B4%BF%E0%B4%AF_%E0%B4%AE%E0%B4%BE%E0%B4%A4%E0%B5%8D%E0%B4%A4%E0%B4%AE%E0%B4%BE%E0%B4%B1%E0%B5%8D%E0%B4%B1%E0%B4%BF%E0%B4%95%E0%B5%8D%E0%B4%95" title="ഫിലോസോഫിയ നാച്ചുറാലി പ്രിൻസിപ്പിയ മാത്തമാറ്റിക്ക – Malayalam" lang="ml" hreflang="ml" data-title="ഫിലോസോഫിയ നാച്ചുറാലി പ്രിൻസിപ്പിയ മാത്തമാറ്റിക്ക" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target">മലയാളം</a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Philosophiae_Naturalis_Principia_Mathematica" title="Philosophiae Naturalis Principia Mathematica – Malay" lang="ms" hreflang="ms" data-title="Philosophiae Naturalis Principia Mathematica" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target">Bahasa Melayu</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Philosophiae_Naturalis_Principia_Mathematica" title="Philosophiae Naturalis Principia Mathematica – Dutch" lang="nl" hreflang="nl" data-title="Philosophiae Naturalis Principia Mathematica" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%87%AA%E7%84%B6%E5%93%B2%E5%AD%A6%E3%81%AE%E6%95%B0%E5%AD%A6%E7%9A%84%E8%AB%B8%E5%8E%9F%E7%90%86" title="自然哲学の数学的諸原理 – Japanese" lang="ja" hreflang="ja" data-title="自然哲学の数学的諸原理" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-no badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://no.wikipedia.org/wiki/Philosophi%C3%A6_naturalis_principia_mathematica" title="Philosophiæ naturalis principia mathematica – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Philosophiæ naturalis principia mathematica" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Philosophiae_Naturalis_Principia_Mathematica" title="Philosophiae Naturalis Principia Mathematica – Occitan" lang="oc" hreflang="oc" data-title="Philosophiae Naturalis Principia Mathematica" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target">Occitan</a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Naturfalsafaning_matematik_tamoyillari" title="Naturfalsafaning matematik tamoyillari – Uzbek" lang="uz" hreflang="uz" data-title="Naturfalsafaning matematik tamoyillari" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target">Oʻzbekcha / ўзбекча</a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%BE%D8%B1%D9%86%D8%B3%DB%8C%D9%BE%DB%8C%D8%A7_%D9%85%DB%8C%D8%AA%DA%BE%D9%85%D9%B9%DB%8C%D8%B4%DB%8C%D8%A7" title="پرنسیپیا میتھمٹیشیا – Western Punjabi" lang="pnb" hreflang="pnb" data-title="پرنسیپیا میتھمٹیشیا" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target">پنجابی</a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Matimatikal_Prinsipl_a_Nachral_Filasafi" title="Matimatikal Prinsipl a Nachral Filasafi – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Matimatikal Prinsipl a Nachral Filasafi" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target">Patois</a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Matematyczne_zasady_filozofii_naturalnej" title="Matematyczne zasady filozofii naturalnej – Polish" lang="pl" hreflang="pl" data-title="Matematyczne zasady filozofii naturalnej" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Princ%C3%ADpios_Matem%C3%A1ticos_da_Filosofia_Natural" title="Princípios Matemáticos da Filosofia Natural – Portuguese" lang="pt" hreflang="pt" data-title="Princípios Matemáticos da Filosofia Natural" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Philosophiae_Naturalis_Principia_Mathematica" title="Philosophiae Naturalis Principia Mathematica – Romanian" lang="ro" hreflang="ro" data-title="Philosophiae Naturalis Principia Mathematica" data-language-autonym="Română" data-language-local-name="Romanian" 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div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For Whitehead and Russell's work, see <a href="/wiki/Principia_Mathematica" title="Principia Mathematica">Principia Mathematica</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox vcard"><caption class="infobox-title" style="font-size:125%; font-style:italic; padding-bottom:0.2em;">Philosophiæ Naturalis Principia Mathematica <span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Philosophi%C3%A6+Naturalis+Principia+Mathematica&rft.author=%5B%5BIsaac+Newton%5D%5D&rft.date=1687&rft.place=England"></caption><tbody><tr><td colspan="2" class="infobox-image"><a href="/wiki/File:Newton%27s_Principia_title_page.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Newton%27s_Principia_title_page.png/220px-Newton%27s_Principia_title_page.png" decoding="async" width="220" height="305" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Newton%27s_Principia_title_page.png/330px-Newton%27s_Principia_title_page.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Newton%27s_Principia_title_page.png/440px-Newton%27s_Principia_title_page.png 2x" data-file-width="1930" data-file-height="2674" /></a><div class="infobox-caption">Title page of Principia, first edition (1687)</div></td></tr><tr><th scope="row" class="infobox-label">Author</th><td class="infobox-data"><a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a></td></tr><tr><th scope="row" class="infobox-label">Original title</th><td class="infobox-data">Philosophiæ Naturalis Principia Mathematica</td></tr><tr><th scope="row" class="infobox-label">Language</th><td class="infobox-data"><a href="/wiki/Neo-Latin" title="Neo-Latin">Neo-Latin</a></td></tr><tr><th scope="row" class="infobox-label"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Publication date</div></th><td class="infobox-data">1687</td></tr><tr><th scope="row" class="infobox-label">Publication place</th><td class="infobox-data">England</td></tr><tr><th scope="row" class="infobox-label"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Published in English</div></th><td class="infobox-data">1728</td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/LCC_(identifier)" class="mw-redirect" title="LCC (identifier)"><abbr title="Library of Congress Classification">LC Class</abbr></a></th><td class="infobox-data">QA803 .A53</td></tr><tr><th scope="row" class="infobox-label"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Original text</div></th><td class="infobox-data"><a href="https://en.wikisource.org/wiki/la:Philosophiae_Naturalis_Principia_Mathematica" class="extiw" title="s:la:Philosophiae Naturalis Principia Mathematica">Philosophiæ Naturalis Principia Mathematica</a> at Latin <a href="/wiki/Wikisource" title="Wikisource">Wikisource</a></td></tr><tr><th scope="row" class="infobox-label">Translation</th><td class="infobox-data"><a href="https://en.wikisource.org/wiki/The_Mathematical_Principles_of_Natural_Philosophy" class="extiw" title="s:The Mathematical Principles of Natural Philosophy">Philosophiæ Naturalis Principia Mathematica</a> at Wikisource</td></tr></tbody></table> Philosophiæ Naturalis Principia Mathematica (English: The Mathematical Principles of <a href="/wiki/Natural_Philosophy" class="mw-redirect" title="Natural Philosophy">Natural Philosophy</a>)<a href="#cite_note-1">[1]</a> often referred to as simply the Principia (<a href="/wiki/Help:IPA/English" title="Help:IPA/English">/prɪnˈsɪpiə, prɪnˈkɪpiə/</a>), is a book by <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> that expounds <a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newton's laws of motion</a> and his <a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation">law of universal gravitation</a>. The Principia is written in <a href="/wiki/Latin" title="Latin">Latin</a> and comprises three volumes, and was authorized, <a href="/wiki/Imprimatur" title="Imprimatur">imprimatur</a>, by <a href="/wiki/Samuel_Pepys" title="Samuel Pepys">Samuel Pepys</a>, then-President of the <a href="/wiki/Royal_Society" title="Royal Society">Royal Society</a> on 5 July 1686 and first published in 1687.<a href="#cite_note-Principia-2">[2]</a><a href="#cite_note-Motte-3">[3]</a> The Principia is considered one of the most important works in the <a href="/wiki/History_of_science" title="History of science">history of science</a>.<a href="#cite_note-4">[4]</a> The French mathematical physicist <a href="/wiki/Alexis_Clairaut" title="Alexis Clairaut">Alexis Clairaut</a> assessed it in 1747: "The famous book of Mathematical Principles of Natural Philosophy marked the epoch of a great revolution in physics. The method followed by its illustrious author Sir Newton ... spread the light of mathematics on a science which up to then had remained in the darkness of conjectures and hypotheses."<a href="#cite_note-5">[5]</a> The French scientist <a href="/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange">Joseph-Louis Lagrange</a> described it as "the greatest production of a human mind",<a href="#cite_note-6">[6]</a> and French polymath <a href="/wiki/Pierre-Simon_Laplace" title="Pierre-Simon Laplace">Pierre-Simon Laplace</a> stated that "The Principia is pre-eminent above any other production of human genius".<a href="#cite_note-7">[7]</a> Newton's work has also been called the "greatest scientific work in history", and the "supreme expression in human thought of the mind's ability to hold the universe fixed as an object of contemplation".<a href="#cite_note-8">[8]</a> A more recent assessment has been that while acceptance of Newton's laws was not immediate, by the end of the century after publication in 1687, "no one could deny that [out of the Principia] a science had emerged that, at least in certain respects, so far exceeded anything that had ever gone before that it stood alone as the ultimate exemplar of science generally".<a href="#cite_note-9">[9]</a> The Principia forms a mathematical foundation for the theory of <a href="/wiki/Classical_mechanics" title="Classical mechanics">classical mechanics</a>. Among other achievements, it explains <a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Johannes Kepler</a>'s <a href="/wiki/Kepler%27s_laws_of_planetary_motion" title="Kepler's laws of planetary motion">laws of planetary motion</a>, which Kepler had first obtained <a href="/wiki/Empiricism" title="Empiricism">empirically</a>. In formulating his physical laws, Newton developed and used mathematical methods now included in the field of <a href="/wiki/Calculus" title="Calculus">calculus</a>, expressing them in the form of <a href="/wiki/Geometry" title="Geometry">geometric</a> propositions about "vanishingly small" shapes.<a href="#cite_note-geomcalc-10">[10]</a> In a revised conclusion to the Principia (<style data-mw-deduplicate="TemplateStyles:r1033199720">.mw-parser-output div.crossreference{padding-left:0}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951">see <a href="#General_Scholium">§ General Scholium</a>), Newton emphasized the empirical nature of the work with the expression <a href="/wiki/Hypotheses_non_fingo" title="Hypotheses non fingo">Hypotheses non fingo</a> ("I frame/feign no hypotheses").<a href="#cite_note-gschol-hnf-11">[11]</a> After annotating and correcting his personal copy of the first edition,<a href="#cite_note-12">[12]</a> Newton published two further editions, during 1713<a href="#cite_note-variorum-13">[13]</a> with errors of the 1687 corrected, and an improved version<a href="#cite_note-14">[14]</a> of 1726.<a href="#cite_note-variorum-13">[13]</a> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Contents">Contents</h2>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=1" title="Edit section: Contents">edit</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Expressed_aim_and_topics_covered">Expressed aim and topics covered</h3>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=2" title="Edit section: Expressed aim and topics covered">edit</a>]</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Portrait_of_Sir_Isaac_Newton,_1689.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Portrait_of_Sir_Isaac_Newton%2C_1689.jpg/220px-Portrait_of_Sir_Isaac_Newton%2C_1689.jpg" decoding="async" width="220" height="265" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Portrait_of_Sir_Isaac_Newton%2C_1689.jpg/330px-Portrait_of_Sir_Isaac_Newton%2C_1689.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Portrait_of_Sir_Isaac_Newton%2C_1689.jpg/440px-Portrait_of_Sir_Isaac_Newton%2C_1689.jpg 2x" data-file-width="2218" data-file-height="2671" /></a><figcaption>Portrait of Sir <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> (1643–1727), author of the Principia, by <a href="/wiki/Godfrey_Kneller" title="Godfrey Kneller">Godfrey Kneller</a> (1689)</figcaption></figure> The Preface of the work states:<a href="#cite_note-15">[15]</a> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote">... Rational Mechanics will be the sciences of motion resulting from any forces whatsoever, and of the forces required to produce any motion, accurately proposed and demonstrated ... And therefore we offer this work as mathematical principles of his philosophy. For all the difficulty of philosophy seems to consist in this—from the phenomena of motions to investigate the forces of Nature, and then from these forces to demonstrate the other phenomena ...</blockquote> The Principia deals primarily with massive bodies in motion, initially under a variety of conditions and hypothetical laws of force in both non-resisting and resisting media, thus offering criteria to decide, by observations, which laws of force are operating in phenomena that may be observed. It attempts to cover hypothetical or possible motions both of celestial bodies and of terrestrial projectiles. It explores difficult problems of motions perturbed by multiple attractive forces. Its third and final book deals with the interpretation of observations about the movements of planets and their satellites. The book: <ul><li>shows how astronomical observations verify the <a href="/wiki/Inverse_square_law" class="mw-redirect" title="Inverse square law">inverse square law</a> of gravitation (to an accuracy that was high by the standards of Newton's time);</li> <li>offers estimates of relative masses for the known giant planets and for the Earth and the Sun;</li> <li>defines the motion of the Sun relative to the Solar System <a href="/wiki/Barycenter" class="mw-redirect" title="Barycenter">barycenter</a>;</li> <li>shows how the theory of gravity can account for <a href="/wiki/Irregularities_in_the_motion_of_the_Moon" class="mw-redirect" title="Irregularities in the motion of the Moon">irregularities in the motion of the Moon</a>;</li> <li>identifies the oblateness of the shape of the Earth;</li> <li>accounts approximately for marine tides including phenomena of spring and <a href="/wiki/Neap_tide" class="mw-redirect" title="Neap tide">neap tides</a> by the perturbing (and varying) gravitational attractions of the Sun and Moon on the Earth's waters;</li> <li>explains the <a href="/wiki/Axial_precession#Polar_shift_and_equinoxes_shift" title="Axial precession">precession of the equinoxes</a> as an effect of the gravitational attraction of the Moon on the Earth's equatorial bulge; and</li> <li>gives theoretical basis for numerous phenomena about comets and their elongated, near-parabolic orbits.</li></ul> The opening sections of the Principia contain, in revised and extended form, nearly<a href="#cite_note-16">[16]</a> all of the content of Newton's 1684 tract <a href="/wiki/De_motu_corporum_in_gyrum" title="De motu corporum in gyrum">De motu corporum in gyrum</a>. The Principia begin with "Definitions"<a href="#cite_note-17">[17]</a> and "Axioms or Laws of Motion",<a href="#cite_note-18">[18]</a> and continues in three books: <div class="mw-heading mw-heading3"><h3 id="Book_1,_De_motu_corporum">Book 1, De motu corporum</h3>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=3" title="Edit section: Book 1, De motu corporum">edit</a>]</div> Book 1, subtitled De motu corporum (On the motion of bodies) concerns motion in the absence of any resisting medium. It opens with a collection of mathematical <a href="/wiki/Lemma_(mathematics)" title="Lemma (mathematics)">lemmas</a> on "the method of first and last ratios",<a href="#cite_note-19">[19]</a> a geometrical form of infinitesimal calculus.<a href="#cite_note-geomcalc-10">[10]</a> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Newtons_proof_of_Keplers_second_law.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Newtons_proof_of_Keplers_second_law.gif/300px-Newtons_proof_of_Keplers_second_law.gif" decoding="async" width="300" height="154" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/6/60/Newtons_proof_of_Keplers_second_law.gif 1.5x" data-file-width="390" data-file-height="200" /></a><figcaption>Newton's proof of Kepler's second law, as described in the book. If a continuous centripetal force (red arrow) is considered on the planet during its orbit, the area of the triangles defined by the path of the planet will be the same. This is true for any fixed time interval. When the interval tends to zero, the force can be considered instantaneous. (Click image for a detailed description).</figcaption></figure> The second section establishes relationships between centripetal forces and the law of areas now known as <a href="/wiki/Kepler%27s_second_law" class="mw-redirect" title="Kepler's second law">Kepler's second law</a> (Propositions 1–3),<a href="#cite_note-20">[20]</a> and relates circular velocity and radius of path-curvature to radial force<a href="#cite_note-21">[21]</a> (Proposition 4), and relationships between centripetal forces varying as the inverse-square of the distance to the center and orbits of conic-section form (Propositions 5–10). Propositions 11–31<a href="#cite_note-22">[22]</a> establish properties of motion in paths of eccentric conic-section form including ellipses, and their relationship with inverse-square central forces directed to a focus and include <a href="/wiki/Newton%27s_theorem_about_ovals" title="Newton's theorem about ovals">Newton's theorem about ovals</a> (lemma 28). Propositions 43–45<a href="#cite_note-23">[23]</a> are demonstration that in an eccentric orbit under centripetal force where the <a href="/wiki/Apsis" title="Apsis">apse</a> may move, a steady non-moving orientation of the line of apses is an indicator of an inverse-square law of force. Book 1 contains some proofs with little connection to real-world dynamics. But there are also sections with far-reaching application to the solar system and universe: Propositions 57–69<a href="#cite_note-24">[24]</a> deal with the "motion of bodies drawn to one another by centripetal forces". This section is of primary interest for its application to the <a href="/wiki/Solar_System" title="Solar System">Solar System</a>, and includes Proposition 66<a href="#cite_note-25">[25]</a> along with its 22 corollaries:<a href="#cite_note-26">[26]</a> here Newton took the first steps in the definition and study of the problem of the movements of three massive bodies subject to their mutually perturbing gravitational attractions, a problem which later gained name and fame (among other reasons, for its great difficulty) as the <a href="/wiki/Three-body_problem" title="Three-body problem">three-body problem</a>. Propositions 70–84<a href="#cite_note-27">[27]</a> deal with the attractive forces of spherical bodies. The section contains Newton's proof that a massive spherically symmetrical body attracts other bodies outside itself as if all its mass were concentrated at its centre. This fundamental result, called the <a href="/wiki/Shell_theorem" title="Shell theorem">Shell theorem</a>, enables the inverse square law of gravitation to be applied to the real solar system to a very close degree of approximation. <div class="mw-heading mw-heading3"><h3 id="Book_2,_part_2_of_De_motu_corporum">Book 2, part 2 of De motu corporum</h3>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=4" title="Edit section: Book 2, part 2 of De motu corporum">edit</a>]</div> Part of the contents originally planned for the first book was divided out into a second book, which largely concerns motion through resisting mediums. Just as Newton examined consequences of different conceivable laws of attraction in Book 1, here he examines different conceivable laws of resistance; thus <a href="https://en.wikisource.org/wiki/The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookII-I" class="extiw" title="s:The Mathematical Principles of Natural Philosophy (1846)/BookII-I">Section 1</a> discusses resistance in direct proportion to velocity, and <a href="https://en.wikisource.org/wiki/The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookII-II" class="extiw" title="s:The Mathematical Principles of Natural Philosophy (1846)/BookII-II">Section 2</a> goes on to examine the implications of resistance in proportion to the square of velocity. Book 2 also discusses (in <a href="https://en.wikisource.org/wiki/The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookII-V" class="extiw" title="s:The Mathematical Principles of Natural Philosophy (1846)/BookII-V">Section 5</a>) hydrostatics and the properties of compressible fluids; Newton also derives <a href="/wiki/Boyle%27s_law" title="Boyle's law">Boyle's law</a>.<a href="#cite_note-28">[28]</a> The effects of air resistance on pendulums are studied in <a href="https://en.wikisource.org/wiki/The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookII-VI" class="extiw" title="s:The Mathematical Principles of Natural Philosophy (1846)/BookII-VI">Section 6</a>, along with Newton's account of experiments that he carried out, to try to find out some characteristics of air resistance in reality by observing the motions of pendulums under different conditions. Newton compares the resistance offered by a medium against motions of globes with different properties (material, weight, size). In Section 8, he derives rules to determine the speed of waves in fluids and relates them to the density and condensation (Proposition 48;<a href="#cite_note-29">[29]</a> this would become very important in acoustics). He assumes that these rules apply equally to light and sound and estimates that the speed of sound is around 1088 feet per second and can increase depending on the amount of water in air.<a href="#cite_note-30">[30]</a> Less of Book 2 has stood the test of time than of Books 1 and 3, and it has been said that Book 2 was largely written to refute a theory of <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">Descartes</a> which had some wide acceptance before Newton's work (and for some time after). According to Descartes's theory of vortices, planetary motions were produced by the whirling of fluid <a href="/wiki/Vortex" title="Vortex">vortices</a> that filled interplanetary space and carried the planets along with them.<a href="#cite_note-31">[31]</a> Newton concluded Book 2<a href="#cite_note-32">[32]</a> by commenting that the hypothesis of vortices was completely at odds with the astronomical phenomena, and served not so much to explain as to confuse them. <div class="mw-heading mw-heading3"><h3 id="Book_3,_De_mundi_systemate">Book 3, De mundi systemate</h3>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=5" title="Edit section: Book 3, De mundi systemate">edit</a>]</div> Book 3, subtitled De mundi systemate (On the system of the world), is an exposition of many consequences of universal gravitation, especially its consequences for astronomy. It builds upon the propositions of the previous books and applies them with further specificity than in Book 1 to the motions observed in the Solar System. Here (introduced by Proposition 22,<a href="#cite_note-33">[33]</a> and continuing in Propositions 25–35<a href="#cite_note-34">[34]</a>) are developed <a href="/wiki/Lunar_theory#Newton" title="Lunar theory">several of the features and irregularities</a> of the orbital motion of the Moon, especially the <a href="/wiki/Variation_(astronomy)" title="Variation (astronomy)">variation</a>. Newton lists the astronomical observations on which he relies,<a href="#cite_note-35">[35]</a> and establishes in a stepwise manner that the inverse square law of mutual gravitation applies to Solar System bodies, starting with the satellites of Jupiter<a href="#cite_note-36">[36]</a> and going on by stages to show that the law is of universal application.<a href="#cite_note-37">[37]</a> He also gives starting at Lemma 4<a href="#cite_note-38">[38]</a> and Proposition 40<a href="#cite_note-39">[39]</a> the theory of the motions of comets, for which much data came from <a href="/wiki/John_Flamsteed" title="John Flamsteed">John Flamsteed</a> and <a href="/wiki/Edmond_Halley" title="Edmond Halley">Edmond Halley</a>, and accounts for the tides,<a href="#cite_note-40">[40]</a> attempting quantitative estimates of the contributions of the Sun<a href="#cite_note-41">[41]</a> and Moon<a href="#cite_note-42">[42]</a> to the tidal motions; and offers the first theory of the <a href="/wiki/Axial_precession" title="Axial precession">precession of the equinoxes</a>.<a href="#cite_note-43">[43]</a> Book 3 also considers the <a href="/wiki/Harmonic_oscillator" title="Harmonic oscillator">harmonic oscillator</a> in three dimensions, and motion in arbitrary force laws. In Book 3 Newton also made clear his heliocentric view of the Solar System, modified in a somewhat modern way, since already in the mid-1680s he recognised the "deviation of the Sun" from the centre of gravity of the Solar System.<a href="#cite_note-44">[44]</a> For Newton, "the common centre of gravity of the Earth, the Sun and all the Planets is to be esteem'd the Centre of the World",<a href="#cite_note-45">[45]</a> and that this centre "either is at rest, or moves uniformly forward in a right line".<a href="#cite_note-prop11-46">[46]</a> Newton rejected the second alternative after adopting the position that "the centre of the system of the world is immoveable", which "is acknowledg'd by all, while some contend that the Earth, others, that the Sun is fix'd in that centre".<a href="#cite_note-prop11-46">[46]</a> Newton estimated the mass ratios Sun:Jupiter and Sun:Saturn,<a href="#cite_note-47">[47]</a> and pointed out that these put the centre of the Sun usually a little way off the common center of gravity, but only a little, the distance at most "would scarcely amount to one diameter of the Sun".<a href="#cite_note-48">[48]</a> <div class="mw-heading mw-heading3"><h3 id="Commentary_on_the_Principia">Commentary on the Principia</h3>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=6" title="Edit section: Commentary on the Principia">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></div></td><td class="mbox-text"><div class="mbox-text-span">This section needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a>. Please help <a href="/wiki/Special:EditPage/Philosophi%C3%A6_Naturalis_Principia_Mathematica" title="Special:EditPage/Philosophiæ Naturalis Principia Mathematica">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a> in this section. Unsourced material may be challenged and removed. Find sources: <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Philosophi%C3%A6+Naturalis+Principia+Mathematica%22">"Philosophiæ Naturalis Principia Mathematica"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Philosophi%C3%A6+Naturalis+Principia+Mathematica%22+-wikipedia&tbs=ar:1">news</a> · <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Philosophi%C3%A6+Naturalis+Principia+Mathematica%22&tbs=bkt:s&tbm=bks">newspapers</a> · <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Philosophi%C3%A6+Naturalis+Principia+Mathematica%22+-wikipedia">books</a> · <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Philosophi%C3%A6+Naturalis+Principia+Mathematica%22">scholar</a> · <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Philosophi%C3%A6+Naturalis+Principia+Mathematica%22&acc=on&wc=on">JSTOR</a> (July 2018) (<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a>)</div></td></tr></tbody></table> The sequence of definitions used in setting up dynamics in the Principia is recognisable in many textbooks today. Newton first set out the definition of mass <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote">The quantity of matter is that which arises conjointly from its density and magnitude. A body twice as dense in double the space is quadruple in quantity. This quantity I designate by the name of body or of mass.</blockquote> This was then used to define the "quantity of motion" (today called <a href="/wiki/Momentum" title="Momentum">momentum</a>), and the principle of inertia in which mass replaces the previous Cartesian notion of intrinsic force. This then set the stage for the introduction of forces through the change in momentum of a body. Curiously, for today's readers, the exposition looks dimensionally incorrect, since Newton does not introduce the dimension of time in rates of changes of quantities. He defined space and time "not as they are well known to all". Instead, he defined "true" time and space as "absolute"<a href="#cite_note-49">[49]</a> and explained: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote">Only I must observe, that the vulgar conceive those quantities under no other notions but from the relation they bear to perceptible objects. And it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common. ... instead of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs; but in philosophical discussions, we ought to step back from our senses, and consider things themselves, distinct from what are only perceptible measures of them.</blockquote> To some modern readers it can appear that some dynamical quantities recognised today were used in the Principia but not named. The mathematical aspects of the first two books were so clearly consistent that they were easily accepted; for example, <a href="/wiki/John_Locke" title="John Locke">Locke</a> asked <a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Huygens</a> whether he could trust the mathematical proofs and was assured about their correctness. However, the concept of an attractive force acting at a distance received a cooler response. In his notes, Newton wrote that the inverse square law arose naturally due to the structure of matter. However, he retracted this sentence in the published version, where he stated that the motion of planets is consistent with an inverse square law, but refused to speculate on the origin of the law. Huygens and <a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Leibniz</a> noted that the law was incompatible with the notion of the <a href="/wiki/Aether_(classical_element)" title="Aether (classical element)">aether</a>. From a Cartesian point of view, therefore, this was a faulty theory. Newton's defence has been adopted since by many famous physicists—he pointed out that the mathematical form of the theory had to be correct since it explained the data, and he refused to speculate further on the basic nature of gravity. The sheer number of phenomena that could be organised by the theory was so impressive that younger "philosophers" soon adopted the methods and language of the Principia. <div class="mw-heading mw-heading2"><h2 id="Rules_of_Reason">Rules of Reason</h2>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=7" title="Edit section: Rules of Reason">edit</a>]</div> Perhaps to reduce the risk of public misunderstanding, Newton included at the beginning of Book 3 (in the second (1713) and third (1726) editions) a section titled "Rules of Reasoning in Philosophy". In the four rules, as they came finally to stand in the 1726 edition, Newton effectively offers a methodology for handling unknown phenomena in nature and reaching towards explanations for them. The four Rules of the 1726 edition run as follows (omitting some explanatory comments that follow each): <ol><li>We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.</li> <li>Therefore to the same natural effects we must, as far as possible, assign the same causes.</li> <li>The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.</li> <li>In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, not withstanding any contrary hypothesis that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.</li></ol> This section of Rules for philosophy is followed by a listing of "Phenomena", in which are listed a number of mainly astronomical observations, that Newton used as the basis for inferences later on, as if adopting a consensus set of facts from the astronomers of his time. Both the "Rules" and the "Phenomena" evolved from one edition of the Principia to the next. Rule 4 made its appearance in the third (1726) edition; Rules 1–3 were present as "Rules" in the second (1713) edition, and predecessors of them were also present in the first edition of 1687, but there they had a different heading: they were not given as "Rules", but rather in the first (1687) edition the predecessors of the three later "Rules", and of most of the later "Phenomena", were all lumped together under a single heading "Hypotheses" (in which the third item was the predecessor of a heavy revision that gave the later Rule 3). From this textual evolution, it appears that Newton wanted by the later headings "Rules" and "Phenomena" to clarify for his readers his view of the roles to be played by these various statements. In the third (1726) edition of the Principia, Newton explains each rule in an alternative way and/or gives an example to back up what the rule is claiming. The first rule is explained as a philosophers' principle of economy. The second rule states that if one cause is assigned to a natural effect, then the same cause so far as possible must be assigned to natural effects of the same kind: for example, respiration in humans and in animals, fires in the home and in the Sun, or the reflection of light whether it occurs terrestrially or from the planets. An extensive explanation is given of the third rule, concerning the qualities of bodies, and Newton discusses here the generalisation of observational results, with a caution against making up fancies contrary to experiments, and use of the rules to illustrate the observation of gravity and space. <div class="mw-heading mw-heading3"><h3 id="General_Scholium">General Scholium</h3>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=8" title="Edit section: General Scholium">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/General_Scholium" title="General Scholium">General Scholium</a></div> The General Scholium is a concluding essay added to the second edition, 1713 (and amended in the third edition, 1726).<a href="#cite_note-50">[50]</a> It is not to be confused with the General Scholium at the end of Book 2, Section 6, which discusses his pendulum experiments and resistance due to air, water, and other fluids. Here Newton used the expression <a href="/wiki/Hypotheses_non_fingo" title="Hypotheses non fingo">hypotheses non fingo</a>, "I formulate no hypotheses",<a href="#cite_note-gschol-hnf-11">[11]</a> in response to criticisms of the first edition of the Principia. ("Fingo" is sometimes nowadays translated "feign" rather than the traditional "frame," although "feign" does not properly translate "fingo"). Newton's gravitational attraction, an invisible <a href="/wiki/Action_at_a_distance_(physics)" class="mw-redirect" title="Action at a distance (physics)">force able to act over vast distances</a>, had led to criticism that he had introduced "<a href="/wiki/Occult" title="Occult">occult</a> agencies" into science.<a href="#cite_note-Edelglass_p._54-51">[51]</a> Newton firmly rejected such criticisms and wrote that it was enough that the phenomena implied gravitational attraction, as they did; but the phenomena did not so far indicate the cause of this gravity, and it was both unnecessary and improper to frame hypotheses of things not implied by the phenomena: such hypotheses "have no place in experimental philosophy", in contrast to the proper way in which "particular propositions are inferr'd from the phenomena and afterwards rendered general by induction".<a href="#cite_note-52">[52]</a> Newton also underlined his criticism of the vortex theory of planetary motions, of Descartes, pointing to its incompatibility with the highly eccentric orbits of comets, which carry them "through all parts of the heavens indifferently". Newton also gave theological argument. From the system of the world, he inferred the existence of a god, along lines similar to what is sometimes called the <a href="/wiki/Teleological_argument" title="Teleological argument">argument from intelligent or purposive design</a>. It has been suggested that Newton gave "an oblique argument for a unitarian conception of God and an implicit attack on the doctrine of the <a href="/wiki/Trinity" title="Trinity">Trinity</a>".<a href="#cite_note-The_General_Scholium_to_Isaac_Newton's_''Principia_mathematica''-53">[53]</a><a href="#cite_note-54">[54]</a> The General Scholium does not address or attempt to refute the church doctrine; it simply does not mention Jesus, the Holy Ghost, or the hypothesis of the Trinity. <div class="mw-heading mw-heading2"><h2 id="Publishing_the_book">Publishing the book</h2>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=9" title="Edit section: Publishing the book">edit</a>]</div> <div class="mw-heading mw-heading3"><h3 id="Halley_and_Newton's_initial_stimulus">Halley and Newton's initial stimulus</h3>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=10" title="Edit section: Halley and Newton's initial stimulus">edit</a>]</div> In January 1684, <a href="/wiki/Edmond_Halley" title="Edmond Halley">Edmond Halley</a>, <a href="/wiki/Christopher_Wren" title="Christopher Wren">Christopher Wren</a> and <a href="/wiki/Robert_Hooke" title="Robert Hooke">Robert Hooke</a> had a conversation in which Hooke claimed to not only have derived the inverse-square law but also all the laws of planetary motion. Wren was unconvinced, Hooke did not produce the claimed derivation although the others gave him time to do it, and Halley, who could derive the inverse-square law for the restricted circular case (by substituting Kepler's relation into Huygens' formula for the centrifugal force) but failed to derive the relation generally, resolved to ask Newton.<a href="#cite_note-55">[55]</a> Halley's visits to Newton in 1684 thus resulted from Halley's debates about planetary motion with Wren and Hooke, and they seem to have provided Newton with the incentive and spur to develop and write what became Philosophiae Naturalis Principia Mathematica. Halley was at that time a Fellow and Council member of the <a href="/wiki/Royal_Society" title="Royal Society">Royal Society</a> in London (positions that in 1686 he resigned to become the Society's paid Clerk).<a href="#cite_note-56">[56]</a> Halley's visit to Newton in Cambridge in 1684 probably occurred in August.<a href="#cite_note-57">[57]</a> When Halley asked Newton's opinion on the problem of planetary motions discussed earlier that year between Halley, Hooke and Wren,<a href="#cite_note-58">[58]</a> Newton surprised Halley by saying that he had already made the derivations some time ago; but that he could not find the papers. (Matching accounts of this meeting come from Halley and <a href="/wiki/Abraham_De_Moivre" class="mw-redirect" title="Abraham De Moivre">Abraham De Moivre</a> to whom Newton confided.) Halley then had to wait for Newton to "find" the results, and in November 1684 Newton sent Halley an amplified version of whatever previous work Newton had done on the subject. This took the form of a 9-page manuscript, <a href="/wiki/De_motu_corporum_in_gyrum" title="De motu corporum in gyrum">De motu corporum in gyrum</a> (Of the motion of bodies in an orbit): the title is shown on some surviving copies, although the (lost) original may have been without a title. Newton's tract De motu corporum in gyrum, which he sent to Halley in late 1684, derived what is now known as the three laws of Kepler, assuming an inverse square law of force, and generalised the result to conic sections. It also extended the methodology by adding the solution of a problem on the motion of a body through a resisting medium. The contents of De motu so excited Halley by their mathematical and physical originality and far-reaching implications for astronomical theory, that he immediately went to visit Newton again, in November 1684, to ask Newton to let the Royal Society have more of such work.<a href="#cite_note-59">[59]</a> The results of their meetings clearly helped to stimulate Newton with the enthusiasm needed to take his investigations of mathematical problems much further in this area of physical science, and he did so in a period of highly concentrated work that lasted at least until mid-1686.<a href="#cite_note-60">[60]</a> Newton's single-minded attention to his work generally, and to his project during this time, is shown by later reminiscences from his secretary and copyist of the period, Humphrey Newton. His account tells of Isaac Newton's absorption in his studies, how he sometimes forgot his food, or his sleep, or the state of his clothes, and how when he took a walk in his garden he would sometimes rush back to his room with some new thought, not even waiting to sit before beginning to write it down.<a href="#cite_note-61">[61]</a> Other evidence also shows Newton's absorption in the Principia: Newton for years kept up a regular programme of chemical or alchemical experiments, and he normally kept dated notes of them, but for a period from May 1684 to April 1686, Newton's chemical notebooks have no entries at all.<a href="#cite_note-62">[62]</a> So, it seems that Newton abandoned pursuits to which he was formally dedicated and did very little else for well over a year and a half, but concentrated on developing and writing what became his great work. The first of the three constituent books was sent to Halley for the printer in spring 1686, and the other two books somewhat later. The complete work, published by Halley at his own financial risk,<a href="#cite_note-63">[63]</a> appeared in July 1687. Newton had also communicated De motu to Flamsteed, and during the period of composition, he exchanged a few letters with Flamsteed about observational data on the planets, eventually acknowledging Flamsteed's contributions in the published version of the Principia of 1687. <div class="mw-heading mw-heading3"><h3 id="Preliminary_version">Preliminary version</h3>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=11" title="Edit section: Preliminary version">edit</a>]</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:NewtonsPrincipia.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/NewtonsPrincipia.jpg/170px-NewtonsPrincipia.jpg" decoding="async" width="170" height="113" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/NewtonsPrincipia.jpg/255px-NewtonsPrincipia.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/41/NewtonsPrincipia.jpg/340px-NewtonsPrincipia.jpg 2x" data-file-width="1266" data-file-height="842" /></a><figcaption><a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton's</a> own first edition copy of his Principia, with handwritten corrections for the second edition</figcaption></figure> The process of writing that first edition of the Principia went through several stages and drafts: some parts of the preliminary materials still survive, while others are lost except for fragments and cross-references in other documents.<a href="#cite_note-64">[64]</a> Surviving materials show that Newton (up to some time in 1685) conceived his book as a two-volume work. The first volume was to be titled De motu corporum, Liber primus, with contents that later appeared in extended form as Book 1 of the Principia.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] A fair-copy draft of Newton's planned second volume De motu corporum, Liber Secundus survives, its completion dated to about the summer of 1685. It covers the application of the results of Liber primus to the Earth, the Moon, the tides, the Solar System, and the universe; in this respect, it has much the same purpose as the final Book 3 of the Principia, but it is written much less formally and is more easily read.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Manchester_John_Rylands_Library_Isaac_Newton_16-10-2009_13-54-26.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Manchester_John_Rylands_Library_Isaac_Newton_16-10-2009_13-54-26.JPG/220px-Manchester_John_Rylands_Library_Isaac_Newton_16-10-2009_13-54-26.JPG" decoding="async" width="220" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Manchester_John_Rylands_Library_Isaac_Newton_16-10-2009_13-54-26.JPG/330px-Manchester_John_Rylands_Library_Isaac_Newton_16-10-2009_13-54-26.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Manchester_John_Rylands_Library_Isaac_Newton_16-10-2009_13-54-26.JPG/440px-Manchester_John_Rylands_Library_Isaac_Newton_16-10-2009_13-54-26.JPG 2x" data-file-width="3568" data-file-height="2386" /></a><figcaption>Titlepage and frontispiece of the third edition, London, 1726 (<a href="/wiki/John_Rylands_Library" class="mw-redirect" title="John Rylands Library">John Rylands Library</a>)</figcaption></figure> It is not known just why Newton changed his mind so radically about the final form of what had been a readable narrative in De motu corporum, Liber Secundus of 1685, but he largely started afresh in a new, tighter, and less accessible mathematical style, eventually to produce Book 3 of the Principia as we know it. Newton frankly admitted that this change of style was deliberate when he wrote that he had (first) composed this book "in a popular method, that it might be read by many", but to "prevent the disputes" by readers who could not "lay aside the[ir] prejudices", he had "reduced" it "into the form of propositions (in the mathematical way) which should be read by those only, who had first made themselves masters of the principles established in the preceding books".<a href="#cite_note-65">[65]</a> The final Book 3 also contained in addition some further important quantitative results arrived at by Newton in the meantime, especially about the theory of the motions of comets, and some of the perturbations of the motions of the Moon. The result was numbered Book 3 of the Principia rather than Book 2 because in the meantime, drafts of Liber primus had expanded and Newton had divided it into two books. The new and final Book 2 was concerned largely with the motions of bodies through resisting mediums.<a href="#cite_note-Stanford-66">[66]</a> But the Liber Secundus of 1685 can still be read today. Even after it was superseded by Book 3 of the Principia, it survived complete, in more than one manuscript. After Newton's death in 1727, the relatively accessible character of its writing encouraged the publication of an English translation in 1728 (by persons still unknown, not authorised by Newton's heirs). It appeared under the English title A Treatise of the System of the World.<a href="#cite_note-67">[67]</a> This had some amendments relative to Newton's manuscript of 1685, mostly to remove cross-references that used obsolete numbering to cite the propositions of an early draft of Book 1 of the Principia. Newton's heirs shortly afterwards published the Latin version in their possession, also in 1728, under the (new) title De Mundi Systemate, amended to update cross-references, citations and diagrams to those of the later editions of the Principia, making it look superficially as if it had been written by Newton after the Principia, rather than before.<a href="#cite_note-68">[68]</a> The System of the World was sufficiently popular to stimulate two revisions (with similar changes as in the Latin printing), a second edition (1731), and a "corrected" reprint<a href="#cite_note-69">[69]</a> of the second edition (1740). <div class="mw-heading mw-heading3"><h3 id="Halley's_role_as_publisher">Halley's role as publisher</h3>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=12" title="Edit section: Halley's role as publisher">edit</a>]</div> The text of the first of the three books of the Principia was presented to the Royal Society at the close of April 1686. Hooke made some priority claims (but failed to substantiate them), causing some delay. When Hooke's claim was made known to Newton, who hated disputes, Newton threatened to withdraw and suppress Book 3 altogether, but Halley, showing considerable diplomatic skills, tactfully persuaded Newton to withdraw his threat and let it go forward to publication. <a href="/wiki/Samuel_Pepys" title="Samuel Pepys">Samuel Pepys</a>, as president, gave his <a href="/wiki/Imprimatur" title="Imprimatur">imprimatur</a> on 30 June 1686, licensing the book for publication. The Society had just spent its book budget on <a href="/wiki/De_Historia_piscium" title="De Historia piscium">De Historia piscium</a>,<a href="#cite_note-70">[70]</a> and the cost of publication was borne by Edmund Halley (who was also then acting as publisher of the <a href="/wiki/Philosophical_Transactions_of_the_Royal_Society" title="Philosophical Transactions of the Royal Society">Philosophical Transactions of the Royal Society</a>):<a href="#cite_note-71">[71]</a> the book appeared in summer 1687.<a href="#cite_note-72">[72]</a> After Halley had personally financed the publication of Principia, he was informed that the society could no longer afford to provide him the promised annual salary of £50. Instead, Halley was paid with leftover copies of De Historia piscium.<a href="#cite_note-73">[73]</a> <div class="mw-heading mw-heading2"><h2 id="Historical_context">Historical context</h2>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=13" title="Edit section: Historical context">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/History_of_gravitational_theory" title="History of gravitational theory">History of gravitational theory</a></div> <div class="mw-heading mw-heading3"><h3 id="Beginnings_of_the_Scientific_Revolution">Beginnings of the Scientific Revolution</h3>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=14" title="Edit section: Beginnings of the Scientific Revolution">edit</a>]</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Nikolaus_Kopernikus.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Nikolaus_Kopernikus.jpg/180px-Nikolaus_Kopernikus.jpg" decoding="async" width="180" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Nikolaus_Kopernikus.jpg/270px-Nikolaus_Kopernikus.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Nikolaus_Kopernikus.jpg/360px-Nikolaus_Kopernikus.jpg 2x" data-file-width="1024" data-file-height="1001" /></a><figcaption><a href="/wiki/Nicolaus_Copernicus" title="Nicolaus Copernicus">Nicolaus Copernicus</a> (1473–1543) formulated a <a href="/wiki/Heliocentricism" class="mw-redirect" title="Heliocentricism">heliocentric</a> model of the universe</figcaption></figure> <a href="/wiki/Nicolaus_Copernicus" title="Nicolaus Copernicus">Nicolaus Copernicus</a> had moved the Earth away from the center of the universe with the <a href="/wiki/Heliocentric" class="mw-redirect" title="Heliocentric">heliocentric</a> theory for which he presented evidence in his book <a href="/wiki/De_revolutionibus_orbium_coelestium" title="De revolutionibus orbium coelestium">De revolutionibus orbium coelestium</a> (On the revolutions of the heavenly spheres) published in 1543. <a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Johannes Kepler</a> wrote the book <a href="/wiki/Astronomia_nova" title="Astronomia nova">Astronomia nova</a> (A new astronomy) in 1609, setting out the evidence that planets move in <a href="/wiki/Ellipse" title="Ellipse">elliptical</a> orbits with the Sun at one <a href="/wiki/Focus_(geometry)" title="Focus (geometry)">focus</a>, and that planets do not move with constant speed along this orbit. Rather, their speed varies so that the line joining the centres of the sun and a planet sweeps out equal areas in equal times. To these two laws he added a third a decade later, in his 1619 book <a href="/wiki/Harmonices_Mundi" title="Harmonices Mundi">Harmonices Mundi</a> (Harmonies of the world). This law sets out a proportionality between the third power of the characteristic distance of a planet from the Sun and the square of the length of its year. <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Justus_Sustermans_-_Portrait_of_Galileo_Galilei,_1636.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Justus_Sustermans_-_Portrait_of_Galileo_Galilei%2C_1636.jpg/180px-Justus_Sustermans_-_Portrait_of_Galileo_Galilei%2C_1636.jpg" decoding="async" width="180" height="229" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Justus_Sustermans_-_Portrait_of_Galileo_Galilei%2C_1636.jpg/270px-Justus_Sustermans_-_Portrait_of_Galileo_Galilei%2C_1636.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Justus_Sustermans_-_Portrait_of_Galileo_Galilei%2C_1636.jpg/360px-Justus_Sustermans_-_Portrait_of_Galileo_Galilei%2C_1636.jpg 2x" data-file-width="2500" data-file-height="3176" /></a><figcaption><a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo Galilei</a> (1564–1642), a champion of <a href="/wiki/Copernicanism" class="mw-redirect" title="Copernicanism">Copernicanism</a>, worked on kinematics and classical mechanics</figcaption></figure>The foundation of modern dynamics was set out in Galileo's book <a href="/wiki/Dialogo_sopra_i_due_massimi_sistemi_del_mondo" class="mw-redirect" title="Dialogo sopra i due massimi sistemi del mondo">Dialogo sopra i due massimi sistemi del mondo</a> (Dialogue on the two main world systems) where the notion of inertia was implicit and used. In addition, Galileo's experiments with inclined planes had yielded precise mathematical relations between elapsed time and acceleration, velocity or distance for uniform and uniformly accelerated motion of bodies. Descartes' book of 1644 <a href="/wiki/Principia_philosophiae" class="mw-redirect" title="Principia philosophiae">Principia philosophiae</a> (Principles of philosophy) stated that bodies can act on each other only through contact: a principle that induced people, among them himself, to hypothesize a universal medium as the carrier of interactions such as light and gravity—the <a href="/wiki/Aether_(classical_element)" title="Aether (classical element)">aether</a>. Newton was criticized for apparently introducing forces that acted at distance without any medium.<a href="#cite_note-Edelglass_p._54-51">[51]</a> Not until the development of <a href="/wiki/Particle_theory" class="mw-redirect" title="Particle theory">particle theory</a> was Descartes' notion vindicated when it was possible to describe all interactions, like the <a href="/wiki/Strong_interaction" title="Strong interaction">strong</a>, <a href="/wiki/Weak_interaction" title="Weak interaction">weak</a>, and <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetic</a> <a href="/wiki/Fundamental_interaction" title="Fundamental interaction">fundamental interactions</a>, using mediating <a href="/wiki/Gauge_boson" title="Gauge boson">gauge bosons</a><a href="#cite_note-74">[74]</a> and gravity through hypothesized <a href="/wiki/Gravitons" class="mw-redirect" title="Gravitons">gravitons</a>.<a href="#cite_note-75">[75]</a> <div class="mw-heading mw-heading3"><h3 id="Newton's_role">Newton's role</h3>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=15" title="Edit section: Newton's role">edit</a>]</div> Newton had studied these books, or, in some cases, secondary sources based on them, and taken notes entitled <a href="/wiki/Quaestiones_quaedam_philosophicae" title="Quaestiones quaedam philosophicae">Quaestiones quaedam philosophicae</a> (Questions about philosophy) during his days as an undergraduate. During this period (1664–1666) he created the basis of calculus and performed the first experiments in the optics of colour. At this time, his proof that white light was a combination of primary colours (found via prismatics) replaced the prevailing theory of colours and received an overwhelmingly favourable response and occasioned bitter disputes with <a href="/wiki/Robert_Hooke" title="Robert Hooke">Robert Hooke</a> and others, which forced him to sharpen his ideas to the point where he already composed sections of his later book <a href="/wiki/Opticks" title="Opticks">Opticks</a> by the 1670s in response. Work on calculus is shown in various papers and letters, including two to <a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Leibniz</a>. He became a fellow of the <a href="/wiki/Royal_Society" title="Royal Society">Royal Society</a> and the second <a href="/wiki/Lucasian_Professor_of_Mathematics" title="Lucasian Professor of Mathematics">Lucasian Professor of Mathematics</a> (succeeding <a href="/wiki/Isaac_Barrow" title="Isaac Barrow">Isaac Barrow</a>) at <a href="/wiki/Trinity_College,_Cambridge" title="Trinity College, Cambridge">Trinity College</a>, <a href="/wiki/University_of_Cambridge" title="University of Cambridge">Cambridge</a>. <div class="mw-heading mw-heading3"><h3 id="Newton's_early_work_on_motion">Newton's early work on motion</h3>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=16" title="Edit section: Newton's early work on motion">edit</a>]</div> In the 1660s Newton studied the motion of colliding bodies and deduced that the centre of mass of two colliding bodies remains in uniform motion. Surviving manuscripts of the 1660s also show Newton's interest in planetary motion and that by 1669 he had shown, for a circular case of planetary motion, that the force he called "endeavour to recede" (now called <a href="/wiki/Centrifugal_force" title="Centrifugal force">centrifugal force</a>) had an inverse-square relation with distance from the center.<a href="#cite_note-T_Whiteside_1991_pages_11–61-76">[76]</a> After his 1679–1680 correspondence with Hooke, described below, Newton adopted the language of inward or centripetal force. According to Newton scholar J. Bruce Brackenridge, although much has been made of the change in language and difference of point of view, as between centrifugal or centripetal forces, the actual computations and proofs remained the same either way. They also involved the combination of tangential and radial displacements, which Newton was making in the 1660s. The difference between the centrifugal and centripetal points of view, though a significant change of perspective, did not change the analysis.<a href="#cite_note-77">[77]</a> Newton also clearly expressed the concept of linear inertia in the 1660s: for this Newton was indebted to Descartes' work published 1644.<a href="#cite_note-dtw1970-78">[78]</a> <div class="mw-heading mw-heading3"><h3 id="Controversy_with_Hooke">Controversy with Hooke</h3>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=17" title="Edit section: Controversy with Hooke">edit</a>]</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:13_Portrait_of_Robert_Hooke.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/13_Portrait_of_Robert_Hooke.JPG/220px-13_Portrait_of_Robert_Hooke.JPG" decoding="async" width="220" height="262" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/13_Portrait_of_Robert_Hooke.JPG/330px-13_Portrait_of_Robert_Hooke.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/10/13_Portrait_of_Robert_Hooke.JPG/440px-13_Portrait_of_Robert_Hooke.JPG 2x" data-file-width="1359" data-file-height="1620" /></a><figcaption>Artist's impression of English polymath <a href="/wiki/Robert_Hooke" title="Robert Hooke">Robert Hooke</a> (1635–1703)</figcaption></figure> Hooke published <a href="/wiki/Robert_Hooke#Gravitation" title="Robert Hooke">his ideas about gravitation</a> in the 1660s and again in 1674. He argued for an attracting principle of gravitation in <a href="/wiki/Micrographia" title="Micrographia">Micrographia</a> of 1665, in a 1666 Royal Society lecture On gravity, and again in 1674, when he published his ideas about the System of the World in somewhat developed form, as an addition to An Attempt to Prove the Motion of the Earth from Observations.<a href="#cite_note-attempt-79">[79]</a> Hooke clearly postulated mutual attractions between the Sun and planets, in a way that increased with nearness to the attracting body, along with a principle of linear inertia. Hooke's statements up to 1674 made no mention, however, that an inverse square law applies or might apply to these attractions. Hooke's gravitation was also not yet universal, though it approached universality more closely than previous hypotheses.<a href="#cite_note-80">[80]</a> Hooke also did not provide accompanying evidence or mathematical demonstration. On these two aspects, Hooke stated in 1674: "Now what these several degrees [of gravitational attraction] are I have not yet experimentally verified" (indicating that he did not yet know what law the gravitation might follow); and as to his whole proposal: "This I only hint at present", "having my self many other things in hand which I would first compleat, and therefore cannot so well attend it" (i.e., "prosecuting this Inquiry").<a href="#cite_note-attempt-79">[79]</a> In November 1679, Hooke began an exchange of letters with Newton, of which the full text is now published.<a href="#cite_note-167986letters-81">[81]</a> Hooke told Newton that Hooke had been appointed to manage the Royal Society's correspondence,<a href="#cite_note-82">[82]</a> and wished to hear from members about their researches, or their views about the researches of others; and as if to whet Newton's interest, he asked what Newton thought about various matters, giving a whole list, mentioning "compounding the celestial motions of the planets of a direct motion by the tangent and an attractive motion towards the central body", and "my hypothesis of the lawes or causes of springinesse", and then a new hypothesis from Paris about planetary motions (which Hooke described at length), and then efforts to carry out or improve national surveys, the difference of latitude between London and Cambridge, and other items. Newton's reply offered "a fansy of my own" about a terrestrial experiment (not a proposal about celestial motions) which might detect the Earth's motion, by the use of a body first suspended in air and then dropped to let it fall. The main point was to indicate how Newton thought the falling body could experimentally reveal the Earth's motion by its direction of deviation from the vertical, but he went on hypothetically to consider how its motion could continue if the solid Earth had not been in the way (on a spiral path to the centre). Hooke disagreed with Newton's idea of how the body would continue to move.<a href="#cite_note-83">[83]</a> A short further correspondence developed, and towards the end of it Hooke, writing on 6 January 1680 to Newton, communicated his "supposition ... that the Attraction always is in a duplicate proportion to the Distance from the Center Reciprocall, and Consequently that the Velocity will be in a subduplicate proportion to the Attraction and Consequently as Kepler Supposes Reciprocall to the Distance."<a href="#cite_note-84">[84]</a> (Hooke's inference about the velocity was actually incorrect.<a href="#cite_note-85">[85]</a>) In 1686, when the first book of <a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a>'s Principia was presented to the <a href="/wiki/Royal_Society" title="Royal Society">Royal Society</a>, Hooke claimed that Newton had obtained from him the "notion" of "the rule of the decrease of Gravity, being reciprocally as the squares of the distances from the Center". At the same time (according to <a href="/wiki/Edmond_Halley" title="Edmond Halley">Edmond Halley</a>'s contemporary report) Hooke agreed that "the Demonstration of the Curves generated therby" was wholly Newton's.<a href="#cite_note-167986letters-81">[81]</a> A recent assessment about the early history of the inverse square law is that "by the late 1660s", the assumption of an "inverse proportion between gravity and the square of distance was rather common and had been advanced by a number of different people for different reasons".<a href="#cite_note-86">[86]</a> Newton himself had shown in the 1660s that for planetary motion under a circular assumption, force in the radial direction had an inverse-square relation with distance from the center.<a href="#cite_note-T_Whiteside_1991_pages_11–61-76">[76]</a> Newton, faced in May 1686 with Hooke's claim on the inverse square law, denied that Hooke was to be credited as author of the idea, giving reasons including the citation of prior work by others before Hooke.<a href="#cite_note-167986letters-81">[81]</a> Newton also firmly claimed that even if it had happened that he had first heard of the inverse square proportion from Hooke, which it had not, he would still have some rights to it in view of his mathematical developments and demonstrations, which enabled observations to be relied on as evidence of its accuracy, while Hooke, without mathematical demonstrations and evidence in favour of the supposition, could only guess (according to Newton) that it was approximately valid "at great distances from the center".<a href="#cite_note-167986letters-81">[81]</a> The background described above shows there was basis for Newton to deny deriving the inverse square law from Hooke. On the other hand, Newton did accept and acknowledge, in all editions of the Principia, that Hooke (but not exclusively Hooke) had separately appreciated the inverse square law in the Solar System. Newton acknowledged Wren, Hooke and Halley in this connection in the Scholium to Proposition 4 in Book 1.<a href="#cite_note-87">[87]</a> Newton also acknowledged to Halley that his correspondence with Hooke in 1679–80 had reawakened his dormant interest in astronomical matters, but that did not mean, according to Newton, that Hooke had told Newton anything new or original: "yet am I not beholden to him for any light into that business but only for the diversion he gave me from my other studies to think on these things & for his dogmaticalness in writing as if he had found the motion in the Ellipsis, which inclined me to try it ...".<a href="#cite_note-167986letters-81">[81]</a>) Newton's reawakening interest in astronomy received further stimulus by the appearance of a comet in the winter of 1680/1681, on which he corresponded with <a href="/wiki/John_Flamsteed" title="John Flamsteed">John Flamsteed</a>.<a href="#cite_note-88">[88]</a> In 1759, decades after the deaths of both Newton and Hooke, <a href="/wiki/Alexis_Clairaut" title="Alexis Clairaut">Alexis Clairaut</a>, mathematical astronomer eminent in his own right in the field of gravitational studies, made his assessment after reviewing what Hooke had published on gravitation. "One must not think that this idea ... of Hooke diminishes Newton's glory", Clairaut wrote; "The example of Hooke" serves "to show what a distance there is between a truth that is glimpsed and a truth that is demonstrated".<a href="#cite_note-89">[89]</a><a href="#cite_note-90">[90]</a> <div class="mw-heading mw-heading2"><h2 id="Location_of_early_edition_copies">Location of early edition copies</h2>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=18" title="Edit section: Location of early edition copies">edit</a>]</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Principia_Page_1726.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Principia_Page_1726.jpg/220px-Principia_Page_1726.jpg" decoding="async" width="220" height="312" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Principia_Page_1726.jpg/330px-Principia_Page_1726.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Principia_Page_1726.jpg/440px-Principia_Page_1726.jpg 2x" data-file-width="441" data-file-height="625" /></a><figcaption>A page from the Principia</figcaption></figure> It has been estimated that as many as 750 copies<a href="#cite_note-EA-20201110-91">[91]</a> of the <a href="/wiki/First_edition" class="mw-redirect" title="First edition">first edition</a> were printed by the Royal Society, and "it is quite remarkable that so many copies of this small first edition are still in existence ... but it may be because the original Latin text was more revered than read".<a href="#cite_note-92">[92]</a> A survey published in 1953 located 189 surviving copies<a href="#cite_note-93">[93]</a> with nearly 200 further copies located by the most recent survey published in 2020, suggesting that the initial print run was larger than previously thought.<a href="#cite_note-94">[94]</a> However, more recent book historical and bibliographical research has examined those prior claims, and concludes that Macomber's earlier estimation of 500 copies is likely correct.<a href="#cite_note-95">[95]</a> <ul><li><a href="/wiki/Cambridge_University_Library" title="Cambridge University Library">Cambridge University Library</a> has Newton's own copy of the first edition, with handwritten notes for the second edition.<a href="#cite_note-96">[96]</a></li> <li>The <a href="/wiki/Earl_Gregg_Swem_Library" title="Earl Gregg Swem Library">Earl Gregg Swem Library</a> at the <a href="/wiki/College_of_William_%26_Mary" title="College of William & Mary">College of William & Mary</a> has a first edition copy of the Principia.<a href="#cite_note-97">[97]</a> Throughout are Latin annotations written by Thomas S. Savage. These handwritten notes are currently being researched at the college.<a href="#cite_note-98">[98]</a></li> <li>The Frederick E. Brasch Collection of Newton and Newtoniana in <a href="/wiki/Stanford_University" title="Stanford University">Stanford University</a> also has a first edition of the Principia.<a href="#cite_note-99">[99]</a></li> <li>A first edition forms part of the Crawford Collection, housed at the <a href="/wiki/Royal_Observatory,_Edinburgh" title="Royal Observatory, Edinburgh">Royal Observatory, Edinburgh</a>.<a href="#cite_note-100">[100]</a></li> <li>The <a href="/wiki/Uppsala_University_Library" title="Uppsala University Library">Uppsala University Library</a> owns a first edition copy, which was stolen in the 1960s and returned to the library in 2009.<a href="#cite_note-101">[101]</a></li> <li>The <a href="/wiki/Folger_Shakespeare_Library" title="Folger Shakespeare Library">Folger Shakespeare Library</a> in <a href="/wiki/Washington,_D.C." title="Washington, D.C.">Washington, D.C.</a> owns a first edition, as well as a 1713 second edition.</li> <li>The <a href="/wiki/Huntington_Library" title="Huntington Library">Huntington Library</a> in <a href="/wiki/San_Marino,_California" title="San Marino, California">San Marino, California</a> owns Isaac Newton's personal copy, with annotations in Newton's own hand.<a href="#cite_note-102">[102]</a></li> <li>The <a href="/wiki/Bodmer_Library" title="Bodmer Library">Bodmer Library</a> in Switzerland keeps a copy of the original edition that was owned by <a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Leibniz</a>. It contains handwritten notes by Leibniz, in particular concerning the <a href="/wiki/Leibniz-Newton_calculus_controversy" class="mw-redirect" title="Leibniz-Newton calculus controversy">controversy of who first formulated calculus</a> (although he published it later, Newton argued that he developed it earlier).<a href="#cite_note-103">[103]</a></li> <li>The <a href="/wiki/Iron_Library" title="Iron Library">Iron Library</a> in Switzerland holds a first edition copy that was formerly in the library of the physicist <a href="/wiki/Ernst_Mach" title="Ernst Mach">Ernst Mach</a>. The copy contains critical marginalia in Mach's hand.<a href="#cite_note-104">[104]</a></li> <li>The <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a> Library holds both variants of the first edition, as well as copies of the 1713 and 1726 editions.<a href="#cite_note-105">[105]</a></li> <li>The <a href="/wiki/Fisher_Library" class="mw-redirect" title="Fisher Library">Fisher Library</a> in the <a href="/wiki/University_of_Sydney" title="University of Sydney">University of Sydney</a> has a first-edition copy, annotated by a mathematician of uncertain identity and corresponding notes from Newton himself.<a href="#cite_note-106">[106]</a></li> <li>The <a href="/wiki/Linda_Hall_Library" title="Linda Hall Library">Linda Hall Library</a> holds the first edition, as well as a copy of the 1713 and 1726 editions.</li> <li>The <a rel="nofollow" class="external text" href="http://www.telekiteka.ro/en">Teleki-Bolyai Library</a> of Târgu-Mureș holds a 2-line imprint first edition.</li> <li>One book is also located at Vasaskolan, <a href="/wiki/G%C3%A4vle" title="Gävle">Gävle</a>, in Sweden.<a href="#cite_note-107">[107]</a></li> <li><a href="/wiki/Dalhousie_University" title="Dalhousie University">Dalhousie University</a> has a copy as part of the <a rel="nofollow" class="external text" href="https://libraries.dal.ca/find/special-collections/morse-collection.html">William I. Morse</a> collection.</li> <li><a href="/wiki/McGill_University" title="McGill University">McGill University</a> in <a href="/wiki/Montreal" title="Montreal">Montreal</a> has the copy once owned by <a href="/wiki/William_Osler" title="William Osler">Sir William Osler</a>.</li> <li>The <a href="/wiki/University_of_Toronto" title="University of Toronto">University of Toronto</a> has a copy in the <a href="/wiki/Thomas_Fisher_Rare_Book_Library" title="Thomas Fisher Rare Book Library">Thomas Fisher Rare Book Collection</a>.</li> <li><a href="/wiki/University_College_London" title="University College London">University College London</a> Special Collections has a copy previously owned by the lawyer and mathematician <a href="/wiki/John_T._Graves" title="John T. Graves">John T. Graves</a>.<a href="#cite_note-108">[108]</a></li></ul> In 2016, a first edition sold for $3.7 million.<a href="#cite_note-109">[109]</a> The second edition (1713) were printed in 750 copies, and the third edition (1726) were printed in 1,250 copies. A <a href="/wiki/Facsimile" title="Facsimile">facsimile</a> edition (based on the 3rd edition of 1726 but with variant readings from earlier editions and important annotations) was published in 1972 by <a href="/wiki/Alexandre_Koyr%C3%A9" title="Alexandre Koyré">Alexandre Koyré</a> and <a href="/wiki/I._Bernard_Cohen" title="I. Bernard Cohen">I. Bernard Cohen</a>.<a href="#cite_note-variorum-13">[13]</a> <div class="mw-heading mw-heading2"><h2 id="Later_editions">Later editions</h2>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=19" title="Edit section: Later editions">edit</a>]</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Newton%27s_Annotated_copy_of_his_Principia_Mathematica.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Newton%27s_Annotated_copy_of_his_Principia_Mathematica.jpg/220px-Newton%27s_Annotated_copy_of_his_Principia_Mathematica.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Newton%27s_Annotated_copy_of_his_Principia_Mathematica.jpg/330px-Newton%27s_Annotated_copy_of_his_Principia_Mathematica.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Newton%27s_Annotated_copy_of_his_Principia_Mathematica.jpg/440px-Newton%27s_Annotated_copy_of_his_Principia_Mathematica.jpg 2x" data-file-width="4025" data-file-height="3021" /></a><figcaption>Newton's personal copy of the first edition of Philosophiæ Naturalis Principia Mathematica, annotated by him for the second edition. Displayed at <a href="/wiki/Cambridge_University_Library" title="Cambridge University Library">Cambridge University Library</a>.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Second_edition,_1713">Second edition, 1713</h3>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=20" title="Edit section: Second edition, 1713">edit</a>]</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Principia_Mathematica_1713.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Principia_Mathematica_1713.JPG/220px-Principia_Mathematica_1713.JPG" decoding="async" width="220" height="119" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Principia_Mathematica_1713.JPG/330px-Principia_Mathematica_1713.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Principia_Mathematica_1713.JPG/440px-Principia_Mathematica_1713.JPG 2x" data-file-width="2967" data-file-height="1600" /></a><figcaption>Second edition opened to title page</figcaption></figure> Two later editions were published by Newton: Newton had been urged to make a new edition of the Principia since the early 1690s, partly because copies of the first edition had already become very rare and expensive within a few years after 1687.<a href="#cite_note-110">[110]</a> Newton referred to his plans for a second edition in correspondence with Flamsteed in November 1694.<a href="#cite_note-111">[111]</a> Newton also maintained annotated copies of the first edition specially bound up with interleaves on which he could note his revisions; two of these copies still survive,<a href="#cite_note-112">[112]</a> but he had not completed the revisions by 1708. Newton had almost severed connections with one would-be editor, <a href="/wiki/Nicolas_Fatio_de_Duillier" title="Nicolas Fatio de Duillier">Nicolas Fatio de Duillier</a>, and another, <a href="/wiki/David_Gregory_(mathematician)" title="David Gregory (mathematician)">David Gregory</a> seems not to have met with his approval and was also terminally ill, dying in 1708. Nevertheless, reasons were accumulating not to put off the new edition any longer.<a href="#cite_note-113">[113]</a> <a href="/wiki/Richard_Bentley" title="Richard Bentley">Richard Bentley</a>, master of <a href="/wiki/Trinity_College,_Cambridge" title="Trinity College, Cambridge">Trinity College</a>, persuaded Newton to allow him to undertake a second edition, and in June 1708 Bentley wrote to Newton with a specimen print of the first sheet, at the same time expressing the (unfulfilled) hope that Newton had made progress towards finishing the revisions.<a href="#cite_note-114">[114]</a> It seems that Bentley then realised that the editorship was technically too difficult for him, and with Newton's consent he appointed <a href="/wiki/Roger_Cotes" title="Roger Cotes">Roger Cotes</a>, Plumian professor of astronomy at Trinity, to undertake the editorship for him as a kind of deputy (but Bentley still made the publishing arrangements and had the financial responsibility and profit). The correspondence of 1709–1713 shows Cotes reporting to two masters, Bentley and Newton, and managing (and often correcting) a large and important set of revisions to which Newton sometimes could not give his full attention.<a href="#cite_note-115">[115]</a> Under the weight of Cotes' efforts, but impeded by priority disputes between Newton and Leibniz,<a href="#cite_note-116">[116]</a> and by troubles at the Mint,<a href="#cite_note-117">[117]</a> Cotes was able to announce publication to Newton on 30 June 1713.<a href="#cite_note-118">[118]</a> Bentley sent Newton only six presentation copies; Cotes was unpaid; Newton omitted any acknowledgement to Cotes. Among those who gave Newton corrections for the Second Edition were: <a href="/wiki/Firmin_Abauzit" title="Firmin Abauzit">Firmin Abauzit</a>, Roger Cotes and David Gregory. However, Newton omitted acknowledgements to some because of the priority disputes. <a href="/wiki/John_Flamsteed" title="John Flamsteed">John Flamsteed</a>, the Astronomer Royal, suffered this especially. The Second Edition was the basis of the first edition to be printed abroad, which appeared in Amsterdam in 1714. <div class="mw-heading mw-heading3"><h3 id="Third_edition,_1726">Third edition, 1726</h3>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=21" title="Edit section: Third edition, 1726">edit</a>]</div> After his serious illness in 1722 and after the appearance of a reprint of the second edition in Amsterdam in 1723, the 80-year-old Newton began to revise once again the Principia in the fall of 1723. The third edition was published 25 March 1726, under the stewardship of <a href="/wiki/Henry_Pemberton" title="Henry Pemberton">Henry Pemberton</a>, M.D., a man of the greatest skill in these matters...; Pemberton later said that this recognition was worth more to him than the two hundred guinea award from Newton.<a href="#cite_note-119">[119]</a> In 1739–1742, two French priests, Pères Thomas LeSeur and <a href="/wiki/Fran%C3%A7ois_Jacquier" title="François Jacquier">François Jacquier</a> (of the <a href="/wiki/Minim_(religious_order)" class="mw-redirect" title="Minim (religious order)">Minim</a> order, but sometimes erroneously identified as <a href="/wiki/Jesuits" title="Jesuits">Jesuits</a>), produced with the assistance of <a href="/wiki/Jean-Louis_Calandrini" title="Jean-Louis Calandrini">J.-L. Calandrini</a> an extensively annotated version of the Principia in the 3rd edition of 1726. Sometimes this is referred to as the Jesuit edition: it was much used, and reprinted more than once in Scotland during the 19th century.<a href="#cite_note-Facsimile-120">[120]</a> <a href="/wiki/%C3%89milie_du_Ch%C3%A2telet" title="Émilie du Châtelet">Émilie du Châtelet</a> also made a translation of Newton's Principia into French. Unlike LeSeur and Jacquier's edition, hers was a complete translation of Newton's three books and their prefaces. She also included a Commentary section where she fused the three books into a much clearer and easier to understand summary. She included an analytical section where she applied the new mathematics of calculus to Newton's most controversial theories. Previously, geometry was the standard mathematics used to analyse theories. Du Châtelet's translation is the only complete one to have been done in French and hers remains the standard French translation to this day.<a href="#cite_note-121">[121]</a> <div class="mw-heading mw-heading3"><h3 id="Translations">Translations</h3>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=22" title="Edit section: Translations">edit</a>]</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Newton-4-3.jpg" class="mw-file-description"><img alt="Title page to a 1848 copy of The Mathematical Principles of Natural Philosophy, translated into English by Andrew Motte" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Newton-4-3.jpg/164px-Newton-4-3.jpg" decoding="async" width="164" height="274" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Newton-4-3.jpg/246px-Newton-4-3.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/42/Newton-4-3.jpg/329px-Newton-4-3.jpg 2x" data-file-width="2465" data-file-height="4108" /></a><figcaption>Title page to an 1848 copy of The Mathematical Principles of Natural Philosophy, translated into English by Andrew Motte</figcaption></figure> Four full English translations of Newton's Principia have appeared, all based on Newton's 3rd edition of 1726. The first, from 1729, by Andrew Motte,<a href="#cite_note-Motte-3">[3]</a> was described by Newton scholar <a href="/wiki/I._Bernard_Cohen" title="I. Bernard Cohen">I. Bernard Cohen</a> (in 1968) as "still of enormous value in conveying to us the sense of Newton's words in their own time, and it is generally faithful to the original: clear, and well written".<a href="#cite_note-122">[122]</a> The 1729 version was the basis for several republications, often incorporating revisions, among them a widely used modernised English version of 1934, which appeared under the editorial name of <a href="/wiki/Florian_Cajori" title="Florian Cajori">Florian Cajori</a> (though completed and published only some years after his death). Cohen pointed out ways in which the 18th-century terminology and punctuation of the 1729 translation might be confusing to modern readers, but he also made severe criticisms of the 1934 modernised English version, and showed that the revisions had been made without regard to the original, also demonstrating gross errors "that provided the final impetus to our decision to produce a wholly new translation".<a href="#cite_note-123">[123]</a> The second full English translation, into modern English, is the work that resulted from this decision by collaborating translators I. Bernard Cohen, Anne Whitman, and Julia Budenz; it was published in 1999 with a guide by way of introduction.<a href="#cite_note-124">[124]</a> The third such translation is due to Ian Bruce, and appears, with many other translations of mathematical works of the 17th and 18th centuries, on his website.<a href="#cite_note-125">[125]</a> The fourth complete English translation is due to <a href="/wiki/Charles_Leedham-Green" title="Charles Leedham-Green">Charles Leedham-Green</a>, professor emeritus of mathematics at <a href="/wiki/Queen_Mary_University_of_London" title="Queen Mary University of London">Queen Mary University of London</a>, and was published in 2021 by <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>.<a href="#cite_note-126">[126]</a> Prof. Leedham-Green was motivated to produce that translation, on which he worked for twenty years, in part because of his dissatisfaction with the work of Cohen, Whitman, and Budenz, whose translation of the Principia he found unnecessarily obscure. Leedham-Green's aim was to convey Newton's own reasoning and arguments in a way intelligible to a modern mathematical scientist. His translation is heavily annotated and his explanatory notes make use of the modern secondary literature on some of the more difficult technical aspects of Newton's work. Dana Densmore and William H. Donahue have published a translation of the work's central argument, published in 1996, along with expansion of included proofs and ample commentary.<a href="#cite_note-127">[127]</a> The book was developed as a textbook for classes at <a href="/wiki/St._John%27s_College_(Annapolis/Santa_Fe)" title="St. John's College (Annapolis/Santa Fe)">St. John's College</a> and the aim of this translation is to be faithful to the Latin text.<a href="#cite_note-128">[128]</a> <div class="mw-heading mw-heading2"><h2 id="Varia">Varia</h2>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=23" title="Edit section: Varia">edit</a>]</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Voyager_golden_record_111_systemoftheworld.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Voyager_golden_record_111_systemoftheworld.gif/220px-Voyager_golden_record_111_systemoftheworld.gif" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Voyager_golden_record_111_systemoftheworld.gif/330px-Voyager_golden_record_111_systemoftheworld.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/44/Voyager_golden_record_111_systemoftheworld.gif/440px-Voyager_golden_record_111_systemoftheworld.gif 2x" data-file-width="640" data-file-height="480" /></a><figcaption>Picture from Newton's Philosophiæ Naturalis Principia Mathematica on board the Voyager 1 and 2 spacecraft</figcaption></figure> In 1977, the spacecraft <a href="/wiki/Voyager_1" title="Voyager 1">Voyager 1</a> and <a href="/wiki/Voyager_2" title="Voyager 2">2</a> left earth for the interstellar space carrying a picture of a page from Newton's Principia Mathematica, as part of the <a href="/wiki/Contents_of_the_Voyager_Golden_Record" title="Contents of the Voyager Golden Record">Golden Record</a>, a collection of messages from humanity to extraterrestrials. In 2014, British <a href="/wiki/Astronaut" title="Astronaut">astronaut</a> <a href="/wiki/Tim_Peake" title="Tim Peake">Tim Peake</a> named his upcoming mission to the <a href="/wiki/International_Space_Station" title="International Space Station">International Space Station</a> Principia after the book, in "honour of Britain's greatest scientist".<a href="#cite_note-129">[129]</a> Tim Peake's Principia launched on 15 December 2015 aboard <a href="/wiki/Soyuz_TMA-19M" title="Soyuz TMA-19M">Soyuz TMA-19M</a>.<a href="#cite_note-130">[130]</a> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=24" title="Edit section: See also">edit</a>]</div> <ul><li><a href="/wiki/Atomism" title="Atomism">Atomism</a></li> <li><a href="/wiki/Elements_of_the_Philosophy_of_Newton" title="Elements of the Philosophy of Newton">Elements of the Philosophy of Newton</a></li> <li><a href="/wiki/Isaac_Newton%27s_occult_studies" title="Isaac Newton's occult studies">Isaac Newton's occult studies</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=25" title="Edit section: References">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">^</a> <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation cs2"><a rel="nofollow" class="external text" href="http://www.britannica.com/EBchecked/topic/369153/The-Mathematical-Principles-of-Natural-Philosophy">"The Mathematical Principles of Natural Philosophy"</a>, Encyclopædia Britannica, London, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150502052922/http://www.britannica.com/EBchecked/topic/369153/The-Mathematical-Principles-of-Natural-Philosophy">archived</a> from the original on 2 May 2015, retrieved 13 February 2015</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Mathematical+Principles+of+Natural+Philosophy&rft.btitle=Encyclop%C3%A6dia+Britannica&rft.place=London&rft_id=http%3A%2F%2Fwww.britannica.com%2FEBchecked%2Ftopic%2F369153%2FThe-Mathematical-Principles-of-Natural-Philosophy&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-Principia-2"><a href="#cite_ref-Principia_2-0">^</a> Among versions of the Principia online: <a rel="nofollow" class="external autonumber" href="https://archive.org/details/newtonspmathema00newtrich">[1]</a>. </li> <li id="cite_note-Motte-3">^ <a href="#cite_ref-Motte_3-0">a</a> <a href="#cite_ref-Motte_3-1">b</a> Volume 1 of the 1729 English translation is available as an <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Tm0FAAAAQAAJ&q=Newton+mathematical+principles+Motte">online scan</a>; limited parts of the 1729 translation (misidentified as based on the 1687 edition) have also been <a rel="nofollow" class="external text" href="http://members.tripod.com/~gravitee/axioms.htm">transcribed online</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20081222040441/http://members.tripod.com/~gravitee/axioms.htm">Archived</a> 22 December 2008 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. </li> <li id="cite_note-4"><a href="#cite_ref-4">^</a> J. M. Steele, University of Toronto, (<a rel="nofollow" class="external text" href="http://www.cap.ca/brms/Reviews/Reading-Steele.html">review online</a> from <a href="/wiki/Canadian_Association_of_Physicists" title="Canadian Association of Physicists">Canadian Association of Physicists</a>) <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100401071521/http://www.cap.ca/brms/Reviews/Reading-Steele.html">Archived</a> 1 April 2010 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> of N. Guicciardini's "Reading the Principia: The Debate on Newton's Mathematical Methods for Natural Philosophy from 1687 to 1736" (Cambridge UP, 1999), a book which also states (summary before title page) that the "Principia" "is considered one of the masterpieces in the history of science". </li> <li id="cite_note-5"><a href="#cite_ref-5">^</a> (in French) Alexis Clairaut, "Du systeme du monde, dans les principes de la gravitation universelle", in "Histoires (& Memoires) de l'Academie Royale des Sciences" for 1745 (published 1749), at p. 329 (according to a note on p. 329, Clairaut's paper was read at a session of November 1747). </li> <li id="cite_note-6"><a href="#cite_ref-6">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOuellette2020" class="citation web cs1"><a href="/wiki/Jennifer_Ouellette" title="Jennifer Ouellette">Ouellette, Jennifer</a> (11 November 2020). <a rel="nofollow" class="external text" href="https://arstechnica.com/science/2020/11/historical-detectives-discover-more-first-editions-of-isaac-newtons-principia/">"Historical detectives discover more first editions of Isaac Newton's Principia"</a>. <a href="/wiki/Ars_Technica" title="Ars Technica">Ars Technica</a>. Retrieved 14 October 2023.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Ars+Technica&rft.atitle=Historical+detectives+discover+more+first+editions+of+Isaac+Newton%27s+Principia&rft.date=2020-11-11&rft.aulast=Ouellette&rft.aufirst=Jennifer&rft_id=https%3A%2F%2Farstechnica.com%2Fscience%2F2020%2F11%2Fhistorical-detectives-discover-more-first-editions-of-isaac-newtons-principia%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-7"><a href="#cite_ref-7">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewman1956" class="citation book cs1">Newman, James R. (1956). <a rel="nofollow" class="external text" href="https://archive.org/details/dli.ernet.448891/page/275/mode/1up?q=Genius">The World of Mathematics</a>. Vol. 1. <a href="/wiki/George_Allen_%26_Unwin" class="mw-redirect" title="George Allen & Unwin">George Allen & Unwin</a>. p. 275.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+World+of+Mathematics&rft.pages=275&rft.pub=George+Allen+%26+Unwin&rft.date=1956&rft.aulast=Newman&rft.aufirst=James+R.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fdli.ernet.448891%2Fpage%2F275%2Fmode%2F1up%3Fq%3DGenius&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-8"><a href="#cite_ref-8">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBerlinski1995" class="citation book cs1">Berlinski, David (1995). A Tour of the Calculus (1st ed.). New York: Pantheon Books. p. 5. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-679-42645-5" title="Special:BookSources/978-0-679-42645-5"><bdi>978-0-679-42645-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Tour+of+the+Calculus&rft.place=New+York&rft.pages=5&rft.edition=1st&rft.pub=Pantheon+Books&rft.date=1995&rft.isbn=978-0-679-42645-5&rft.aulast=Berlinski&rft.aufirst=David&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-9"><a href="#cite_ref-9">^</a> G. E. Smith, <a rel="nofollow" class="external text" href="http://plato.stanford.edu/archives/win2008/entries/newton-principia/">"Newton's Philosophiae Naturalis Principia Mathematica"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170713094347/https://plato.stanford.edu/archives/win2008/entries/newton-principia/">Archived</a> 13 July 2017 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, The Stanford Encyclopedia of Philosophy (Winter 2008 Edition), E. N. Zalta (ed.). </li> <li id="cite_note-geomcalc-10">^ <a href="#cite_ref-geomcalc_10-0">a</a> <a href="#cite_ref-geomcalc_10-1">b</a> The content of infinitesimal calculus in the "Principia" was recognized both in Newton's lifetime and later, among others by the <a href="/wiki/Guillaume_de_l%27H%C3%B4pital" title="Guillaume de l'Hôpital">Marquis de l'Hospital</a>, whose 1696 book "Analyse des infiniment petits" (Infinitesimal analysis) stated in its preface, about the "Principia", that "nearly all of it is of this calculus" ("lequel est presque tout de ce calcul"). See also D. T. Whiteside (1970), "The mathematical principles underlying Newton's Principia Mathematica", Journal for the History of Astronomy, vol. 1 (1970), 116–138, especially at p. 120. </li> <li id="cite_note-gschol-hnf-11">^ <a href="#cite_ref-gschol-hnf_11-0">a</a> <a href="#cite_ref-gschol-hnf_11-1">b</a> Or <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n436">"frame" no hypotheses</a> (as traditionally translated at vol. 2, p. 392, in the 1729 English version). </li> <li id="cite_note-12"><a href="#cite_ref-12">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton" class="citation web cs1">Newton, Isaac. <a rel="nofollow" class="external text" href="http://cudl.lib.cam.ac.uk/view/PR-ADV-B-00039-00001/">"Philosophiæ Naturalis Principia Mathematica (Newton's personally annotated 1st edition)"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120108031556/http://cudl.lib.cam.ac.uk/view/PR-ADV-B-00039-00001/">Archived</a> from the original on 8 January 2012. Retrieved 12 December 2011.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Philosophi%C3%A6+Naturalis+Principia+Mathematica+%28Newton%27s+personally+annotated+1st+edition%29&rft.aulast=Newton&rft.aufirst=Isaac&rft_id=http%3A%2F%2Fcudl.lib.cam.ac.uk%2Fview%2FPR-ADV-B-00039-00001%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-variorum-13">^ <a href="#cite_ref-variorum_13-0">a</a> <a href="#cite_ref-variorum_13-1">b</a> <a href="#cite_ref-variorum_13-2">c</a> [In Latin] Isaac Newton's Philosophiae Naturalis Principia Mathematica: the Third edition (1726) with variant readings, assembled and ed. by Alexandre Koyré and I Bernard Cohen with the assistance of Anne Whitman (Cambridge, MA, 1972, Harvard UP). </li> <li id="cite_note-14"><a href="#cite_ref-14">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHermann2008" class="citation journal cs1 cs1-prop-foreign-lang-source">Hermann, Claudine (2008). <a rel="nofollow" class="external text" href="https://journals.openedition.org/bibnum/722?lang=en#tocto2n2">"La traduction et les commentaires des Principia de Newton par Émilie du Châtelet"</a>. Bibnum. Textes Fondateurs de la Science (in French). <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.4000%2Fbibnum.722">10.4000/bibnum.722</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:164354455">164354455</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210709183524/https://journals.openedition.org/bibnum/722?lang=en#tocto2n2">Archived</a> from the original on 9 July 2021. Retrieved 11 March 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bibnum.+Textes+Fondateurs+de+la+Science&rft.atitle=La+traduction+et+les+commentaires+des+Principia+de+Newton+par+%C3%89milie+du+Ch%C3%A2telet&rft.date=2008&rft_id=info%3Adoi%2F10.4000%2Fbibnum.722&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A164354455%23id-name%3DS2CID&rft.aulast=Hermann&rft.aufirst=Claudine&rft_id=https%3A%2F%2Fjournals.openedition.org%2Fbibnum%2F722%3Flang%3Den%23tocto2n2&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> <a rel="nofollow" class="external text" href="https://translate.google.co.uk/?sl=auto&tl=en&text=am%C3%A9lior%C3%A9e&op=translate">translate.google.co.uk : "améliorée"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210709183406/https://translate.google.co.uk/?sl=auto&tl=en&text=am%C3%A9lior%C3%A9e&op=translate">Archived</a> 9 July 2021 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> </li> <li id="cite_note-15"><a href="#cite_ref-15">^</a> From Motte's translation of 1729 (at 3rd page of Author's Preface); and see also <a href="/wiki/J._W._Herivel" class="mw-redirect" title="J. W. Herivel">J. W. Herivel</a>, The background to Newton's "Principia", Oxford University Press, 1965. </li> <li id="cite_note-16"><a href="#cite_ref-16">^</a> The <a href="/wiki/De_motu_corporum_in_gyrum" title="De motu corporum in gyrum">De motu corporum in gyrum</a> article indicates the topics that reappear in the Principia. </li> <li id="cite_note-17"><a href="#cite_ref-17">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). "Definitions". <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ">The Mathematical Principles of Natural Philosophy, Volume I</a>. B. Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ/page/n54">1</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Definitions&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+I&rft.pages=1&rft.pub=B.+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_Tm0FAAAAQAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-18"><a href="#cite_ref-18">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). "Axioms or Laws of Motion". <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ">The Mathematical Principles of Natural Philosophy, Volume I</a>. B. Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ/page/n62">19</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Axioms+or+Laws+of+Motion&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+I&rft.pages=19&rft.pub=B.+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_Tm0FAAAAQAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-19"><a href="#cite_ref-19">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). "Section I". <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ">The Mathematical Principles of Natural Philosophy, Volume I</a>. B. Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ/page/n84">41</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Section+I&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+I&rft.pages=41&rft.pub=B.+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_Tm0FAAAAQAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-20"><a href="#cite_ref-20">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). "Section II". <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ">The Mathematical Principles of Natural Philosophy, Volume I</a>. B. Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ/page/n102">57</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Section+II&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+I&rft.pages=57&rft.pub=B.+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_Tm0FAAAAQAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-21"><a href="#cite_ref-21">^</a> This relationship between circular curvature, speed and radial force, now often known as Huygens' formula, was independently found by Newton (in the 1660s) and by Huygens in the 1650s: the conclusion was published (without proof) by Huygens in 1673.This was given by Isaac Newton through his Inverse Square Law. </li> <li id="cite_note-22"><a href="#cite_ref-22">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewtonMachin1729" class="citation book cs1">Newton, Sir Isaac; Machin, John (1729). <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ">The Mathematical Principles of Natural Philosophy, Volume I</a>. B. Motte. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ/page/n128">79</a>–153.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+I&rft.pages=79-153&rft.pub=B.+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft.au=Machin%2C+John&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_Tm0FAAAAQAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-23"><a href="#cite_ref-23">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). "Section IX". <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ">The Mathematical Principles of Natural Philosophy, Volume I</a>. B. Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ/page/n251">177</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Section+IX&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+I&rft.pages=177&rft.pub=B.+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_Tm0FAAAAQAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-24"><a href="#cite_ref-24">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). "Section XI". <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ">The Mathematical Principles of Natural Philosophy, Volume I</a>. B. Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ/page/n298">218</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Section+XI&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+I&rft.pages=218&rft.pub=B.+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_Tm0FAAAAQAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-25"><a href="#cite_ref-25">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). "Section XI, Proposition LXVI". <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ">The Mathematical Principles of Natural Philosophy, Volume I</a>. B. Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ/page/n316">234</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Section+XI%2C+Proposition+LXVI&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+I&rft.pages=234&rft.pub=B.+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_Tm0FAAAAQAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-26"><a href="#cite_ref-26">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewtonMachin1729" class="citation book cs1">Newton, Sir Isaac; Machin, John (1729). <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ">The Mathematical Principles of Natural Philosophy, Volume I</a>. B. Motte. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ/page/n321">239</a>–256.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+I&rft.pages=239-256&rft.pub=B.+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft.au=Machin%2C+John&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_Tm0FAAAAQAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-27"><a href="#cite_ref-27">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). "Section XII". <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ">The Mathematical Principles of Natural Philosophy, Volume I</a>. B. Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_Tm0FAAAAQAAJ/page/n345">263</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Section+XII&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+I&rft.pages=263&rft.pub=B.+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_Tm0FAAAAQAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-28"><a href="#cite_ref-28">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGillispie1960" class="citation book cs1"><a href="/wiki/Charles_Coulston_Gillispie" title="Charles Coulston Gillispie">Gillispie, Charles Coulston</a> (1960). <a rel="nofollow" class="external text" href="https://archive.org/details/edgeofobjectivit00char">The Edge of Objectivity: An Essay in the History of Scientific Ideas</a>. Princeton University Press. p. <a rel="nofollow" class="external text" href="https://archive.org/details/edgeofobjectivit00char/page/254">254</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-691-02350-6" title="Special:BookSources/0-691-02350-6"><bdi>0-691-02350-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Edge+of+Objectivity%3A+An+Essay+in+the+History+of+Scientific+Ideas&rft.pages=254&rft.pub=Princeton+University+Press&rft.date=1960&rft.isbn=0-691-02350-6&rft.aulast=Gillispie&rft.aufirst=Charles+Coulston&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fedgeofobjectivit00char&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-29"><a href="#cite_ref-29">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). "Proposition 48". <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC">The Mathematical Principles of Natural Philosophy, Volume II</a>. Benjamin Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n418">176</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Proposition+48&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+II&rft.pages=176&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_6EqxPav3vIsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-30"><a href="#cite_ref-30">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). "Scholium to proposition 50". <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC">The Mathematical Principles of Natural Philosophy, Volume II</a>. Benjamin Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n423">181</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Scholium+to+proposition+50&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+II&rft.pages=181&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_6EqxPav3vIsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-31"><a href="#cite_ref-31">^</a> Eric J Aiton, The Cartesian vortex theory, chapter 11 in Planetary astronomy from the Renaissance to the rise of astrophysics, Part A: Tycho Brahe to Newton, eds. R Taton & C Wilson, Cambridge (Cambridge University press) 1989; at pp. 207–221. </li> <li id="cite_note-32"><a href="#cite_ref-32">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). "Scholium to proposition 53". <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC">The Mathematical Principles of Natural Philosophy, Volume II</a>. Benjamin Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n219">197</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Scholium+to+proposition+53&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+II&rft.pages=197&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_6EqxPav3vIsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-33"><a href="#cite_ref-33">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC">The Mathematical Principles of Natural Philosophy, Volume II</a>. Benjamin Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n276">252</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+II&rft.pages=252&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_6EqxPav3vIsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-34"><a href="#cite_ref-34">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC">The Mathematical Principles of Natural Philosophy, Volume II</a>. Benjamin Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n286">262</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+II&rft.pages=262&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_6EqxPav3vIsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-35"><a href="#cite_ref-35">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). "The Phaenomena". <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC">The Mathematical Principles of Natural Philosophy, Volume II</a>. Benjamin Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n230">206</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Phaenomena&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+II&rft.pages=206&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_6EqxPav3vIsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-36"><a href="#cite_ref-36">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC">The Mathematical Principles of Natural Philosophy, Volume II</a>. Benjamin Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n238">213</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+II&rft.pages=213&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_6EqxPav3vIsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-37"><a href="#cite_ref-37">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC">The Mathematical Principles of Natural Philosophy, Volume II</a>. Benjamin Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n244">220</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+II&rft.pages=220&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_6EqxPav3vIsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-38"><a href="#cite_ref-38">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC">The Mathematical Principles of Natural Philosophy, Volume II</a>. Benjamin Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n355">323</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+II&rft.pages=323&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_6EqxPav3vIsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-39"><a href="#cite_ref-39">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC">The Mathematical Principles of Natural Philosophy, Volume II</a>. Benjamin Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n366">332</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+II&rft.pages=332&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_6EqxPav3vIsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-40"><a href="#cite_ref-40">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC">The Mathematical Principles of Natural Philosophy, Volume II</a>. Benjamin Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n279">255</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+II&rft.pages=255&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_6EqxPav3vIsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-41"><a href="#cite_ref-41">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC">The Mathematical Principles of Natural Philosophy, Volume II</a>. Benjamin Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n337">305</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+II&rft.pages=305&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_6EqxPav3vIsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-42"><a href="#cite_ref-42">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC">The Mathematical Principles of Natural Philosophy, Volume II</a>. Benjamin Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n338">306</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+II&rft.pages=306&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_6EqxPav3vIsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-43"><a href="#cite_ref-43">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC">The Mathematical Principles of Natural Philosophy, Volume II</a>. Benjamin Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n352">320</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+II&rft.pages=320&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_6EqxPav3vIsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-44"><a href="#cite_ref-44">^</a> See Curtis Wilson, "The Newtonian achievement in astronomy", pp. 233–274 in R Taton & C Wilson (eds) (1989) The General History of Astronomy, Volume, 2A', <a rel="nofollow" class="external text" href="https://books.google.com/books?id=rkQKU-wfPYMC&pg=PA233">at p. 233</a>). </li> <li id="cite_note-45"><a href="#cite_ref-45">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). "Proposition 12, Corollary". <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC">The Mathematical Principles of Natural Philosophy, Volume II</a>. Benjamin Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n257">233</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Proposition+12%2C+Corollary&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+II&rft.pages=233&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_6EqxPav3vIsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-prop11-46">^ <a href="#cite_ref-prop11_46-0">a</a> <a href="#cite_ref-prop11_46-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). "Proposition 11 & preceding Hypothesis". <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC">The Mathematical Principles of Natural Philosophy, Volume II</a>. Benjamin Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n256">232</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Proposition+11+%26+preceding+Hypothesis&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+II&rft.pages=232&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_6EqxPav3vIsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-47"><a href="#cite_ref-47">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). "Proposition 8, Corollary 2". <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC">The Mathematical Principles of Natural Philosophy, Volume II</a>. Benjamin Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n252">228</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Proposition+8%2C+Corollary+2&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+II&rft.pages=228&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_6EqxPav3vIsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-48"><a href="#cite_ref-48">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). "Proposition 12". <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC">The Mathematical Principles of Natural Philosophy, Volume II</a>. Benjamin Motte. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n256">232</a>–233.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Proposition+12&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+II&rft.pages=232-233&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_6EqxPav3vIsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> Newton's position is seen to go beyond literal Copernican heliocentrism practically to the modern position in regard to the Solar System barycenter (see <a href="/wiki/Barycenter#Inside_or_outside_the_Sun.3F" class="mw-redirect" title="Barycenter">Barycenter – Inside or outside the Sun?</a>). </li> <li id="cite_note-49"><a href="#cite_ref-49">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKnudsenHjorth2012" class="citation book cs1">Knudsen, Jens M.; Hjorth, Poul (2012). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=rkP1CAAAQBAJ">Elements of Newtonian Mechanics</a> (illustrated ed.). Springer Science & Business Media. p. 30. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-642-97599-8" title="Special:BookSources/978-3-642-97599-8"><bdi>978-3-642-97599-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Elements+of+Newtonian+Mechanics&rft.pages=30&rft.edition=illustrated&rft.pub=Springer+Science+%26+Business+Media&rft.date=2012&rft.isbn=978-3-642-97599-8&rft.aulast=Knudsen&rft.aufirst=Jens+M.&rft.au=Hjorth%2C+Poul&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DrkP1CAAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> <a rel="nofollow" class="external text" href="https://books.google.com/books?id=rkP1CAAAQBAJ&pg=PA30">Extract of p. 30</a> </li> <li id="cite_note-50"><a href="#cite_ref-50">^</a> See online Principia (1729 translation) vol. 2, Books 2 & 3, <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n431">starting at p. 387 of volume 2 (1729)</a>. </li> <li id="cite_note-Edelglass_p._54-51">^ <a href="#cite_ref-Edelglass_p._54_51-0">a</a> <a href="#cite_ref-Edelglass_p._54_51-1">b</a> Edelglass et al., Matter and Mind, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-940262-45-2" title="Special:BookSources/0-940262-45-2">0-940262-45-2</a>, p. 54. </li> <li id="cite_note-52"><a href="#cite_ref-52">^</a> See online Principia (1729 translation) vol. 2, Books 2 & 3, <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n436">at p. 392 of volume 2 (1729)</a>. </li> <li id="cite_note-The_General_Scholium_to_Isaac_Newton's_''Principia_mathematica''-53"><a href="#cite_ref-The_General_Scholium_to_Isaac_Newton's_''Principia_mathematica''_53-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSnobelen" class="citation web cs1"><a href="/wiki/Stephen_Snobelen" title="Stephen Snobelen">Snobelen, Stephen</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080608071737/http://isaac-newton.org/scholium.htm">"The General Scholium to Isaac Newton's Principia mathematica"</a>. Archived from <a rel="nofollow" class="external text" href="http://isaac-newton.org/scholium.htm">the original</a> on 8 June 2008. Retrieved 31 May 2008.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+General+Scholium+to+Isaac+Newton%27s+Principia+mathematica&rft.aulast=Snobelen&rft.aufirst=Stephen&rft_id=http%3A%2F%2Fisaac-newton.org%2Fscholium.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-54"><a href="#cite_ref-54">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDucheyne" class="citation journal cs1">Ducheyne, Steffen. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20081217040531/http://logica.ugent.be/steffen/GS.pdf">"The General Scholium: Some notes on Newton's published and unpublished endeavours"</a> (PDF). Lias: Sources and Documents Relating to the Early Modern History of Ideas. 33 (2): 223–274. Archived from <a rel="nofollow" class="external text" href="http://logica.ugent.be/steffen/GS.pdf">the original</a> (PDF) on 17 December 2008. Retrieved 19 November 2008.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Lias%3A+Sources+and+Documents+Relating+to+the+Early+Modern+History+of+Ideas&rft.atitle=The+General+Scholium%3A+Some+notes+on+Newton%27s+published+and+unpublished+endeavours&rft.volume=33&rft.issue=2&rft.pages=223-274&rft.aulast=Ducheyne&rft.aufirst=Steffen&rft_id=http%3A%2F%2Flogica.ugent.be%2Fsteffen%2FGS.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-55"><a href="#cite_ref-55">^</a> Paraphrase of 1686 report by Halley, in H. W. Turnbull (ed.), "Correspondence of Isaac Newton", Vol. 2, cited above, pp. 431–448. </li> <li id="cite_note-56"><a href="#cite_ref-56">^</a> 'Cook, 1998': A. Cook, Edmond Halley, Charting the Heavens and the Seas, Oxford University Press 1998, at pp. 147 and 152. </li> <li id="cite_note-57"><a href="#cite_ref-57">^</a> As dated e.g. by D. T. Whiteside, in The Prehistory of the Principia from 1664 to 1686, Notes and Records of the Royal Society of London, 45 (1991) 11–61. </li> <li id="cite_note-58"><a href="#cite_ref-58">^</a> Cook, 1998; at p. 147. </li> <li id="cite_note-59"><a href="#cite_ref-59">^</a> Westfall, 1980: R. S. Westfall, Never at Rest: A Biography of Isaac Newton, Cambridge University Press 1980, at p. 404. </li> <li id="cite_note-60"><a href="#cite_ref-60">^</a> Cook, 1998; at p. 151. </li> <li id="cite_note-61"><a href="#cite_ref-61">^</a> Westfall, 1980; at p. 406, also pp. 191–192. </li> <li id="cite_note-62"><a href="#cite_ref-62">^</a> Westfall, 1980; at p. 406, n. 15. </li> <li id="cite_note-63"><a href="#cite_ref-63">^</a> Westfall, 1980; at pp. 153–156. </li> <li id="cite_note-64"><a href="#cite_ref-64">^</a> The fundamental study of Newton's progress in writing the Principia is in I. Bernard Cohen's Introduction to Newton's 'Principia', (Cambridge, Cambridge University Press, 1971), at part 2: "The writing and the first publication of the 'Principia'", pp. 47–142. </li> <li id="cite_note-65"><a href="#cite_ref-65">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1729" class="citation book cs1">Newton, Sir Isaac (1729). "Introduction to Book 3". <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC">The Mathematical Principles of Natural Philosophy, Volume II</a>. Benjamin Motte. p. <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n224">200</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Introduction+to+Book+3&rft.btitle=The+Mathematical+Principles+of+Natural+Philosophy%2C+Volume+II&rft.pages=200&rft.pub=Benjamin+Motte&rft.date=1729&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_6EqxPav3vIsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-Stanford-66"><a href="#cite_ref-Stanford_66-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSmith,_G.2008" class="citation journal cs1 cs1-prop-long-vol">Smith, G. (2008). <a rel="nofollow" class="external text" href="https://plato.stanford.edu/entries/newton-principia/">"Newton's Philosophiae Naturalis Principia Mathematica"</a>. The Stanford Encyclopedia of Philosophy, Zalta, E.N. Ed. Winter 2008. Metaphysics Research Lab, Dept. of Philosophy, Stanford University. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1095-5054">1095-5054</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20221021220151/https://plato.stanford.edu/entries/newton-principia/">Archived</a> from the original on 21 October 2022. Retrieved 21 October 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Stanford+Encyclopedia+of+Philosophy%2C+Zalta%2C+E.N.+Ed.&rft.atitle=Newton%27s+Philosophiae+Naturalis+Principia+Mathematica&rft.volume=Winter+2008&rft.date=2008&rft.issn=1095-5054&rft.au=Smith%2C+G.&rft_id=https%3A%2F%2Fplato.stanford.edu%2Fentries%2Fnewton-principia%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-67"><a href="#cite_ref-67">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1728" class="citation book cs1">Newton, Isaac (1728). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=rEYUAAAAQAAJ&pg=PR1">A Treatise of the System of the World</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Treatise+of+the+System+of+the+World&rft.date=1728&rft.aulast=Newton&rft.aufirst=Isaac&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DrEYUAAAAQAAJ%26pg%3DPR1&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-68"><a href="#cite_ref-68">^</a> I. Bernard Cohen, Introduction to Newton's A Treatise of the System of the World (facsimile of second English edition of 1731), London (Dawsons of Pall Mall) 1969; reprinted in <a rel="nofollow" class="external text" href="https://books.google.com/books?id=UvyPx-DwnrAC">A Treatise of the System of the World</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210914210955/https://books.google.com/books?id=UvyPx-DwnrAC">Archived</a> 14 September 2021 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, Dover Phoenix Editions, 2004, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-486-43880-5" title="Special:BookSources/0-486-43880-5">0-486-43880-5</a>. </li> <li id="cite_note-69"><a href="#cite_ref-69">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1740" class="citation book cs1">Newton, Sir Isaac (1740). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=02xbAAAAQAAJ&pg=PP7">The System of the World: Demonstrated in an Easy and Popular Manner. Being a Proper Introduction to the Most Sublime Philosophy. By the Illustrious Sir Isaac Newton. Translated into English</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+System+of+the+World%3A+Demonstrated+in+an+Easy+and+Popular+Manner.+Being+a+Proper+Introduction+to+the+Most+Sublime+Philosophy.+By+the+Illustrious+Sir+Isaac+Newton.+Translated+into+English&rft.date=1740&rft.aulast=Newton&rft.aufirst=Sir+Isaac&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D02xbAAAAQAAJ%26pg%3DPP7&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> A "corrected" reprint of the second edition. </li> <li id="cite_note-70"><a href="#cite_ref-70">^</a> Richard Westfall (1980), Never at Rest, p. 453, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-27435-4" title="Special:BookSources/0-521-27435-4">0-521-27435-4</a>. </li> <li id="cite_note-71"><a href="#cite_ref-71">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFClerk2013" class="citation web cs1">Clerk, Halley's (29 October 2013). <a rel="nofollow" class="external text" href="https://halleyslog.wordpress.com/2013/10/29/halley-and-the-principia/">"Halley and the Principia"</a>. Halley's Log. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20191207233818/https://halleyslog.wordpress.com/2013/10/29/halley-and-the-principia/">Archived</a> from the original on 7 December 2019. Retrieved 7 December 2019.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Halley%27s+Log&rft.atitle=Halley+and+the+Principia&rft.date=2013-10-29&rft.aulast=Clerk&rft.aufirst=Halley%27s&rft_id=https%3A%2F%2Fhalleyslog.wordpress.com%2F2013%2F10%2F29%2Fhalley-and-the-principia%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-72"><a href="#cite_ref-72">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20120331192529/http://www.museumoflondon.org.uk/archive/exhibits/pepys/pages/largeImage.asp?id=101&size=3&nav=none">"Museum of London exhibit including facsimile of title page from John Flamsteed's copy of 1687 edition of Newton's Principia"</a>. Museumoflondon.org.uk. Archived from <a rel="nofollow" class="external text" href="http://www.museumoflondon.org.uk/archive/exhibits/pepys/pages/largeImage.asp?id=101&size=3&nav=none">the original</a> on 31 March 2012. Retrieved 16 March 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Museum+of+London+exhibit+including+facsimile+of+title+page+from+John+Flamsteed%27s+copy+of+1687+edition+of+Newton%27s+Principia&rft.pub=Museumoflondon.org.uk&rft_id=http%3A%2F%2Fwww.museumoflondon.org.uk%2Farchive%2Fexhibits%2Fpepys%2Fpages%2FlargeImage.asp%3Fid%3D101%26size%3D3%26nav%3Dnone&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-73"><a href="#cite_ref-73">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBill_Bryson2004" class="citation book cs1">Bill Bryson (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=RKHLD9qNs64C">A Short History of Nearly Everything</a>. Random House, Inc. p. 74. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-385-66004-4" title="Special:BookSources/978-0-385-66004-4"><bdi>978-0-385-66004-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Short+History+of+Nearly+Everything&rft.pages=74&rft.pub=Random+House%2C+Inc.&rft.date=2004&rft.isbn=978-0-385-66004-4&rft.au=Bill+Bryson&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DRKHLD9qNs64C&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-74"><a href="#cite_ref-74">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThe_Henryk_Niewodniczanski_Institute_of_Nuclear_Physics" class="citation web cs1">The Henryk Niewodniczanski Institute of Nuclear Physics. "Particle Physics and Astrophysics Research".</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Particle+Physics+and+Astrophysics+Research&rft.au=The+Henryk+Niewodniczanski+Institute+of+Nuclear+Physics&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> <code class="cs1-code">{{<a href="/wiki/Template:Cite_web" title="Template:Cite web">cite web</a>}}</code>: Missing or empty <code class="cs1-code">|url=</code> (<a href="/wiki/Help:CS1_errors#cite_web_url" title="Help:CS1 errors">help</a>) </li> <li id="cite_note-75"><a href="#cite_ref-75">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRovelli2000" class="citation arxiv cs1">Rovelli, Carlo (2000). "Notes for a brief history of quantum gravity". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/gr-qc/0006061">gr-qc/0006061</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Notes+for+a+brief+history+of+quantum+gravity&rft.date=2000&rft_id=info%3Aarxiv%2Fgr-qc%2F0006061&rft.aulast=Rovelli&rft.aufirst=Carlo&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-T_Whiteside_1991_pages_11–61-76">^ <a href="#cite_ref-T_Whiteside_1991_pages_11–61_76-0">a</a> <a href="#cite_ref-T_Whiteside_1991_pages_11–61_76-1">b</a> D. T. Whiteside, "The pre-history of the 'Principia' from 1664 to 1686", Notes and Records of the Royal Society of London, 45 (1991), pages 11–61; especially at 13–20. <a rel="nofollow" class="external autonumber" href="https://www.jstor.org/pss/531520">[2]</a>. </li> <li id="cite_note-77"><a href="#cite_ref-77">^</a> See J. Bruce Brackenridge, "The key to Newton's dynamics: the Kepler problem and the Principia", (University of California Press, 1995), especially at <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ovOTK7X_mMkC&pg=PA20">pages 20–21</a>. </li> <li id="cite_note-dtw1970-78"><a href="#cite_ref-dtw1970_78-0">^</a> See page 10 in D. T. Whiteside, "Before the Principia: the maturing of Newton's thoughts on dynamical astronomy, 1664–1684", Journal for the History of Astronomy, i (1970), pages 5–19. </li> <li id="cite_note-attempt-79">^ <a href="#cite_ref-attempt_79-0">a</a> <a href="#cite_ref-attempt_79-1">b</a> Hooke's 1674 statement in "An Attempt to Prove the Motion of the Earth from Observations", is available in <a rel="nofollow" class="external text" href="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView/ECHOzogiLib?mode=imagepath&url=/mpiwg/online/permanent/library/XXTBUC3U/pageimg">online facsimile here</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100416051258/http://echo.mpiwg-berlin.mpg.de/ECHOdocuView/ECHOzogiLib?mode=imagepath&url=/mpiwg/online/permanent/library/XXTBUC3U/pageimg">Archived</a> 16 April 2010 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. </li> <li id="cite_note-80"><a href="#cite_ref-80">^</a> See page 239 in Curtis Wilson (1989), "The Newtonian achievement in astronomy", ch. 13 (pages 233–274) in "Planetary astronomy from the Renaissance to the rise of astrophysics: 2A: Tycho Brahe to Newton", CUP 1989. </li> <li id="cite_note-167986letters-81">^ <a href="#cite_ref-167986letters_81-0">a</a> <a href="#cite_ref-167986letters_81-1">b</a> <a href="#cite_ref-167986letters_81-2">c</a> <a href="#cite_ref-167986letters_81-3">d</a> <a href="#cite_ref-167986letters_81-4">e</a> H. W. Turnbull (ed.), Correspondence of Isaac Newton, Vol. 2 (1676–1687), (Cambridge University Press, 1960), giving the Hooke-Newton correspondence (of November 1679 to January 1679/80) at pp. 297–314, and the 1686 correspondence over Hooke's priority claim at pp. 431–448. </li> <li id="cite_note-82"><a href="#cite_ref-82">^</a> "Correspondence", vol. 2 already cited, at p. 297. </li> <li id="cite_note-83"><a href="#cite_ref-83">^</a> Several commentators have followed Hooke in calling Newton's spiral path mistaken, or even a "blunder", but there are also the following facts: (a) that Hooke left out of account Newton's specific statement that the motion resulted from dropping "a heavy body suspended in the Air" (i.e. a resisting medium), see Newton to Hooke, 28 November 1679, document #236 at page 301, "Correspondence", vol. 2 cited above, and compare Hooke's report to the Royal Society on 11 December 1679, where Hooke reported the matter "supposing no resistance", see D Gjertsen, "Newton Handbook" (1986), at page 259); and (b) that Hooke's reply of 9 December 1679 to Newton considered the cases of motion both with and without air resistance: The resistance-free path was what Hooke called an 'elliptueid'; but a line in Hooke's diagram showing the path for his case of air resistance was, though elongated, also another inward-spiralling path ending at the Earth's centre: Hooke wrote "where the Medium ... has a power of impeding and destroying its motion the curve in wch it would move would be some what like the Line AIKLMNOP &c and ... would terminate in the center C". Hooke's path including air resistance was therefore to this extent like Newton's (see "Correspondence", vol. 2, cited above, at pages 304–306, document #237, with accompanying figure). The diagrams are also available online: see Curtis Wilson, chapter 13 in "Planetary Astronomy from the Renaissance to the Rise of Astrophysics, Part A, Tycho Brahe to Newton", (Cambridge UP 1989), at page 241 showing <a rel="nofollow" class="external text" href="https://books.google.com/books?id=rkQKU-wfPYMC&pg=PA241">Newton's 1679 diagram</a> with spiral, and extract of his letter; also at page 242 showing <a rel="nofollow" class="external text" href="https://books.google.com/books?id=rkQKU-wfPYMC&pg=PA242">Hooke's 1679 diagram</a> including two paths, closed curve and spiral. Newton pointed out in his later correspondence over the priority claim that the descent in a spiral "is true in a resisting medium such as our air is", see "Correspondence", vol. 2 cited above, at page 433, document #286. </li> <li id="cite_note-84"><a href="#cite_ref-84">^</a> See page 309 in "Correspondence of Isaac Newton", Vol. 2 cited above, at document #239. </li> <li id="cite_note-85"><a href="#cite_ref-85">^</a> See Curtis Wilson (1989) at page 244. </li> <li id="cite_note-86"><a href="#cite_ref-86">^</a> See "Meanest foundations and nobler superstructures: Hooke, Newton and the 'Compounding of the Celestiall Motions of the Planetts'", Ofer Gal, 2003 <a rel="nofollow" class="external text" href="https://books.google.com/books?id=0nKYlXxIemoC&pg=RA1-PA9">at page 9</a>. </li> <li id="cite_note-87"><a href="#cite_ref-87">^</a> See for example the 1729 English translation of the 'Principia', <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Tm0FAAAAQAAJ&pg=PA66">at page 66</a>. </li> <li id="cite_note-88"><a href="#cite_ref-88">^</a> R. S. Westfall, "Never at Rest", 1980, at pages 391–292. </li> <li id="cite_note-89"><a href="#cite_ref-89">^</a> The second extract is quoted and translated in W. W. Rouse Ball, "An Essay on Newton's 'Principia'" (London and New York: Macmillan, 1893), at page 69. </li> <li id="cite_note-90"><a href="#cite_ref-90">^</a> The original statements by Clairaut (in French) are found (with orthography here as in the original) in "Explication abregée du systême du monde, et explication des principaux phénomenes astronomiques tirée des Principes de M. Newton" (1759), at Introduction (section IX), page 6: "Il ne faut pas croire que cette idée ... de Hook diminue la gloire de M. Newton", [and] "L'exemple de Hook" [serves] "à faire voir quelle distance il y a entre une vérité entrevue & une vérité démontrée". </li> <li id="cite_note-EA-20201110-91"><a href="#cite_ref-EA-20201110_91-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCalifornia_Institute_of_Technology2020" class="citation news cs1"><a href="/wiki/California_Institute_of_Technology" title="California Institute of Technology">California Institute of Technology</a> (10 November 2020). <a rel="nofollow" class="external text" href="https://www.eurekalert.org/pub_releases/2020-11/ciot-hoc111020.php">"News Release 10-Nov-2020 – Hundreds of copies of Newton's Principia found in new census – Findings suggest that Isaac Newton's 17th-century masterpiece was more widely read"</a>. <a href="/wiki/EurekAlert!" class="mw-redirect" title="EurekAlert!">EurekAlert!</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20201110210451/https://www.eurekalert.org/pub_releases/2020-11/ciot-hoc111020.php">Archived</a> from the original on 10 November 2020. Retrieved 11 November 2020.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=EurekAlert%21&rft.atitle=News+Release+10-Nov-2020+%E2%80%93+Hundreds+of+copies+of+Newton%27s+Principia+found+in+new+census+%E2%80%93+Findings+suggest+that+Isaac+Newton%27s+17th-century+masterpiece+was+more+widely+read&rft.date=2020-11-10&rft.au=California+Institute+of+Technology&rft_id=https%3A%2F%2Fwww.eurekalert.org%2Fpub_releases%2F2020-11%2Fciot-hoc111020.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-92"><a href="#cite_ref-92">^</a> Henry P. Macomber, "Census of Owners of 1687 First, and 1726 Presentation Edition of Newton's 'Principia'", The Papers of the Bibliographical Society of America, volume 47 (1953), pp. 269–300, at p. 269. </li> <li id="cite_note-93"><a href="#cite_ref-93">^</a> Macomber, op. cit., p. 270. </li> <li id="cite_note-94"><a href="#cite_ref-94">^</a> Feingold, Mordechai and Svorenčík, Andrej (2020) <a rel="nofollow" class="external text" href="https://authors.library.caltech.edu/105262/">A preliminary census of copies of the first edition of Newton's Principia (1687)</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20201111021832/https://authors.library.caltech.edu/105262/">Archived</a> 11 November 2020 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. Annals of Science, 77 (3), pp. 253–348. </li> <li id="cite_note-95"><a href="#cite_ref-95">^</a> Dean, Jason W. and Cumby, Jamie (2021) <a rel="nofollow" class="external text" href="https://hcommons.org/deposits/item/hc:41769/">Principles of Principia: Some Notes on the Print Run for the First Edition</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220818170402/https://hcommons.org/deposits/item/hc:41769/">Archived</a> 18 August 2022 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. The Book Collector, 70 (3), pp. 418–435. </li> <li id="cite_note-96"><a href="#cite_ref-96">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton" class="citation web cs1">Newton, Isaac. <a rel="nofollow" class="external text" href="http://cudl.lib.cam.ac.uk/view/PR-ADV-B-00039-00001/">"Philosophiæ naturalis principia mathematica"</a>. Cambridge Digital Library. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120108031556/http://cudl.lib.cam.ac.uk/view/PR-ADV-B-00039-00001/">Archived</a> from the original on 8 January 2012. Retrieved 3 July 2013.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Philosophi%C3%A6+naturalis+principia+mathematica&rft.place=Cambridge+Digital+Library&rft.aulast=Newton&rft.aufirst=Isaac&rft_id=http%3A%2F%2Fcudl.lib.cam.ac.uk%2Fview%2FPR-ADV-B-00039-00001%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-97"><a href="#cite_ref-97">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton1687" class="citation web cs1 cs1-prop-foreign-lang-source">Newton, Isaac (1687). <a rel="nofollow" class="external text" href="https://archive.today/20121215132513/https://catalog.swem.wm.edu/Record/117047">"Philosophiae naturalis principia mathematica"</a> (in Latin). Swem Library: Jussu Societatis Regiae ac Typis Josephi Streater. Archived from <a rel="nofollow" class="external text" href="https://catalog.swem.wm.edu/Record/117047">the original</a> on 15 December 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Philosophiae+naturalis+principia+mathematica&rft.place=Swem+Library&rft.pub=Jussu+Societatis+Regiae+ac+Typis+Josephi+Streater&rft.date=1687&rft.aulast=Newton&rft.aufirst=Isaac&rft_id=https%3A%2F%2Fcatalog.swem.wm.edu%2FRecord%2F117047&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-98"><a href="#cite_ref-98">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://libraries.wm.edu/news/2020/03/principia-mystery-annotations-we%E2%80%99re-pretty-sure-whodunit-%E2%80%94-what-was-he-thinking">"Principia mystery annotations: We're pretty sure whodunit – but what was he thinking?"</a>. 4 March 2020. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20211121220332/https://libraries.wm.edu/news/2020/03/principia-mystery-annotations-we%E2%80%99re-pretty-sure-whodunit-%E2%80%94-what-was-he-thinking">Archived</a> from the original on 21 November 2021. Retrieved 23 September 2020.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Principia+mystery+annotations%3A+We%27re+pretty+sure+whodunit+%E2%80%93+but+what+was+he+thinking%3F&rft.date=2020-03-04&rft_id=https%3A%2F%2Flibraries.wm.edu%2Fnews%2F2020%2F03%2Fprincipia-mystery-annotations-we%25E2%2580%2599re-pretty-sure-whodunit-%25E2%2580%2594-what-was-he-thinking&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-99"><a href="#cite_ref-99">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www-sul.stanford.edu/depts/spc/rbc/history_science/newton.html">"Special Collections & University Archives"</a>. stanford.edu. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130521125441/http://www-sul.stanford.edu/depts/spc/rbc/history_science/newton.html">Archived</a> from the original on 21 May 2013. Retrieved 18 April 2008.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=stanford.edu&rft.atitle=Special+Collections+%26+University+Archives&rft_id=http%3A%2F%2Fwww-sul.stanford.edu%2Fdepts%2Fspc%2Frbc%2Fhistory_science%2Fnewton.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-100"><a href="#cite_ref-100">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.roe.ac.uk/roe/library/crawford/index.html">"The Crawford collection at the Royal Observatory Edinburgh"</a>. The Royal Observatory, Edinburgh. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210125150815/http://www.roe.ac.uk/roe/library/crawford/index.html">Archived</a> from the original on 25 January 2021. Retrieved 3 July 2013.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Crawford+collection+at+the+Royal+Observatory+Edinburgh&rft.pub=The+Royal+Observatory%2C+Edinburgh&rft_id=http%3A%2F%2Fwww.roe.ac.uk%2Froe%2Flibrary%2Fcrawford%2Findex.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-101"><a href="#cite_ref-101">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.uu.se/en/news/news-document/?id=469&area=2,3,16&typ=pm&na=&lang=en">"Newton's book back in Uppsala University Library"</a>. Uppsala University. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140512214819/http://www.uu.se/en/news/news-document/?id=469&area=2,3,16&typ=pm&na=&lang=en">Archived</a> from the original on 12 May 2014. Retrieved 10 May 2014.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Newton%27s+book+back+in+Uppsala+University+Library&rft.pub=Uppsala+University&rft_id=http%3A%2F%2Fwww.uu.se%2Fen%2Fnews%2Fnews-document%2F%3Fid%3D469%26area%3D2%2C3%2C16%26typ%3Dpm%26na%3D%26lang%3Den&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-102"><a href="#cite_ref-102">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.huntington.org/webassets/templates/general.aspx?id=16993">"Beautiful Science: Ideas that Changed the World – Astronomy"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20151224133031/http://www.huntington.org/webassets/templates/general.aspx?id=16993">Archived</a> from the original on 24 December 2015. Retrieved 2 January 2016.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Beautiful+Science%3A+Ideas+that+Changed+the+World+%E2%80%93+Astronomy&rft_id=http%3A%2F%2Fwww.huntington.org%2Fwebassets%2Ftemplates%2Fgeneral.aspx%3Fid%3D16993&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-103"><a href="#cite_ref-103">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://fondationbodmer.ch/en/library/the-gems/the-sciences/">"A scientific gem: Isaac Newton (1643–1727)"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160920044424/http://fondationbodmer.ch/en/library/the-gems/the-sciences/">Archived</a> from the original on 20 September 2016. Retrieved 5 July 2016.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=A+scientific+gem%3A+Isaac+Newton+%281643%E2%80%931727%29&rft_id=http%3A%2F%2Ffondationbodmer.ch%2Fen%2Flibrary%2Fthe-gems%2Fthe-sciences%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-104"><a href="#cite_ref-104">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLork2021" class="citation web cs1">Lork, Tim (December 2021). <a rel="nofollow" class="external text" href="https://www.eisenbibliothek.ch/en/research/favorite/favorite22.html">"Chapter 22: Principia"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230220111610/https://www.eisenbibliothek.ch/en/research/favorite/favorite22.html">Archived</a> from the original on 20 February 2023. Retrieved 20 February 2023.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Chapter+22%3A+Principia&rft.date=2021-12&rft.aulast=Lork&rft.aufirst=Tim&rft_id=https%3A%2F%2Fwww.eisenbibliothek.ch%2Fen%2Fresearch%2Ffavorite%2Ffavorite22.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-105"><a href="#cite_ref-105">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://standrewsrarebooks.wordpress.com/2017/07/05/celebrating-330-years-of-isaac-newtons-principia/">"Echoes from the Vault"</a>. Echoes from the Vault. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20171107031416/https://standrewsrarebooks.wordpress.com/2017/07/05/celebrating-330-years-of-isaac-newtons-principia/">Archived</a> from the original on 7 November 2017. Retrieved 6 November 2017.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Echoes+from+the+Vault&rft.atitle=Echoes+from+the+Vault&rft_id=https%3A%2F%2Fstandrewsrarebooks.wordpress.com%2F2017%2F07%2F05%2Fcelebrating-330-years-of-isaac-newtons-principia%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-106"><a href="#cite_ref-106">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://digital.library.sydney.edu.au/nodes/view/7166">"Annotated first edition copy of Newton's Principia"</a>. University of Sydney Library. University of Sydney. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190331214832/https://digital.library.sydney.edu.au/nodes/view/7166">Archived</a> from the original on 31 March 2019. Retrieved 17 April 2019.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=University+of+Sydney+Library&rft.atitle=Annotated+first+edition+copy+of+Newton%27s+Principia&rft_id=https%3A%2F%2Fdigital.library.sydney.edu.au%2Fnodes%2Fview%2F7166&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-107"><a href="#cite_ref-107">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWestrin2012" class="citation news cs1 cs1-prop-foreign-lang-source">Westrin, Stefan (2 September 2012). <a rel="nofollow" class="external text" href="https://www.arbetarbladet.se/artikel/boktjuven-pa-vasa">"Boktjuven på Vasa"</a>. <a href="/wiki/Arbetarbladet" title="Arbetarbladet">Arbetarbladet</a> (in Swedish). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200623140227/https://www.arbetarbladet.se/artikel/boktjuven-pa-vasa">Archived</a> from the original on 23 June 2020. Retrieved 20 June 2020.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Arbetarbladet&rft.atitle=Boktjuven+p%C3%A5+Vasa&rft.date=2012-09-02&rft.aulast=Westrin&rft.aufirst=Stefan&rft_id=https%3A%2F%2Fwww.arbetarbladet.se%2Fartikel%2Fboktjuven-pa-vasa&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-108"><a href="#cite_ref-108">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNewton" class="citation web cs1">Newton, Isaac. <a rel="nofollow" class="external text" href="https://ucl.primo.exlibrisgroup.com/discovery/fulldisplay?&context=L&vid=44UCL_INST:UCL_VU2&search_scope=MyInst_and_CI&tab=Everything&docid=alma990005807450204761">"Philosophiae naturalis principia mathematica"</a>. UCL Explore. Retrieved 5 December 2023.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=UCL+Explore&rft.atitle=Philosophiae+naturalis+principia+mathematica&rft.aulast=Newton&rft.aufirst=Isaac&rft_id=https%3A%2F%2Fucl.primo.exlibrisgroup.com%2Fdiscovery%2Ffulldisplay%3F%26context%3DL%26vid%3D44UCL_INST%3AUCL_VU2%26search_scope%3DMyInst_and_CI%26tab%3DEverything%26docid%3Dalma990005807450204761&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-109"><a href="#cite_ref-109">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRawlinson2016" class="citation news cs1">Rawlinson, Kevin (15 December 2016). <a rel="nofollow" class="external text" href="https://www.theguardian.com/science/2016/dec/15/isaac-newton-masterwork-becomes-most-expensive-science-book-sold">"Isaac Newton masterwork becomes most expensive science book sold"</a>. <a href="/wiki/The_Guardian" title="The Guardian">The Guardian</a>. London. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20161218181510/https://www.theguardian.com/science/2016/dec/15/isaac-newton-masterwork-becomes-most-expensive-science-book-sold">Archived</a> from the original on 18 December 2016. Retrieved 19 December 2016.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Guardian&rft.atitle=Isaac+Newton+masterwork+becomes+most+expensive+science+book+sold&rft.date=2016-12-15&rft.aulast=Rawlinson&rft.aufirst=Kevin&rft_id=https%3A%2F%2Fwww.theguardian.com%2Fscience%2F2016%2Fdec%2F15%2Fisaac-newton-masterwork-becomes-most-expensive-science-book-sold&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-110"><a href="#cite_ref-110">^</a> The Correspondence of Isaac Newton, vol. 4, Cambridge University Press 1967, at p. 519, n. 2. </li> <li id="cite_note-111"><a href="#cite_ref-111">^</a> The Correspondence of Isaac Newton, vol. 4, Cambridge University press 1967, at p. 42. </li> <li id="cite_note-112"><a href="#cite_ref-112">^</a> I Bernard Cohen, Introduction to the Principia, Cambridge 1971. </li> <li id="cite_note-113"><a href="#cite_ref-113">^</a> <a href="/wiki/Richard_S._Westfall" title="Richard S. Westfall">Richard S. Westfall</a>. Never at Rest: A Biography of Isaac Newton. Cambridge U. Press. 1980 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-23143-4" title="Special:BookSources/0-521-23143-4">0-521-23143-4</a>, at p. 699. </li> <li id="cite_note-114"><a href="#cite_ref-114">^</a> The Correspondence of Isaac Newton, vol. 4, Cambridge University Press 1967, at pp. 518–520. </li> <li id="cite_note-115"><a href="#cite_ref-115">^</a> The Correspondence of Isaac Newton, vol. 5, Cambridge University press 1975. Bentley's letter to Newton of October 1709 (at pp. 7–8) describes Cotes' perhaps unenviable position in relation to his master Bentley: "You need not be so shy of giving Mr. Cotes too much trouble: he has more esteem for you, and obligations to you, than to think that trouble too grievous: but however he does it at my Orders, to whom he owes more than that." </li> <li id="cite_note-116"><a href="#cite_ref-116">^</a> Westfall, pp. 712–716. </li> <li id="cite_note-117"><a href="#cite_ref-117">^</a> Westfall, pp. 751–760. </li> <li id="cite_note-118"><a href="#cite_ref-118">^</a> Westfall, p. 750. </li> <li id="cite_note-119"><a href="#cite_ref-119">^</a> Westfall, p. 802. </li> <li id="cite_note-Facsimile-120"><a href="#cite_ref-Facsimile_120-0">^</a> [In Latin] Isaac Newton, Philosophiae naturalis principia mathematica <a rel="nofollow" class="external text" href="https://books.google.com/books?id=WqaGuP1HqE0C&q=Isaac+Newton%27s+Philosophiae+naturalis+principia+mathematica">volume 1 of a facsimile of a reprint (1833) of the 3rd (1726) edition, as annotated in 1740–42 by Thomas LeSeur & François Jacquier, with the assistance of J-L Calandrini</a>. </li> <li id="cite_note-121"><a href="#cite_ref-121">^</a> See "Translating Newton's 'Principia': The Marquise du Châtelet's Revisions and Additions for a French Audience". Author: Judith P. Zinsser. Source: Notes and Records of the Royal Society of London, Vol. 55, No. 2 (May 2001), pp. 227–245. </li> <li id="cite_note-122"><a href="#cite_ref-122">^</a> I Bernard Cohen (1968), "Introduction" (at page i) to (facsimile) reprint of 1729 English translation of Newton's "Principia" (London (1968), Dawsons of Pall Mall). </li> <li id="cite_note-123"><a href="#cite_ref-123">^</a> See pp. 29–37 in <a href="/wiki/I._Bernard_Cohen" title="I. Bernard Cohen">I. Bernard Cohen</a> (1999), "A Guide to Newton's Principia", published as an introduction to Isaac Newton: The Principia, Mathematical principles of natural philosophy, a new translation by I Bernard Cohen and Anne Whitman, University of California Press, 1999. </li> <li id="cite_note-124"><a href="#cite_ref-124">^</a> Isaac Newton: The Principia, Mathematical principles of natural philosophy, a new translation by I. Bernard Cohen and Anne Whitman, preceded by "A Guide to Newton's Principia" by I. Bernard Cohen, University of California Press, 1999, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-520-08816-0" title="Special:BookSources/978-0-520-08816-0">978-0-520-08816-0</a>, <a href="/wiki/Special:BookSources/978-0-520-08817-7" title="Special:BookSources/978-0-520-08817-7">978-0-520-08817-7</a>. </li> <li id="cite_note-125"><a href="#cite_ref-125">^</a> Ian Bruce <a rel="nofollow" class="external free" href="http://www.17centurymaths.com">http://www.17centurymaths.com</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110517094956/http://www.17centurymaths.com/">Archived</a> 17 May 2011 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. </li> <li id="cite_note-126"><a href="#cite_ref-126">^</a> C. R. Leedham-Green, translator and editor, The Mathematical Principles of Natural Philosophy (Cambridge University Press, 2021) <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1107020658" title="Special:BookSources/978-1107020658">978-1107020658</a> </li> <li id="cite_note-127"><a href="#cite_ref-127">^</a> Dana Densmore and William H. Donahue, Newton's Principia: The Central Argument: Translation, Notes, and Expanded Proofs (Green Lion Press; 3rd ed., 2003) <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-888009-23-1" title="Special:BookSources/978-1-888009-23-1">978-1-888009-23-1</a>, <a href="/wiki/Special:BookSources/978-1-888009-23-1" title="Special:BookSources/978-1-888009-23-1">978-1-888009-23-1</a> </li> <li id="cite_note-128"><a href="#cite_ref-128">^</a> Densmore and Donahue, pp. xv–xvi. </li> <li id="cite_note-129"><a href="#cite_ref-129">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGhosh2014" class="citation news cs1">Ghosh, Pallab (17 July 2014). <a rel="nofollow" class="external text" href="https://www.bbc.com/news/science-environment-28329097">"Tim Peake mission name pays tribute to Isaac Newton"</a>. BBC News. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190603105513/https://www.bbc.com/news/science-environment-28329097">Archived</a> from the original on 3 June 2019. Retrieved 21 June 2018.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Tim+Peake+mission+name+pays+tribute+to+Isaac+Newton&rft.date=2014-07-17&rft.aulast=Ghosh&rft.aufirst=Pallab&rft_id=https%3A%2F%2Fwww.bbc.com%2Fnews%2Fscience-environment-28329097&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> <li id="cite_note-130"><a href="#cite_ref-130">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://blogs.nasa.gov/spacestation/2015/06/09/roscosmos-announces-new-soyuzprogress-launch-dates/?linkId=14819770">"Roscosmos Announces New Soyuz/Progress Launch Dates"</a>. NASA. 9 June 2015. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150905213558/http://blogs.nasa.gov/spacestation/2015/06/09/roscosmos-announces-new-soyuzprogress-launch-dates/?linkId=14819770">Archived</a> from the original on 5 September 2015. Retrieved 31 August 2015.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Roscosmos+Announces+New+Soyuz%2FProgress+Launch+Dates&rft.pub=NASA&rft.date=2015-06-09&rft_id=http%3A%2F%2Fblogs.nasa.gov%2Fspacestation%2F2015%2F06%2F09%2Froscosmos-announces-new-soyuzprogress-launch-dates%2F%3FlinkId%3D14819770&rfr_id=info%3Asid%2Fen.wikipedia.org%3APhilosophi%C3%A6+Naturalis+Principia+Mathematica" class="Z3988"> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=26" title="Edit section: Further reading">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li>Miller, Laura, Reading Popular Newtonianism: Print, the Principia, and the Dissemination of Newtonian Science (University of Virginia Press, 2018) <a rel="nofollow" class="external text" href="http://www.h-net.org/reviews/showrev.php?id=53076">online review</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220419230052/https://www.h-net.org/reviews/showrev.php?id=53076">Archived</a> 19 April 2022 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a href="/wiki/Alexandre_Koyr%C3%A9" title="Alexandre Koyré">Alexandre Koyré</a>, Newtonian studies (London: Chapman and Hall, 1965).</li> <li><a href="/wiki/I._Bernard_Cohen" title="I. Bernard Cohen">I. Bernard Cohen</a>, Introduction to Newton's Principia (Harvard University Press, 1971).</li> <li><a href="/wiki/Richard_S._Westfall" title="Richard S. Westfall">Richard S. Westfall</a>, Force in Newton's physics; the science of dynamics in the seventeenth century (New York: American Elsevier, 1971).</li> <li><a href="/wiki/Subrahmanyan_Chandrasekhar" title="Subrahmanyan Chandrasekhar">S. Chandrasekhar</a>, Newton's Principia for the common reader (New York: Oxford University Press, 1995).</li> <li>Guicciardini, N., 2005, "Philosophia Naturalis..." in <a href="/wiki/Ivor_Grattan-Guinness" title="Ivor Grattan-Guinness">Grattan-Guinness, I.</a>, ed., Landmark Writings in Western Mathematics. Elsevier: 59–87.</li> <li>Andrew Janiak, Newton as Philosopher (Cambridge University Press, 2008).</li> <li>François De Gandt, Force and geometry in Newton's Principia trans. Curtis Wilson (Princeton, NJ: Princeton University Press, c1995).</li> <li><a href="/w/index.php?title=Steffen_Ducheyne&action=edit&redlink=1" class="new" title="Steffen Ducheyne (page does not exist)">Steffen Ducheyne</a>, The main Business of Natural Philosophy: Isaac Newton's Natural-Philosophical Methodology (Dordrecht e.a.: Springer, 2012).</li> <li><a href="/wiki/John_Herivel" title="John Herivel">John Herivel</a>, The background to Newton's Principia; a study of Newton's dynamical researches in the years 1664–84 (Oxford, Clarendon Press, 1965).</li> <li><a href="/wiki/Brian_David_Ellis" title="Brian David Ellis">Brian Ellis</a>, "The Origin and Nature of Newton's Laws of Motion" in Beyond the Edge of Certainty, ed. R. G. Colodny. (Pittsburgh: University Pittsburgh Press, 1965), 29–68.</li> <li><a href="/wiki/Edwin_Arthur_Burtt" title="Edwin Arthur Burtt">E.A. Burtt</a>, Metaphysical Foundations of Modern Science (Garden City, NY: Doubleday and Company, 1954).</li> <li><a href="/wiki/Colin_Pask" title="Colin Pask">Colin Pask</a>, Magnificent Principia: Exploring Isaac Newton's Masterpiece (New York: Prometheus Books, 2013).</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=27" title="Edit section: External links">edit</a>]</div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 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<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <a href="https://commons.wikimedia.org/wiki/Category:Philosophiae_Naturalis_Principia_Mathematica" class="extiw" 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srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/57px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/76px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></div> <div class="side-box-text plainlist"><a href="/wiki/Wikisource" title="Wikisource">Wikisource</a> has original text related to this article: <div style="margin-left: 10px;"><a href="https://en.wikisource.org/wiki/Philosophiae_Naturalis_Principia_Mathematica" class="extiw" title="wikisource:Philosophiae Naturalis Principia Mathematica">Philosophiae Naturalis Principia Mathematica</a></div></div></div> </div> First edition (1687) <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20180909104431/http://sites.trin.cam.ac.uk/manuscripts/NQ_16_200/manuscript.php?fullpage=1%2F">Trinity College Library, Cambridge</a> High resolution digitised version of Newton's own copy of the first edition, with annotations.</li> <li><a rel="nofollow" class="external text" href="http://cudl.lib.cam.ac.uk/view/PR-ADV-B-00039-00001/">Cambridge University, Cambridge Digital Library</a> High resolution digitised version of Newton's own copy of the first edition, interleaved with blank pages for his annotations and corrections.</li> <li><a rel="nofollow" class="external text" href="https://ntnu.tind.io/record/115139?ln=no">1687: Newton's Principia, first edition (1687, in Latin)</a>. High-resolution presentation of the <a href="/wiki/Gunnerus_Library" title="Gunnerus Library">Gunnerus Library</a> copy.</li> <li><a rel="nofollow" class="external text" href="https://books.google.com/books?id=XJwx0lnKvOgC&pg=PP2">1687: Newton's Principia, first edition (1687, in Latin)</a>.</li> <li><a rel="nofollow" class="external text" href="http://www.gutenberg.org/ebooks/28233">Project Gutenberg</a>.</li> <li><a rel="nofollow" class="external text" href="http://www.e-rara.ch/zut/wihibe/content/titleinfo/129833">ETH-Bibliothek Zürich</a>. From the library of <a href="/wiki/Gabriel_Cramer" title="Gabriel Cramer">Gabriel Cramer</a>.</li> <li><a rel="nofollow" class="external text" href="http://hdl.loc.gov/loc.rbc/General.20872.1">Philosophiæ Naturalis Principia Mathematica</a> From the Rare Book and Special Collection Division at the <a href="/wiki/Library_of_Congress" title="Library of Congress">Library of Congress</a></li></ul> Second edition (1713) <ul><li><a rel="nofollow" class="external text" href="http://www.e-rara.ch/zut/wihibe/content/titleinfo/338618">ETH-Bibliothek Zürich</a>.</li> <li><a rel="nofollow" class="external text" href="http://www.e-rara.ch/zut/content/titleinfo/555514">ETH-Bibliothek Zürich (pirated Amsterdam reprint of 1723)</a>.</li> <li><a rel="nofollow" class="external text" href="https://cudl.lib.cam.ac.uk/view/PR-ADV-B-00039-00002">Philosophiæ naturalis principia mathematica (Adv.b.39.2)</a>, a 1713 edition with annotations by Newton in the collections of <a href="/wiki/Cambridge_University_Library" title="Cambridge University Library">Cambridge University Library</a> and fully digitised in <a href="/wiki/Cambridge_Digital_Library" title="Cambridge Digital Library">Cambridge Digital Library</a></li></ul> Third edition (1726) <ul><li><a rel="nofollow" class="external text" href="http://www.e-rara.ch/zut/wihibe/content/titleinfo/338026">ETH-Bibliothek Zürich</a>.</li></ul> Later Latin editions <ul><li><a rel="nofollow" class="external text" href="https://books.google.com/books?id=WqaGuP1HqE0C">Principia (in Latin, annotated)</a>. 1833 Glasgow reprint (volume 1) with Books 1 and 2 of the Latin edition annotated by Leseur, Jacquier and Calandrini 1739–42 (described <a href="#Annotated_and_other_editions">above</a>).</li> <li><a rel="nofollow" class="external text" href="https://archive.org/details/sirisaacnewtons01newtgoog">Archive.org (1871 reprint of the 1726 edition)</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="English_translations">English translations</h3>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=29" title="Edit section: English translations">edit</a>]</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/38px-Wikisource-logo.svg.png" decoding="async" width="38" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/57px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/76px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></div> <div class="side-box-text plainlist"><a href="/wiki/Wikisource" title="Wikisource">Wikisource</a> has original text related to this article: <div style="margin-left: 10px;"><a href="https://en.wikisource.org/wiki/The_Mathematical_Principles_of_Natural_Philosophy_(1846)" class="extiw" title="wikisource:The Mathematical Principles of Natural Philosophy (1846)">The Mathematical Principles of Natural Philosophy (American edition, 1846)</a></div></div></div> </div> <ul><li>Andrew Motte, 1729, first English translation of third edition (1726) <ul><li><a href="https://en.wikisource.org/wiki/The_Mathematical_Principles_of_Natural_Philosophy_(1729)" class="extiw" title="s:The Mathematical Principles of Natural Philosophy (1729)">WikiSource, Partial</a></li> <li><a rel="nofollow" class="external text" href="https://books.google.com/books?id=Tm0FAAAAQAAJ&pg=PA1">Google books, vol. 1 with Book 1</a>.</li> <li><a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n20">Internet Archive, vol. 2 with Books 2 and 3</a>. (Book 3 starts at <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n224">p.200</a>.) (Google's metadata wrongly labels this vol. 1).</li> <li><a rel="nofollow" class="external text" href="http://gravitee.tripod.com/toc.htm">Partial HTML</a></li></ul></li> <li>Robert Thorpe 1802 translation</li> <li>N. W. Chittenden, ed., 1846 "American Edition" a partly modernised English version, largely the Motte translation of 1729. <ul><li><a href="https://en.wikisource.org/wiki/The_Mathematical_Principles_of_Natural_Philosophy_(1846)" class="extiw" title="s:The Mathematical Principles of Natural Philosophy (1846)">Wikisource</a></li> <li><a rel="nofollow" class="external text" href="https://archive.org/details/newtonspmathema00newtrich">Archive.org #1</a></li> <li><a rel="nofollow" class="external text" href="https://archive.org/details/100878576">Archive.org #2</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20150907222406/https://ebooks.adelaide.edu.au/n/newton/isaac/mathematical-principles-of-natural-philosophy/complete.html">eBooks@Adelaide</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150907090106/https://ebooks.adelaide.edu.au/n/newton/isaac/system%2Dof%2Dthe%2Dworld/complete.html">eBooks@Adelaide</a></li></ul></li> <li>Percival Frost 1863 translation with interpolations <a rel="nofollow" class="external text" href="https://archive.org/details/newtonsprincipi04newtgoog">Archive.org</a></li> <li>Florian Cajori 1934 modernisation of 1729 Motte and 1802 Thorpe translations</li> <li>Ian Bruce has made a complete <a rel="nofollow" class="external text" href="http://www.17centurymaths.com/contents/newtoncontents.html">translation of the third edition, with notes, on his website</a>.</li> <li>Charles Leedham-Green 2021 has published a complete and heavily annotated translation. Cambridge; Cambridge University Press.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Other_links">Other links</h3>[<a href="/w/index.php?title=Philosophi%C3%A6_Naturalis_Principia_Mathematica&action=edit&section=30" title="Edit section: Other links">edit</a>]</div> <ul><li>David R. 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abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Isaac_Newton" title="Template:Isaac Newton"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Isaac_Newton" title="Template talk:Isaac Newton"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Isaac_Newton" title="Special:EditPage/Template:Isaac Newton"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Sir_Isaac_Newton" style="font-size:114%;margin:0 4em"><a href="/wiki/Isaac_Newton" title="Isaac Newton">Sir Isaac Newton</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Publications</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Method_of_Fluxions" title="Method of Fluxions">Fluxions</a> (1671)</li> <li><a href="/wiki/De_motu_corporum_in_gyrum" title="De motu corporum in gyrum">De Motu</a> (1684)</li> <li><a class="mw-selflink selflink">Principia</a> (1687)</li> <li><a href="/wiki/Opticks" title="Opticks">Opticks</a> (1704)</li> <li><a href="/wiki/The_Queries" class="mw-redirect" title="The Queries">Queries</a> (1704)</li> <li><a href="/wiki/Arithmetica_Universalis" title="Arithmetica Universalis">Arithmetica</a> (1707)</li> <li><a href="/wiki/De_analysi_per_aequationes_numero_terminorum_infinitas" title="De analysi per aequationes numero terminorum infinitas">De Analysi</a> (1711)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Other writings</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quaestiones_quaedam_philosophicae" title="Quaestiones quaedam philosophicae">Quaestiones</a> (1661–1665)</li> <li>"<a href="/wiki/Standing_on_the_shoulders_of_giants" title="Standing on the shoulders of giants">standing on the shoulders of giants</a>" (1675)</li> <li><a href="/wiki/Notes_on_the_Jewish_Temple" title="Notes on the Jewish Temple">Notes on the Jewish Temple</a> (c. 1680)</li> <li>"<a href="/wiki/General_Scholium" title="General Scholium">General Scholium</a>" (1713; "<a href="/wiki/Hypotheses_non_fingo" title="Hypotheses non fingo">hypotheses non fingo</a>" )</li> <li><a href="/wiki/The_Chronology_of_Ancient_Kingdoms_Amended" title="The Chronology of Ancient Kingdoms Amended">Ancient Kingdoms Amended</a> (1728)</li> <li><a href="/wiki/An_Historical_Account_of_Two_Notable_Corruptions_of_Scripture" title="An Historical Account of Two Notable Corruptions of Scripture">Corruptions of Scripture</a> (1754)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Contributions</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Calculus" title="Calculus">Calculus</a> <ul><li><a href="/wiki/Fluxion" title="Fluxion">fluxion</a></li></ul></li> <li><a href="/wiki/Impact_depth" title="Impact depth">Impact depth</a></li> <li><a href="/wiki/Inertia" title="Inertia">Inertia</a></li> <li><a href="/wiki/Newton_disc" title="Newton disc">Newton disc</a></li> <li><a href="/wiki/Newton_polygon" title="Newton polygon">Newton polygon</a> <ul><li><a href="/wiki/Newton%E2%80%93Okounkov_body" title="Newton–Okounkov body">Newton–Okounkov body</a></li></ul></li> <li><a href="/wiki/Newton%27s_reflector" title="Newton's reflector">Newton's reflector</a></li> <li><a href="/wiki/Newtonian_telescope" title="Newtonian telescope">Newtonian telescope</a></li> <li><a href="/wiki/Newton_scale" title="Newton scale">Newton scale</a></li> <li><a href="/wiki/Newton%27s_metal" title="Newton's metal">Newton's metal</a></li> <li><a href="/wiki/Spectrum" title="Spectrum">Spectrum</a></li> <li><a href="/wiki/Structural_coloration" title="Structural coloration">Structural coloration</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;"><a href="/wiki/Newtonianism" title="Newtonianism">Newtonianism</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bucket_argument" title="Bucket argument">Bucket argument</a></li> <li><a href="/wiki/Newton%27s_inequalities" title="Newton's inequalities">Newton's inequalities</a></li> <li><a href="/wiki/Newton%27s_law_of_cooling" title="Newton's law of cooling">Newton's law of cooling</a></li> <li><a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation">Newton's law of universal gravitation</a> <ul><li><a href="/wiki/Post-Newtonian_expansion" title="Post-Newtonian expansion">post-Newtonian expansion</a></li> <li><a href="/wiki/Parameterized_post-Newtonian_formalism" title="Parameterized post-Newtonian formalism">parameterized</a></li> <li><a href="/wiki/Gravitational_constant" title="Gravitational constant">gravitational constant</a></li></ul></li> <li><a href="/wiki/Newton%E2%80%93Cartan_theory" title="Newton–Cartan theory">Newton–Cartan theory</a></li> <li><a href="/wiki/Schr%C3%B6dinger%E2%80%93Newton_equation" title="Schrödinger–Newton equation">Schrödinger–Newton equation</a></li> <li><a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newton's laws of motion</a> <ul><li><a href="/wiki/Kepler%27s_laws_of_planetary_motion" title="Kepler's laws of planetary motion">Kepler's laws</a></li></ul></li> <li><a href="/wiki/Newtonian_dynamics" title="Newtonian dynamics">Newtonian dynamics</a></li> <li><a href="/wiki/Newton%27s_method_in_optimization" title="Newton's method in optimization">Newton's method in optimization</a> <ul><li><a href="/wiki/Problem_of_Apollonius" title="Problem of Apollonius">Apollonius's problem</a></li> <li><a href="/wiki/Truncated_Newton_method" title="Truncated Newton method">truncated Newton method</a></li></ul></li> <li><a href="/wiki/Gauss%E2%80%93Newton_algorithm" title="Gauss–Newton algorithm">Gauss–Newton algorithm</a></li> <li><a href="/wiki/Newton%27s_rings" title="Newton's rings">Newton's rings</a></li> <li><a href="/wiki/Newton%27s_theorem_about_ovals" title="Newton's theorem about ovals">Newton's theorem about ovals</a></li> <li><a href="/wiki/Newton%E2%80%93Pepys_problem" title="Newton–Pepys problem">Newton–Pepys problem</a></li> <li><a href="/wiki/Newtonian_potential" title="Newtonian potential">Newtonian potential</a></li> <li><a href="/wiki/Newtonian_fluid" title="Newtonian fluid">Newtonian fluid</a></li> <li><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a></li> <li><a href="/wiki/Corpuscular_theory_of_light" title="Corpuscular theory of light">Corpuscular theory of light</a></li> <li><a href="/wiki/Leibniz%E2%80%93Newton_calculus_controversy" title="Leibniz–Newton calculus controversy">Leibniz–Newton calculus controversy</a></li> <li><a href="/wiki/Newton%27s_notation" class="mw-redirect" title="Newton's notation">Newton's notation</a></li> <li><a href="/wiki/Rotating_spheres" title="Rotating spheres">Rotating spheres</a></li> <li><a href="/wiki/Newton%27s_cannonball" title="Newton's cannonball">Newton's cannonball</a></li> <li><a href="/wiki/Newton%E2%80%93Cotes_formulas" title="Newton–Cotes formulas">Newton–Cotes formulas</a></li> <li><a href="/wiki/Newton%27s_method" title="Newton's method">Newton's method</a> <ul><li><a href="/wiki/Generalized_Gauss%E2%80%93Newton_method" title="Generalized Gauss–Newton method">generalized Gauss–Newton method</a></li></ul></li> <li><a href="/wiki/Newton_fractal" title="Newton fractal">Newton fractal</a></li> <li><a href="/wiki/Newton%27s_identities" title="Newton's identities">Newton's identities</a></li> <li><a href="/wiki/Newton_polynomial" title="Newton polynomial">Newton polynomial</a></li> <li><a href="/wiki/Newton%27s_theorem_of_revolving_orbits" title="Newton's theorem of revolving orbits">Newton's theorem of revolving orbits</a></li> <li><a href="/wiki/Newton%E2%80%93Euler_equations" title="Newton–Euler equations">Newton–Euler equations</a></li> <li><a href="/wiki/Power_number" title="Power number">Newton number</a> <ul><li><a href="/wiki/Kissing_number" title="Kissing number">kissing number problem</a></li></ul></li> <li><a href="/wiki/Difference_quotient" title="Difference quotient">Newton's quotient</a></li> <li><a href="/wiki/Parallelogram_of_force" title="Parallelogram of force">Parallelogram of force</a></li> <li><a href="/wiki/Puiseux_series" title="Puiseux series">Newton–Puiseux theorem</a></li> <li><a href="/wiki/Absolute_space_and_time#Newton" title="Absolute space and time">Absolute space and time</a></li> <li><a href="/wiki/Luminiferous_aether" title="Luminiferous aether">Luminiferous aether</a></li> <li><a href="/wiki/Finite_difference" title="Finite difference">Newtonian series</a> <ul><li><a href="/wiki/Table_of_Newtonian_series" title="Table of Newtonian series">table</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Personal life</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Woolsthorpe_Manor" title="Woolsthorpe Manor">Woolsthorpe Manor</a> (birthplace)</li> <li><a href="/wiki/Cranbury_Park" title="Cranbury Park">Cranbury Park</a> (home)</li> <li><a href="/wiki/Early_life_of_Isaac_Newton" title="Early life of Isaac Newton">Early life</a></li> <li><a href="/wiki/Later_life_of_Isaac_Newton" title="Later life of Isaac Newton">Later life</a></li> <li><a href="/wiki/Isaac_Newton%27s_apple_tree" title="Isaac Newton's apple tree">Apple tree</a></li> <li><a href="/wiki/Religious_views_of_Isaac_Newton" title="Religious views of Isaac Newton">Religious views</a></li> <li><a href="/wiki/Isaac_Newton%27s_occult_studies" title="Isaac Newton's occult studies">Occult studies</a></li> <li><a href="/wiki/Scientific_Revolution" title="Scientific Revolution">Scientific Revolution</a></li> <li><a href="/wiki/Copernican_Revolution" title="Copernican Revolution">Copernican Revolution</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Relations</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Catherine_Barton" title="Catherine Barton">Catherine Barton</a> (niece)</li> <li><a href="/wiki/John_Conduitt" title="John Conduitt">John Conduitt</a> (nephew-in-law)</li> <li><a href="/wiki/Isaac_Barrow" title="Isaac Barrow">Isaac Barrow</a> (professor)</li> <li><a href="/wiki/William_Clarke_(apothecary)" title="William Clarke (apothecary)">William Clarke</a> (mentor)</li> <li><a href="/wiki/Benjamin_Pulleyn" title="Benjamin Pulleyn">Benjamin Pulleyn</a> (tutor)</li> <li><a href="/wiki/Roger_Cotes" title="Roger Cotes">Roger Cotes</a> (student)</li> <li><a href="/wiki/William_Whiston" title="William Whiston">William Whiston</a> (student)</li> <li><a href="/wiki/John_Keill" title="John Keill">John Keill</a> (disciple)</li> <li><a href="/wiki/William_Stukeley" title="William Stukeley">William Stukeley</a> (friend)</li> <li><a href="/wiki/William_Jones_(mathematician)" title="William Jones (mathematician)">William Jones</a> (friend)</li> <li><a href="/wiki/Abraham_de_Moivre" title="Abraham de Moivre">Abraham de Moivre</a> (friend)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;"><a href="/wiki/Isaac_Newton_in_popular_culture" title="Isaac Newton in popular culture">Depictions</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Newton_(Blake)" title="Newton (Blake)">Newton by Blake</a> (monotype)</li> <li><a href="/wiki/Newton_(Paolozzi)" title="Newton (Paolozzi)">Newton by Paolozzi</a> (sculpture)</li> <li><a href="/wiki/Isaac_Newton_Gargoyle" title="Isaac Newton Gargoyle">Isaac Newton Gargoyle</a></li> <li><a href="/wiki/Astronomers_Monument" title="Astronomers Monument">Astronomers Monument</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;"><a href="/wiki/List_of_things_named_after_Isaac_Newton" title="List of things named after Isaac Newton">Namesake</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Newton_(unit)" title="Newton (unit)">Newton (unit)</a></li> <li><a href="/wiki/Newton%27s_cradle" title="Newton's cradle">Newton's cradle</a></li> <li><a href="/wiki/Isaac_Newton_Institute" title="Isaac Newton Institute">Isaac Newton Institute</a></li> <li><a href="/wiki/Institute_of_Physics_Isaac_Newton_Medal" class="mw-redirect" title="Institute of Physics Isaac Newton Medal">Isaac Newton Medal</a></li> <li><a href="/wiki/Isaac_Newton_Telescope" title="Isaac Newton Telescope">Isaac Newton Telescope</a></li> <li><a href="/wiki/Isaac_Newton_Group_of_Telescopes" title="Isaac Newton Group of Telescopes">Isaac Newton Group of Telescopes</a></li> <li><a href="/wiki/XMM-Newton" title="XMM-Newton">XMM-Newton</a></li> <li><a href="/wiki/Sir_Isaac_Newton_Sixth_Form" title="Sir Isaac Newton Sixth Form">Sir Isaac Newton Sixth Form</a></li> <li><a href="/wiki/Statal_Institute_of_Higher_Education_Isaac_Newton" title="Statal Institute of Higher Education Isaac Newton">Statal Institute of Higher Education Isaac Newton</a></li> <li><a href="/wiki/Newton_International_Fellowship" title="Newton International Fellowship">Newton International Fellowship</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Categories</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"><div class="div-col"> <div class="CategoryTreeTag" data-ct-options="{"mode":20,"hideprefix":20,"showcount":false,"namespaces":false,"notranslations":false}"><div class="CategoryTreeSection"><div class="CategoryTreeItem"><a class="CategoryTreeToggle" data-ct-title="Isaac_Newton" aria-expanded="false"></a> <bdi dir="ltr"><a href="/wiki/Category:Isaac_Newton" title="Category:Isaac Newton">Isaac Newton</a></bdi></div><div class="CategoryTreeChildren" style="display:none"></div></div></div> </div></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q205921#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q205921#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="font-size:114%;margin:0 4em"><a 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