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href="https://azb.wikipedia.org/wiki/%D8%AC%D8%A7%D9%86_%D9%85%DB%8C%DA%86%DB%8C%D9%86" title="جان میچین – South Azerbaijani" lang="azb" hreflang="azb" data-title="جان میچین" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/John_Machin" title="John Machin – Catalan" lang="ca" hreflang="ca" data-title="John Machin" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/John_Machin" title="John Machin – German" lang="de" hreflang="de" data-title="John Machin" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/John_Machin" title="John Machin – Spanish" lang="es" hreflang="es" data-title="John Machin" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AC%D8%A7%D9%86_%D9%85%DB%8C%DA%86%DB%8C%D9%86" title="جان میچین – Persian" lang="fa" hreflang="fa" data-title="جان میچین" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/John_Machin" title="John Machin – French" lang="fr" hreflang="fr" data-title="John Machin" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/John_Machin" title="John Machin – Indonesian" lang="id" hreflang="id" data-title="John Machin" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/John_Machin" title="John Machin – Italian" lang="it" hreflang="it" data-title="John Machin" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/John_Machin" title="John Machin – Haitian Creole" lang="ht" hreflang="ht" data-title="John Machin" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%AC%D9%88%D9%86_%D9%85%D8%A7%D9%83%D9%86" title="جون ماكن – Egyptian Arabic" lang="arz" hreflang="arz" data-title="جون ماكن" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/John_Machin" title="John Machin – Dutch" lang="nl" hreflang="nl" data-title="John Machin" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%B8%E3%83%A7%E3%83%B3%E3%83%BB%E3%83%9E%E3%83%81%E3%83%B3" title="ジョン・マチン – Japanese" lang="ja" hreflang="ja" data-title="ジョン・マチン" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/John_Machin" title="John Machin – Portuguese" lang="pt" hreflang="pt" data-title="John Machin" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/John_Machin" title="John Machin – Romanian" lang="ro" hreflang="ro" data-title="John Machin" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D1%8D%D1%87%D0%B8%D0%BD,_%D0%94%D0%B6%D0%BE%D0%BD" title="Мэчин, Джон – Russian" lang="ru" hreflang="ru" data-title="Мэчин, Джон" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/John_Machin" title="John Machin – Slovenian" lang="sl" hreflang="sl" data-title="John Machin" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/John_Machin" title="John Machin – Finnish" lang="fi" hreflang="fi" data-title="John Machin" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/John_Machin" title="John Machin – Swedish" lang="sv" hreflang="sv" data-title="John Machin" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/John_Machin" title="John Machin – Turkish" lang="tr" hreflang="tr" data-title="John Machin" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%B4%84%E7%BF%B0%C2%B7%E6%A2%85%E6%AC%BD" title="約翰·梅欽 – Chinese" lang="zh" hreflang="zh" data-title="約翰·梅欽" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q726385#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> 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class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">English mathematician (1686–1751)</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output 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 the English nonconformist priest, see <a href="/wiki/John_Machin_(priest)" title="John Machin (priest)">John Machin (priest)</a>.</div> <p class="mw-empty-elt"> </p> <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 biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">John Machin</div></th></tr><tr><td colspan="2" class="infobox-image"><span typeof="mw:File"><a href="/wiki/File:John_machin.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/John_machin.jpg/100px-John_machin.jpg" decoding="async" width="100" height="125" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/John_machin.jpg/150px-John_machin.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cb/John_machin.jpg/200px-John_machin.jpg 2x" data-file-width="261" data-file-height="326" /></a></span><div class="infobox-caption">John Machin</div></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data">c. 1686<sup id="cite_ref-dnb_1-0" class="reference"><a href="#cite_note-dnb-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><br /><div style="display:inline" class="birthplace"><a href="/wiki/England" title="England">England</a></div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">9 June 1751 (aged 70–71)<br /><div style="display:inline" class="deathplace"><a href="/wiki/London" title="London">London</a>, England</div></td></tr><tr><th scope="row" class="infobox-label">Nationality</th><td class="infobox-data category"><a href="/wiki/England" title="England">English</a></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><a href="/wiki/Machin-like_formula" title="Machin-like formula">Machin-like formula</a></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="/wiki/Mathematician" title="Mathematician">Mathematician</a> and <a href="/wiki/Astronomer" title="Astronomer">astronomer</a></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><a href="/wiki/Gresham_College" title="Gresham College">Gresham College</a></td></tr><tr><th scope="row" class="infobox-label">Notable students</th><td class="infobox-data"><a href="/wiki/Brook_Taylor" title="Brook Taylor">Brook Taylor</a></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <p><b>John Machin</b> (bapt. c. 1686 – June 9, 1751)<sup id="cite_ref-dnb_1-1" class="reference"><a href="#cite_note-dnb-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> was a professor of <a href="/wiki/Astronomy" title="Astronomy">astronomy</a> at <a href="/wiki/Gresham_College" title="Gresham College">Gresham College</a>, London. He is best known for developing a quickly <a href="/wiki/Convergent_series" title="Convergent series">converging series</a> for <a href="/wiki/Pi" title="Pi">pi</a> in 1706 and using it to compute pi to 100 decimal places. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=John_Machin&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>John Machin served as secretary of the <a href="/wiki/Royal_Society" title="Royal Society">Royal Society</a> from 1718 to 1747. He was also a member of the commission which decided the <a href="/wiki/Leibniz_and_Newton_calculus_controversy" class="mw-redirect" title="Leibniz and Newton calculus controversy">Calculus priority dispute</a> between <a href="/wiki/Gottfried_Leibniz" class="mw-redirect" title="Gottfried Leibniz">Leibniz</a> and <a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a> in 1712.<sup id="cite_ref-FOOTNOTEClerke1893_2-0" class="reference"><a href="#cite_note-FOOTNOTEClerke1893-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>On 16 May 1713 he succeeded <a href="/w/index.php?title=Alexander_Torriano&action=edit&redlink=1" class="new" title="Alexander Torriano (page does not exist)">Alexander Torriano</a> as professor of astronomy in <a href="/wiki/Gresham_College" title="Gresham College">Gresham College</a>, and held the post until his death, which occurred in London on 9 June 1751. Machin enjoyed a high mathematical reputation. In 1706, Machin computed the value of π with the formula given below to one hundred decimal places. His ingenious quadrature of the circle was later investigated by Charles Hutton. A mass of his manuscripts is preserved by the <a href="/wiki/Royal_Astronomical_Society" title="Royal Astronomical Society">Royal Astronomical Society</a>; and writing to <a href="/wiki/William_Jones_(mathematician)" title="William Jones (mathematician)">William Jones</a> in 1727, he asserted his claim to the parliamentary reward of £10,000 for amending the lunar tables.<sup id="cite_ref-FOOTNOTEClerke1893_2-1" class="reference"><a href="#cite_note-FOOTNOTEClerke1893-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>In 1728, he was listed as one of the subscribers to the <i><a href="/wiki/Cyclopaedia,_or_Universal_Dictionary_of_Arts_and_Sciences" class="mw-redirect" title="Cyclopaedia, or Universal Dictionary of Arts and Sciences">Cyclopaedia</a></i> of <a href="/wiki/Ephraim_Chambers" title="Ephraim Chambers">Ephraim Chambers</a>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Formula">Formula</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=John_Machin&action=edit&section=2" title="Edit section: Formula"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Machin's formula<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> (for which the <a href="/wiki/Machin-like_formula#Derivation" title="Machin-like formula">derivation</a> is straightforward) is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\pi }{4}}=4\arctan {\frac {1}{5}}-\arctan {\frac {1}{239}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>4</mn> </mfrac> </mrow> <mo>=</mo> <mn>4</mn> <mi>arctan</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>5</mn> </mfrac> </mrow> <mo>−</mo> <mi>arctan</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>239</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\pi }{4}}=4\arctan {\frac {1}{5}}-\arctan {\frac {1}{239}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba362ff207097dc35ca873f9a16bcda21a96b278" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:29.685ex; height:5.176ex;" alt="{\displaystyle {\frac {\pi }{4}}=4\arctan {\frac {1}{5}}-\arctan {\frac {1}{239}}}"></span></dd></dl> <p>The benefit of the new formula, a variation on the <a href="/wiki/Leibniz_formula_for_%CF%80" title="Leibniz formula for π">Gregory–Leibniz series</a> (<style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num"><span class="texhtml mvar" style="font-style:italic;">π</span></span><span class="sr-only">/</span><span class="den">4</span></span>⁠</span> = arctan 1), was that it had a significantly increased rate of convergence, which made it a much more practical method of calculation. </p><p>To compute π to 100 decimal places, he combined his formula with the <a href="/wiki/Taylor_series" title="Taylor series">Taylor series</a> expansion for the inverse tangent. (<a href="/wiki/Brook_Taylor" title="Brook Taylor">Brook Taylor</a> was Machin's contemporary in <a href="/wiki/University_of_Cambridge" title="University of Cambridge">Cambridge University</a>.) Machin's formula remained the primary tool of pi-hunters for centuries (well into the computer era). </p><p>Several other <a href="/wiki/Machin-like_formula" title="Machin-like formula">Machin-like formulae</a> are known. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=John_Machin&action=edit&section=3" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Gresham_Professor_of_Astronomy" title="Gresham Professor of Astronomy">Gresham Professor of Astronomy</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=John_Machin&action=edit&section=4" title="Edit section: References"><span>edit</span></a><span 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.sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar nomobile nowraplinks hlist"><tbody><tr><td class="sidebar-pretitle">Part of <a href="/wiki/Category:Pi" title="Category:Pi">a series of articles</a> on the</td></tr><tr><th class="sidebar-title-with-pretitle">mathematical constant <a href="/wiki/Pi" title="Pi"><span class="texhtml mvar" style="font-style:italic;">π</span></a></th></tr><tr><td class="sidebar-content"> <b><span style="white-space:nowrap">3.14159<span style="margin-left:0.25em">26535</span><span style="margin-left:0.25em">89793</span><span style="margin-left:0.25em">23846</span><span style="margin-left:0.25em">26433...</span></span></b></td> </tr><tr><th class="sidebar-heading"> Uses</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Area_of_a_circle" title="Area of a circle">Area of a circle</a></li> <li><a href="/wiki/Circumference" title="Circumference">Circumference</a></li> <li><a href="/wiki/List_of_formulae_involving_%CF%80" title="List of formulae involving π">Use in other formulae</a></li></ul></td> </tr><tr><th class="sidebar-heading"> Properties</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Proof_that_%CF%80_is_irrational" title="Proof that π is irrational">Irrationality</a></li> <li><a href="/wiki/Lindemann%E2%80%93Weierstrass_theorem" title="Lindemann–Weierstrass theorem">Transcendence</a></li></ul></td> </tr><tr><th class="sidebar-heading"> Value</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Proof_that_22/7_exceeds_%CF%80" title="Proof that 22/7 exceeds π">Less than 22/7</a></li> <li><a href="/wiki/Approximations_of_%CF%80" title="Approximations of π">Approximations</a></li> <li><a href="/wiki/Madhava%27s_correction_term" title="Madhava's correction term">Madhava's correction term</a></li> <li><a href="/wiki/Piphilology" title="Piphilology">Memorization</a></li></ul></td> </tr><tr><th class="sidebar-heading"> People</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Method_of_exhaustion#Archimedes" title="Method of exhaustion">Archimedes</a></li> <li><a href="/wiki/Liu_Hui%27s_%CF%80_algorithm" title="Liu Hui's π algorithm">Liu Hui</a></li> <li><a href="/wiki/Zu_Chongzhi" title="Zu Chongzhi">Zu Chongzhi</a></li> <li><a href="/wiki/Aryabhata" title="Aryabhata">Aryabhata</a></li> <li><a href="/wiki/Madhava_of_Sangamagrama" title="Madhava of Sangamagrama">Madhava</a></li> <li><a href="/wiki/Jamsh%C4%ABd_al-K%C4%81sh%C4%AB" class="mw-redirect" title="Jamshīd al-Kāshī">Jamshīd al-Kāshī</a></li> <li><a href="/wiki/Ludolph_van_Ceulen" title="Ludolph van Ceulen">Ludolph van Ceulen</a></li> <li><a href="/wiki/Fran%C3%A7ois_Vi%C3%A8te" title="François Viète">François Viète</a></li> <li><a href="/wiki/Seki_Takakazu#Calculation_of_Pi" title="Seki Takakazu">Seki Takakazu</a></li> <li><a href="/wiki/Takebe_Kenko#Legacy" class="mw-redirect" title="Takebe Kenko"> Takebe Kenko</a></li> <li><a href="/wiki/William_Jones_(mathematician)" title="William Jones (mathematician)">William Jones</a></li> <li><a class="mw-selflink selflink">John Machin</a></li> <li><a href="/wiki/William_Shanks" title="William Shanks">William Shanks</a></li> <li><a href="/wiki/Srinivasa_Ramanujan" title="Srinivasa Ramanujan">Srinivasa Ramanujan</a></li> <li><a href="/wiki/John_Wrench" title="John Wrench">John Wrench</a></li> <li><a href="/wiki/Chudnovsky_brothers" title="Chudnovsky brothers">Chudnovsky brothers</a></li> <li><a href="/wiki/Yasumasa_Kanada" title="Yasumasa Kanada">Yasumasa Kanada</a></li></ul></td> </tr><tr><th class="sidebar-heading"> History</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Chronology_of_computation_of_%CF%80" title="Chronology of computation of π">Chronology</a></li> <li><i><a href="/wiki/A_History_of_Pi" title="A History of Pi">A History of Pi</a></i></li></ul></td> </tr><tr><th class="sidebar-heading"> In culture</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Indiana_pi_bill" title="Indiana pi bill">Indiana pi bill</a></li> <li><a href="/wiki/Pi_Day" title="Pi Day">Pi Day</a></li></ul></td> </tr><tr><th class="sidebar-heading"> Related topics</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Squaring_the_circle" title="Squaring the circle">Squaring the circle</a></li> <li><a href="/wiki/Basel_problem" title="Basel problem">Basel problem</a></li> <li><a href="/wiki/Six_nines_in_pi" title="Six nines in pi">Six nines in <span class="texhtml mvar" style="font-style:italic;">π</span></a></li> <li><a href="/wiki/List_of_topics_related_to_%CF%80" title="List of topics related to π">Other topics related to <span class="texhtml mvar" style="font-style:italic;">π</span></a></li></ul></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output 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template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Pi_box" title="Template talk:Pi box"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Pi_box" title="Special:EditPage/Template:Pi box"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-dnb-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-dnb_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-dnb_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Anita McConnell, ‘Machin, John (bap. 1686?, died 1751)’, Oxford Dictionary of National Biography, Oxford University Press, 2004. Accessed 26 June 2007. <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><a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fref%3Aodnb%2F17533">10.1093/ref:odnb/17533</a></span> </li> <li id="cite_note-FOOTNOTEClerke1893-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEClerke1893_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEClerke1893_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFClerke1893">Clerke 1893</a>.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://digicoll.library.wisc.edu/cgi-bin/HistSciTech/HistSciTech-idx?type=turn&entity=HistSciTech000900240045&isize=M">List of Subscribers to the Cyclopaedia</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20201006091820/http://digicoll.library.wisc.edu/cgi-bin/HistSciTech/HistSciTech-idx?type=turn&entity=HistSciTech000900240045&isize=M">Archived</a> 6 October 2020 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> at library.wisc.edu</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/MachinsFormula.html">"<i>Machin's Formula</i> at MathWorld"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190711181554/http://mathworld.wolfram.com/MachinsFormula.html">Archived</a> from the original on 11 July 2019<span class="reference-accessdate">. Retrieved <span class="nowrap">18 February</span> 2004</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Machin%27s+Formula+at+MathWorld&rft_id=http%3A%2F%2Fmathworld.wolfram.com%2FMachinsFormula.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJohn+Machin" class="Z3988"></span></span> </li> </ol></div> <p><b>Attribution</b> </p> <ul><li><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png" decoding="async" width="12" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/18px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/24px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></span></span> This article incorporates text from a publication now in the <a href="/wiki/Public_domain" title="Public domain">public domain</a>: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFClerke1893" class="citation encyclopaedia cs1">Clerke, Agnes Mary (1893). "<a href="https://en.wikisource.org/wiki/Dictionary_of_National_Biography,_1885-1900/Machin,_John_(d.1751)" class="extiw" title="s:Dictionary of National Biography, 1885-1900/Machin, John (d.1751)">Machin, John (d.1751)</a>". In <a href="/wiki/Sidney_Lee" title="Sidney Lee">Lee, Sidney</a> (ed.). <i><a href="/wiki/Dictionary_of_National_Biography" title="Dictionary of National Biography">Dictionary of National Biography</a></i>. Vol. 35. London: Smith, Elder & Co.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Machin%2C+John+%28d.1751%29&rft.btitle=Dictionary+of+National+Biography&rft.place=London&rft.pub=Smith%2C+Elder+%26+Co&rft.date=1893&rft.aulast=Clerke&rft.aufirst=Agnes+Mary&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJohn+Machin" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=John_Machin&action=edit&section=5" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wikisource-logo.svg" class="mw-file-description" title="Wikisource logo"><img alt="Wikisource logo" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png" decoding="async" width="12" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/18px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/24px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></a></span> Works by or about <a href="https://en.wikisource.org/wiki/Author:John_Machin" class="extiw" title="s:Author:John Machin">John Machin</a> at <a href="/wiki/Wikisource" title="Wikisource">Wikisource</a> </p> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO'ConnorRobertson" class="citation cs2">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" title="Edmund F. Robertson">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Machin.html">"John Machin"</a>, <i><a href="/wiki/MacTutor_History_of_Mathematics_Archive" title="MacTutor History of Mathematics Archive">MacTutor History of Mathematics Archive</a></i>, <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=John+Machin&rft.btitle=MacTutor+History+of+Mathematics+Archive&rft.pub=University+of+St+Andrews&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=https%3A%2F%2Fmathshistory.st-andrews.ac.uk%2FBiographies%2FMachin.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJohn+Machin" class="Z3988"></span></li> <li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" 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href="/wiki/Prince_Augustus_Frederick,_Duke_of_Sussex" title="Prince Augustus Frederick, Duke of Sussex">Duke of Sussex</a> (1813)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related<br />articles</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/History_of_Freemasonry" title="History of Freemasonry">History of Freemasonry</a></li> <li><a href="/wiki/Antient_Grand_Lodge_of_England" title="Antient Grand Lodge of England">Antient Grand Lodge of England</a></li> <li><a href="/wiki/United_Grand_Lodge_of_England" title="United Grand Lodge of England">United Grand Lodge of England</a></li> <li><a href="/wiki/James_Anderson_(Freemason)" title="James Anderson (Freemason)">James Anderson's</a> <i><a href="/wiki/History_of_Freemasonry#Anderson's_''Constitutions''" title="History of Freemasonry">The Constitutions of the Free-Masons</a></i> (1723)</li> 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<li><a href="/wiki/Order_of_the_Bath" title="Order of the Bath">Order of the Bath</a></li> <li><a href="/wiki/Robert_Walpole" title="Robert Walpole">Walpole ministries</a></li> <li><a href="/wiki/Whiggism" title="Whiggism">Whiggism</a> (<a href="/wiki/Kit-Cat_Club" title="Kit-Cat Club">Kit-Cat Club</a>)</li> <li><a href="/wiki/Gormogons" title="Gormogons">Gormogons</a></li> <li><a href="/wiki/Hellfire_Club" title="Hellfire Club">Hellfire Club</a></li> <li><a href="/wiki/Foundling_Hospital" title="Foundling Hospital">Foundling Hospital</a></li> <li><a href="/wiki/Unlawful_Societies_Act_1799" title="Unlawful Societies Act 1799">Unlawful Societies Act 1799</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Members</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/James_Anderson_(Freemason)" title="James Anderson (Freemason)">James Anderson</a></li> <li><a href="/wiki/John_Byrom" title="John Byrom">John Byrom</a></li> <li><a href="/wiki/William_Stukeley" title="William Stukeley">William Stukeley</a></li> <li><a href="/wiki/William_Jones_(mathematician)" title="William Jones (mathematician)">William Jones</a></li> <li><a href="/wiki/Philip_Stanhope,_4th_Earl_of_Chesterfield" title="Philip Stanhope, 4th Earl of Chesterfield">Earl of Chesterfield</a></li> <li><a href="/wiki/Charles_Delafaye" title="Charles Delafaye">Charles Delafaye</a></li> <li><a href="/wiki/George_Carpenter,_2nd_Baron_Carpenter" title="George Carpenter, 2nd Baron Carpenter">Baron Carpenter</a></li> <li><a href="/wiki/William_Billers" title="William Billers">William Billers</a></li> <li><a href="/wiki/Sir_Thomas_Prendergast,_2nd_Baronet" title="Sir Thomas Prendergast, 2nd Baronet">Sir Thomas Prendergast, 2nd Baronet</a></li> <li><a href="/wiki/Brook_Taylor" title="Brook Taylor">Brook Taylor</a></li> <li><a href="/wiki/Martin_Folkes" title="Martin Folkes">Martin Folkes</a></li> <li><a href="/wiki/John_Arbuthnot" title="John Arbuthnot">John Arbuthnot</a></li> <li><a href="/wiki/Charles_Cox_(brewer)" title="Charles Cox (brewer)">Charles Cox</a></li> <li><a href="/wiki/Charles_Cornwallis,_1st_Earl_Cornwallis" title="Charles Cornwallis, 1st Earl Cornwallis">Earl Cornwallis</a></li> <li><a href="/wiki/Richard_Cantillon" title="Richard Cantillon">Richard Cantillon</a></li> <li><a class="mw-selflink selflink">John Machin</a></li> <li><a href="/wiki/William_Rutty" title="William Rutty">William Rutty</a></li> <li><a href="/wiki/James_Vernon_(politician,_born_1646)" title="James Vernon (politician, born 1646)">James Vernon</a></li> <li><a href="/wiki/John_Senex" title="John Senex">John Senex</a></li> <li><a href="/wiki/James_Thornhill" title="James Thornhill">James Thornhill</a></li> <li><a href="/wiki/George_Parker,_2nd_Earl_of_Macclesfield" title="George Parker, 2nd Earl of Macclesfield">Earl of Macclesfield</a></li> <li><a href="/wiki/John_Browne_(chemist)" title="John Browne (chemist)">John Browne</a></li> <li><a href="/wiki/James_Jurin" title="James Jurin">James Jurin</a></li> <li><a href="/wiki/James_Douglas_(physician)" title="James Douglas (physician)">James Douglas</a></li> <li><a href="/wiki/Alexander_Stuart_(scientist)" title="Alexander Stuart (scientist)">Alexander Stuart</a></li> <li><a href="/wiki/Ephraim_Chambers" title="Ephraim Chambers">Ephraim Chambers</a></li> <li><a href="/wiki/Richard_Manningham" title="Richard Manningham">Richard Manningham</a></li> <li><a href="/wiki/Frank_Nicholls" title="Frank Nicholls">Frank Nicholls</a></li> <li><a href="/wiki/Richard_Rawlinson" title="Richard Rawlinson">Richard Rawlinson</a></li> <li><a href="/wiki/Charles_Stanhope_(1673%E2%80%931760)" title="Charles Stanhope (1673–1760)">Charles Stanhope</a></li> <li><a href="/wiki/Lord_James_Cavendish_(MP_for_Derby)" title="Lord James Cavendish (MP for Derby)">Lord James Cavendish</a></li> <li><a href="/wiki/John_Hope,_2nd_Earl_of_Hopetoun" title="John Hope, 2nd Earl of Hopetoun">Earl of Hopetoun</a></li> <li><a href="/wiki/William_Richardson_(antiquary)" title="William Richardson (antiquary)">William Richardson</a></li> <li><a href="/wiki/William_Becket" title="William Becket">William Becket</a></li> <li><a href="/wiki/John_Anstis" title="John Anstis">John Anstis</a></li> <li><a href="/wiki/Peregrine_Bertie,_2nd_Duke_of_Ancaster_and_Kesteven" title="Peregrine Bertie, 2nd Duke of Ancaster and Kesteven">Duke of Ancaster</a></li> <li><a href="/wiki/Charles_Hayes_(mathematician)" title="Charles Hayes (mathematician)">Charles Hayes</a></li> <li><a href="/wiki/Edmund_Prideaux_(artist)" title="Edmund Prideaux (artist)">Edmund Prideaux</a></li> <li><a href="/wiki/George_Shelvocke" title="George Shelvocke">George Shelvocke</a></li> <li><a href="/wiki/John_Woodward_(naturalist)" title="John Woodward (naturalist)">John Woodward</a></li> <li><a href="/wiki/John_Ward_(academic)" title="John Ward (academic)">John Ward</a></li> <li><a href="/wiki/John_Baptist_Grano" title="John Baptist Grano">John Baptist Grano</a></li> <li><a href="/wiki/John_King,_2nd_Baron_King" title="John King, 2nd Baron King">Baron King</a></li> <li><a href="/wiki/Jacob_Christoph_Le_Blon" title="Jacob Christoph Le Blon">Jacques Leblon</a></li> <li><a href="/wiki/Adolphus_Oughton" title="Adolphus Oughton">Adolphus Oughton</a></li> <li><a href="/wiki/Sir_Robert_Rich,_4th_Baronet" title="Sir Robert Rich, 4th Baronet">Sir Robert Rich, 4th Baronet</a></li> <li><a href="/wiki/Richard_Temple,_1st_Viscount_Cobham" title="Richard Temple, 1st Viscount Cobham">Viscount Cobham</a></li> <li><a href="/wiki/Francis_Columbine" title="Francis Columbine">Francis Columbine</a></li> <li><a href="/wiki/Hugh_Warburton" title="Hugh Warburton">Hugh Warburton</a></li> <li><a href="/wiki/Henry_Herbert,_9th_Earl_of_Pembroke" title="Henry Herbert, 9th Earl of Pembroke">Earl of Pembroke</a></li> <li><a href="/wiki/Charles_Townshend,_3rd_Viscount_Townshend" title="Charles Townshend, 3rd Viscount Townshend">Viscount Townshend</a></li> <li><a href="/wiki/Martin_Bladen" title="Martin Bladen">Martin Bladen</a></li> <li><a href="/wiki/James_Waldegrave,_1st_Earl_Waldegrave" title="James Waldegrave, 1st Earl Waldegrave">Earl Waldegrave</a></li> <li><a href="/wiki/Evelyn_Pierrepont,_2nd_Duke_of_Kingston-upon-Hull" title="Evelyn Pierrepont, 2nd Duke of Kingston-upon-Hull">Duke of Kingston</a></li> <li><a href="/wiki/Richard_Boyle,_3rd_Earl_of_Burlington" title="Richard Boyle, 3rd Earl of Burlington">Earl of Burlington</a></li> <li><a href="/wiki/William_Capell,_3rd_Earl_of_Essex" title="William Capell, 3rd Earl of Essex">Earl of Essex</a></li> <li><a href="/wiki/Charles_Douglas,_3rd_Duke_of_Queensberry" title="Charles Douglas, 3rd Duke of Queensberry">Duke of Queensberry</a></li> <li><a href="/wiki/Henry_Scott,_1st_Earl_of_Deloraine" title="Henry Scott, 1st Earl of Deloraine">Earl of Deloraine</a></li> <li><a href="/wiki/Charles_Colyear,_2nd_Earl_of_Portmore" title="Charles Colyear, 2nd Earl of Portmore">Earl of Portmore</a></li> <li><a href="/wiki/Charles_Spencer,_3rd_Duke_of_Marlborough" title="Charles Spencer, 3rd Duke of Marlborough">Duke of Marlborough</a></li> <li><a href="/wiki/Charles_Calvert,_5th_Baron_Baltimore" title="Charles Calvert, 5th Baron Baltimore">Baron Baltimore</a></li> <li><a href="/wiki/James_Murray,_2nd_Duke_of_Atholl" title="James Murray, 2nd Duke of Atholl">Duke of Atholl</a></li> <li><a href="/wiki/William_Kerr,_3rd_Marquess_of_Lothian" title="William Kerr, 3rd Marquess of Lothian">Marquess of Lothian</a></li> <li><a href="/wiki/Alexander_Lindsay,_4th_Earl_of_Balcarres" title="Alexander Lindsay, 4th Earl of Balcarres">Earl of Balcarres</a></li> <li><a href="/wiki/Daniel_Finch,_8th_Earl_of_Winchilsea" title="Daniel Finch, 8th Earl of Winchilsea">Earl of Winchilsea</a></li> <li><a href="/wiki/Sir_Arthur_Acheson,_5th_Baronet" title="Sir Arthur Acheson, 5th Baronet">Sir Arthur Acheson, 5th Baronet</a></li> <li><a href="/w/index.php?title=Sir_Robert_Lawley,_4th_Baronet&action=edit&redlink=1" class="new" title="Sir Robert Lawley, 4th Baronet (page does not exist)">Sir Robert Lawley, 4th Baronet</a></li> <li><a href="/wiki/Alexander_Brodie_(1697%E2%80%931754)" title="Alexander Brodie (1697–1754)">Alexander Brodie</a></li> <li><a href="/wiki/William_Hogarth" title="William Hogarth">William Hogarth</a></li> <li><a href="/wiki/Charles_Labelye" title="Charles Labelye">Charles Labelye</a></li> <li><a href="/wiki/Walter_Calverley-Blackett" class="mw-redirect" title="Walter Calverley-Blackett">Walter Calverley-Blackett</a></li> <li><a href="/wiki/Frederick,_Prince_of_Wales" title="Frederick, Prince of Wales">Frederick, Prince of Wales</a></li> <li><a href="/wiki/Thomas_Wright_(astronomer)" title="Thomas Wright (astronomer)">Thomas Wright</a></li> <li><a href="/wiki/Edward_Gibbon" title="Edward Gibbon">Edward Gibbon</a></li> <li><a href="/wiki/John_Hervey,_2nd_Baron_Hervey" title="John Hervey, 2nd Baron Hervey">Baron Hervey</a></li> <li><a href="/wiki/Thomas_Dunckerley" title="Thomas Dunckerley">Thomas Dunckerley</a></li> <li><a href="/wiki/William_Preston_(Freemason)" title="William Preston (Freemason)">William Preston</a></li> <li><a href="/wiki/Francis_Rawdon-Hastings,_1st_Marquess_of_Hastings" title="Francis Rawdon-Hastings, 1st Marquess of Hastings">Marquess of Hastings</a></li> <li><a href="/wiki/James_Moore_Smythe" title="James Moore Smythe">James Moore Smythe</a></li> <li><a href="/wiki/Robert_Boyle-Walsingham" title="Robert Boyle-Walsingham">Robert Boyle-Walsingham</a></li> <li><a href="/wiki/Sir_Robert_de_Cornwall" title="Sir Robert de Cornwall">Sir Robert de Cornwall</a></li> <li><a href="/wiki/Batty_Langley" title="Batty Langley">Batty Langley</a></li> <li><a href="/wiki/Thomas_Arne" title="Thomas Arne">Thomas Arne</a></li> <li><a href="/wiki/John_Soane" title="John Soane">John Soane</a></li> <li><a href="/wiki/Joseph_Banks" title="Joseph Banks">Joseph Banks</a></li> <li><a href="/wiki/Johan_Zoffany" title="Johan Zoffany">Johan Zoffany</a></li> <li><a href="/wiki/John_Coustos" title="John Coustos">John Coustos</a></li> <li><a href="/wiki/Hip%C3%B3lito_da_Costa" title="Hipólito da Costa">Hipólito da Costa</a></li> <li><a href="/wiki/Meyer_L%C3%B6w_Schomberg" title="Meyer Löw Schomberg">Meyer Löw Schomberg</a></li> <li><a href="/wiki/Joseph_Salvador" title="Joseph Salvador">Joseph Salvador</a></li> <li><a href="/wiki/Sampson_Eardley,_1st_Baron_Eardley" title="Sampson Eardley, 1st Baron Eardley">Sampson Eardley</a></li> <li><a href="/wiki/Moses_Mendez" title="Moses Mendez">Moses Mendez</a></li> <li><a href="/wiki/Meyer_Solomon" title="Meyer Solomon">Meyer Solomon</a></li> <li><a href="/wiki/Moses_Montefiore" title="Moses Montefiore">Moses Montefiore</a></li> <li><a href="/wiki/Nathan_Mayer_Rothschild" title="Nathan Mayer Rothschild">Nathan Mayer Rothschild</a></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Prime_ministers" scope="row" class="navbox-group" style="width:1%">Prime ministers</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Robert_Walpole" title="Robert Walpole">Robert Walpole</a></li> <li><a href="/wiki/Henry_Pelham" title="Henry Pelham">Henry Pelham</a></li> <li><a href="/wiki/Thomas_Pelham-Holles,_1st_Duke_of_Newcastle" title="Thomas Pelham-Holles, 1st Duke of Newcastle">Duke of Newcastle</a></li></ul> </div></td></tr></tbody></table><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"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px 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href="https://isni.org/isni/0000000374388178">ISNI</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/37695659">VIAF</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.worldcat.org/fast/1832036/">FAST</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.oclc.org/worldcat/entity/E39PBJh8Mk4Pw78b9xcFCPWCcP">WorldCat</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/11751733X">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/n82070827">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external 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