Isaac Barrow | English Mathematician & Philosopher

<!doctype html> <html lang="en" class="topic-desktop ui-ie7 ui-ie"> <head prefix="og: https://ogp.me/ns# fb: https://ogp.me/ns/fb#"> <meta charset="utf-8"> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /> <meta name="viewport" content="width=device-width, initial-scale=1.0" /> <link rel="dns-prefetch" href="https://cdn.britannica.com/mendel-resources/3-130"> <link rel="preconnect" href="https://cdn.britannica.com/mendel-resources/3-130"> <link rel="preload" as="script" href="https://www.googletagservices.com/tag/js/gpt.js" /> <link rel="icon" href="/favicon.png" /> <meta name="description" content="Isaac Barrow was an English classical scholar, theologian, and mathematician who was the teacher of Isaac Newton. He developed a method of determining tangents that closely approached the methods of calculus, and he first recognized that what became known as the processes of integration and" /> <meta name="keywords" content="Isaac Barrow, encyclopedia, encyclopeadia, britannica, article" /> <link rel="canonical" href="https://www.britannica.com/biography/Isaac-Barrow" /> <title>Isaac Barrow | English Mathematician & Philosopher | Britannica</title> <script type="text/javascript" data-type="Init Mendel"> window.$UI = {}; window.Constants = {"LICENSE_URL": "/bps/license","DEFAULT_TEST_VERSION": "A","DEFAULT_STATE": "XX","QUIZ_URL": "/quiz","SPOTLIGHT_BROWSE_URL": "/stories/spotlight","CONTENT_TYPE_TEXT": "text/plain;charset=UTF-8","TOPIC_FACTS_DATA_URL": "/facts","QUIZ_BROWSE_IMAGE_QUIZZES": "images","TOPIC_MEDIA_PATH": "/images-videos","USER_PROFILE_URL": "/user","DEBUG_URL": "/debug","ONE_GOOD_FACT_URL": "/one-good-fact","ERROR_404_URL": "/error404","PROCON_CITED_IN_THE_NEWS_URL": "/procon/ProCon-in-the-News","PROCON_URL": "/procon","TOPIC_PAGE_CONTENT_AJAX_URL": "/topic-content/page","INFINITE_SCROLL_PREFIX_URL": "/scroll","TOPIC_TOP_QUESTION_BROWSE_URL": "/questions","CC_USD": "USD","domain": "britannica.com","SURVEY_URL": "/survey","CATEGORY_BROWSE_URL": "/browse","STORY_BROWSE_URL": "/stories","COUNTRY_US": "US","OPEN_MEDIA_OVERLAY_PARAMETER": "/media","NEWSLETTER_SUBSCRIPTION_URL": "/newsletter-subscription","MAINTENANCE_ERROR_URL": "https://maintenance.eb.com","IMARS_EDITOR_ID": "12365882","PROFILE_EB_EDITOR_URL": "/editor","WEB_INF_RESOURCES_PATH": "WEB-INF/resources","AI_ABOUT_PAGE_URL": "/about-britannica-ai","TOPIC_ADDITIONAL_INFO_PATH": "/additional-info","SUDOKU_GAME_URL": "/games/sudoku","CC_INR": "INR","ARTICLE_PRINT_URL": "/print/article","FIRST_EDITION_URL": "/subscriber/firstedition","WW1_PORTAL_URL": "/discover/World-War-I","MENDEL_COOKIE": "__mendel","DEMYSTIFIED_BROWSE_URL": "/stories/demystified","LIST_BROWSE_URL": "/list/browse","PROFILE_EXPERT_URL": "/contributor","ASSEMBLY_IMAGE_URL": "/image/assembly","DAY_IN_HISTORY_URL": "/on-this-day","DEFAULT_CURRENCY": "USD","CONTENT_TYPE_XML": "text/xml;charset=UTF-8","PORTAL_FINANCE_BROWSE_URL_PREFIX": "/money/browse","MONEY_IMARS_CATEGORY": "13000","AJAX_PREFIX_URL": "/ajax","TOPIC_BROWSE_URL": "/topic-browse","MARKETING_CONTENT": "/marketing-content","ENV_RUNTIME": "runtime","GALLERY_URL": "/gallery","topicUrlClassesList": "topic|animal|art|biography|event|place|plant|science|sports|technology|procon","CONTENT_TYPE_HTML": "text/html;charset=UTF-8","ENV_LOCAL": "override","MEDIA_OVERLAY_URL": "/media-overlay","CHATBOT_PAGE_URL": "/chatbot","NEWSLETTER_PAGE_URL": "/newsletters","ENV_DEV": "development","MEDIA_URL": "/media","TOPIC_TOP_QUESTION_URL": "/question","PORTAL_FINANCE_URL_PREFIX": "/money","PODCASTS_URL": "/podcasts","STAND_ALONE_VIDEO_URL": "/video","MORE_ON_THIS_DAY_URL": "/more-on-this-day","TOPIC_QUOTES_URL": "/quotes","SEARCH_PAGE_URL": "/search","PROCON_CLASS": "PROCON","KUSTOM_MENDEL_APPLICATION_ID": "1","TOPIC_CONTENT_AJAX_URL": "/topic-content/topic","ENV_BRANCH": "branch","ERROR_URL": "/error","MAIN_VERSION": "mainVersion","DEFAULT_S3_REGION": "US_EAST_1","TOPIC_COLLECTION_URL": "/summary","LOGINBOX_URL": "/auth/loginbox","ONE_GOOD_FACT_BROWSE_URL": "/one-good-fact/all-good-facts","QUIZ_BROWSE_URL": "/quiz/browse","BIO_BROWSE_URL": "/browse/biographies","LIST_URL": "/list","TIGHTROPE_QUIZ_URL": "/quiz/tightrope","ALPHA_BROWSE_URL": "/sitemap","CONTENT_TYPE_JSON": "application/json","DICTIONARY_URL": "/dictionary","COBRAND_IMAGE_URL": "/image/cobrand","PROCON_IN_THE_NEWS_URL": "/procon/pro-and-con-issues-in-the-news","PROCON_BROWSE_URL": "/procon","QUIZ_BROWSE_VOCAB_QUIZZES": "vocabulary-quizzes","SUBMISSION_URL": "/submission","EB_LOG_OUT": "/auth2/logout","ENV_PRODUCTION": "production","EXPLORE_PORTAL_URL": "/explore","TOPIC_AJAX_URL": "/ajax/topic","TOPIC_SUMMARY_BROWSE_URL": "/summaries","WTFACT_BROWSE_URL": "/stories/wtfact","VIDEO_CHANNEL_URL": "/videos","GALLERY_BROWSE_URL": "/gallery/browse","CACHE_URL": "/cache","PROCON_ABOUT_URL": "/procon/About-ProCon","COMPANION_BROWSE_URL": "/stories/companion","MEDIA_FOLDER": "/eb-media","SHOW_ALL_CONTRIBUTORS": "/additional-info#contributors","BRITANNICA_EDITORS_ID": "4419","ENV_CACHE_DISABLED": "mendelCache","CALCULATORS_BROWSE_URL": "/calculators","STORY_URL": "/story","DEFAULT_COUNTRY": "US","NAVBAR_URL": "/ajax/navbar","EB_LOGIN_URL": "/auth/eb-login","NEW_ARTICLES_URL": "/new-articles",}; window.CDN = "https://cdn.britannica.com"; window.CAM_LOGIN_URL = "https://cam.britannica.com"; window.CAM_SIGN_UP_URL = "https://cam.britannica.com/registration" window.Mendel = { "config" : { "domain": "britannica.com", "page": "Topic", "videoPlayerId": "UyMCoK2v", "sharedUrl": "https://www.britannica.com/biography/Isaac-Barrow", "amuselabsUrl": "https://cdn3.amuselabs.com", "resourcesPrefixUrl": "https://cdn.britannica.com/mendel-resources/3-130/[url]?v=3.130.14", "date": 20241124, "userInfo": { "type": "ANONYMOUS" ,"currency": "AUUS" ,"country": "SG" ,"state": "XX" ,"timezone": "Asia/Singapore" ,"bcomId": "4745120146993424121" ,"hasAds": true ,"testVersion": "A" ,"adsTestVersion": "A" ,"consumerId": "" ,"instId": "" ,"consumerUserName": "" ,"instUserName": "" ,"cognito": null }, "tvs":{ "r":[25,25,25,25], "a": [25,25,25,25]}, "isLoggedInAsUser": false, "isPhone": false, "isDesktop": true, "logoutUrl": "/auth2/logout", "selfServiceUrl": "https://myaccount.britannica.com", "cdnUrl": "https://cdn.britannica.com", "chatbotApi": "https://www.britannica.com/chat-api", "fetchOffset": 800, "mendelCookieName": "__mendel", "mendelCookie": {"surveyShown":false,"visitedTopicId":54184,"currentDate":20241124}, "autocompleteToSearchPage": false,"topicUrl": "https://www.britannica.com/biography/Isaac-Barrow" ,"freeTopicReason": "PERMANENT_FREE_TOPIC" ,"topicId": 54184 ,"template": "DESKTOP" ,"type": "CORE" ,"hasToc": false ,"chatbotApi": "https://www.britannica.com/chat-api" ,"showPreview": false ,"infiniteScrollList": [{"p":1,"t":54184},{"p":1,"t":89161},{"p":5,"t":413189},{"p":10,"t":229851},{"p":2,"t":430511},{"p":1,"t":511584},{"p":3,"t":194901},{"p":3,"t":528960},{"p":27,"t":369194},{"p":1,"t":90655}] ,"sequence": 1 ,"topics": {} }, "GA": {"leg":"A","adLeg":"A","userType":"ANONYMOUS","pageType":"Topic","articleTemplateType":"BIO_MEDIUM","gisted":false,"pageNumber":1,"hasSummarizeButton":false,"hasAskButton":false} }; </script> <meta property="fb:app_id" content="1887621861548296"/ <meta name="twitter:card" content="summary_large_image" /> <meta name="twitter:site" content="@britannica" /> <meta name="twitter:image" content="https://cdn.britannica.com/87/29787-004-A22485F7/Isaac-Barrow-pencil-drawing-David-Loggan-National.jpg" /> <meta name="twitter:description" content="Isaac Barrow was an English classical scholar, theologian, and mathematician who was the teacher of Isaac Newton. He developed a method of determining tangents that closely approached the methods of calculus, and he first recognized that what became known as the processes of integration and"/> <meta property="og:type" content="ARTICLE"/> <meta property="og:title" content="Isaac Barrow | English Mathematician & Philosopher | Britannica"/> <meta property="og:description" content="Isaac Barrow was an English classical scholar, theologian, and mathematician who was the teacher of Isaac Newton. He developed a method of determining tangents that closely approached the methods of calculus, and he first recognized that what became known as the processes of integration and"/> <meta property="og:site_name" content="Encyclopedia Britannica" /> <meta property="og:url" content="https://www.britannica.com/biography/Isaac-Barrow"/> <meta property="og:image" content="https://cdn.britannica.com/87/29787-004-A22485F7/Isaac-Barrow-pencil-drawing-David-Loggan-National.jpg" /> <meta property="og:image:type" content="image/jpeg" /> <script type="text/javascript" data-type="init opengraph"> Mendel.openGraph = {"type":"ARTICLE","title":"Isaac Barrow | English Mathematician & Philosopher","description":"Isaac Barrow was an English classical scholar, theologian, and mathematician who was the teacher of Isaac Newton. He developed a method of determining tangents that closely approached the methods of calculus, and he first recognized that what became known as the processes of integration and","imageUrl":"https://cdn.britannica.com/87/29787-004-A22485F7/Isaac-Barrow-pencil-drawing-David-Loggan-National.jpg","imageType":"image/jpeg","pageUrl":"https://www.britannica.com/biography/Isaac-Barrow"}</script> <link rel="preconnect" href="https://fonts.googleapis.com/"> <link rel="dns-prefetch" href="https://fonts.googleapis.com/" > <link rel="stylesheet" href="https://fonts.googleapis.com/icon?family=Material+Icons"> <link href="https://cdn.britannica.com/mendel-resources/3-130/dist/vendor-bundle.css?v=3.130.14" rel="stylesheet" /> <link href="https://cdn.britannica.com/mendel-resources/3-130/dist/mendel-css.css?v=3.130.14" rel="stylesheet" /> <link href="https://cdn.britannica.com/mendel-resources/3-130/dist/topic-page.css?v=3.130.14" rel="stylesheet" /> <script type="text/javascript"> if (self !== top) { top.location = self.location; } // if ('scrollRestoration' in history) { history.scrollRestoration = 'manual'; } </script> <script src="https://cdn.britannica.com/mendel-resources/3-130/js/at.js?v=3.130.14" async ></script> <script> dataLayer = []; </script> <script type="text/javascript">(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= '//www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); })(window,document,'script','dataLayer','GTM-5W6NC8'); </script> <meta name="last-modified" content="2024-09-27" /> <script type="application/ld+json"> {"headline":"Isaac Barrow | English Mathematician & Philosopher","image":{"url":"https://cdn.britannica.com/87/29787-004-A22485F7/Isaac-Barrow-pencil-drawing-David-Loggan-National.jpg","@type":"ImageObject"},"author":[{"name":"Mordechai Feingold","url":"https://www.britannica.com/contributor/Mordechai-Feingold/4479","@type":"Person"}],"keywords":"Isaac Barrow","wordcount":680,"url":"https://www.britannica.com/biography/Isaac-Barrow","datePublished":"1998-07-20T00:00:00Z","dateModified":"2024-09-27T00:00:00Z","description":"Isaac Barrow was an English classical scholar, theologian, and mathematician who was the teacher of Isaac Newton. He developed a method of determining tangents that closely approached the methods of calculus, and he first recognized that what became known as the processes of integration and","publisher":{"name":"Encyclopedia Britannica","@type":"Organization","logo":{"url":"https://corporate.britannica.com/wp-content/themes/eb-corporate/_img/logo.png","@type":"ImageObject"}},"@context":"https://schema.org","@type":"article"} </script></head> <body data-leg="A" class="new-topic topic-desktop first-page-true user-ANONYMOUS user-ads md-desktop leg-ab-ie">  <script>Mendel.config.adProvider='ay';</script> <script async src="https://securepubads.g.doubleclick.net/tag/js/gpt.js"></script> <script> window.googletag = window.googletag || {cmd: []}; googletag.cmd.push(function() { googletag.defineSlot('/15510053/CMP_1x1', [1, 1], 'div-gpt-ad-1709766812090-0').addService(googletag.pubads()); googletag.pubads().enableSingleRequest(); googletag.enableServices(); }); </script> <script async defer src="https://launchpad-wrapper.privacymanager.io/0ccc6fe8-1870-4ad8-b47b-6d029ac116fc/launchpad-liveramp.js"></script> <script async src="https://JRyhoywLYXNLYMAhs.ay.delivery/manager/JRyhoywLYXNLYMAhs" type="text/javascript" referrerpolicy="no-referrer-when-downgrade" ></script><div class="ie-warning d-flex align-items-center align-self-center justify-content-center site-alert bg-orange"> <div> You are using an <strong>outdated</strong> browser. Please <a class="text-white text-underscore" href="https://browsehappy.com/">upgrade your browser</a> to improve your experience and security. </div> </div> <script id="json-navbar-info" type="application/json"> {"topSectionLinks":[{"title":"Ask the Chatbot","url":"/chatbot","navbarId":"CHATBOT"},{"title":"Games & Quizzes","url":"/quiz/browse","navbarId":"QUIZZES"},{"title":"ProCon","url":"/procon","navbarId":"PROCON"},{"title":"History & Society","url":"/History-Society","navbarId":"HISTORY"},{"title":"Science & Tech","url":"/Science-Tech","navbarId":"SCIENCE"},{"title":"Biographies","url":"/Biographies","navbarId":"BIOS"},{"title":"Animals & Nature","url":"/Animals-Nature","navbarId":"ANIMALS"},{"title":"Geography & Travel","url":"/Geography-Travel","selected":true,"navbarId":"GEOGRAPHY"},{"title":"Arts & Culture","url":"/Arts-Culture","navbarId":"ART"},{"title":"Money","url":"/money","navbarId":"MONEY"},{"title":"Videos","url":"/videos","navbarId":"VIDEOS"}],"selectedSuperCategory":{"id":4,"title":"Geography & Travel","url":"Geography-Travel","description":"Explore geography and travel; geographic regions; historical places; people of the world; countries, states, provinces, cities, and towns; languages; deserts, islands, mountains, plateaus; lakes, oceans, seas, rivers; national parks, tourist attractions","keywords":"geographic regions; historical places; people of the world; countries, states, provinces, cities, and towns; languages; deserts, islands, mountains, plateaus; lakes, oceans, seas, rivers; national parks, tourist attractions ","classId":"GEOGRAPHY","sortOrder":5},"selectedNavbarLink":{"title":"Geography & Travel","url":"/Geography-Travel","selected":true,"navbarId":"GEOGRAPHY"}} </script> <script id="json-hamburger-menu" type="application/json"> {"britannicaMenu1":[{"title":"Home","url":"/"},{"title":"ProCon","url":"/procon"},{"title":"History & Society","url":"/History-Society"},{"title":"Science & Tech","url":"/Science-Tech"},{"title":"Biographies","url":"/Biographies"},{"title":"Animals & Nature","url":"/Animals-Nature"},{"title":"Geography & Travel","url":"/Geography-Travel"},{"title":"Arts & Culture","url":"/Arts-Culture"},{"title":"Money","url":"/money"}],"britannicaMenu2":[{"title":"Games & Quizzes","url":"/quiz/browse"},{"title":"Videos","url":"/videos"},{"title":"On This Day","url":"/on-this-day"},{"title":"One Good Fact","url":"/one-good-fact"},{"title":"Dictionary","url":"/dictionary"},{"title":"New Articles","url":"/new-articles"}],"browseByCategory":[{"title":{"id":5,"title":"History & Society","url":"/History-Society"},"links":[{"title":"Lifestyles & Social Issues","url":"/browse/Lifestyles-Social-Issues"},{"title":"Philosophy & Religion","url":"/browse/Philosophy-Religion"},{"title":"Politics, Law & Government","url":"/browse/Politics-Law-Government"},{"title":"World History","url":"/browse/World-History"}]},{"title":{"id":6,"title":"Science & Tech","url":"/Science-Tech"},"links":[{"title":"Health & Medicine","url":"/browse/Health-Medicine"},{"title":"Science","url":"/browse/Science"},{"title":"Technology","url":"/browse/Technology"}]},{"title":{"id":3,"title":"Biographies","url":"/Biographies"},"links":[{"title":"Browse Biographies","url":"/browse/biographies"}]},{"title":{"id":1,"title":"Animals & Nature","url":"/Animals-Nature"},"links":[{"title":"Birds, Reptiles & Other Vertebrates","url":"/browse/Birds-Reptiles-Vertebrates"},{"title":"Bugs, Mollusks & Other Invertebrates","url":"/browse/Bugs-Mollusks-Invertebrates"},{"title":"Environment","url":"/browse/Environment"},{"title":"Fossils & Geologic Time","url":"/browse/Fossil-Geologic-Time"},{"title":"Mammals","url":"/browse/Mammals"},{"title":"Plants","url":"/browse/Plants"}]},{"title":{"id":4,"title":"Geography & Travel","url":"/Geography-Travel"},"links":[{"title":"Geography & Travel","url":"/browse/Geography-Travel"}]},{"title":{"id":2,"title":"Arts & Culture","url":"/Arts-Culture"},"links":[{"title":"Entertainment & Pop Culture","url":"/browse/Entertainment-Pop-Culture"},{"title":"Literature","url":"/browse/Literature"},{"title":"Sports & Recreation","url":"/browse/Sports-Recreation"},{"title":"Visual Arts","url":"/browse/Visual-Arts"}]}],"browseByFeature":[{"title":"Companions","url":"/stories/companion"},{"title":"Demystified","url":"/stories/demystified"},{"title":"Image Galleries","url":"/gallery/browse"},{"title":"Lists","url":"/list/browse"},{"title":"Podcasts","url":"/podcasts"},{"title":"Spotlight","url":"/stories/spotlight"},{"title":"Summaries","url":"/summary"},{"title":"The Forum","url":"/stories/the-forum"},{"title":"Top Questions","url":"/question"},{"title":"#WTFact","url":"/stories/wtfact"}],"moreFromBritannica":[{"title":"Britannica Kids","url":"https://kids.britannica.com/","newTab":true}],"menuType":"DEFAULT"} </script> <header id="header" class="bg-navy-dark"> <div class="global-nav-top-bar"> <div class="grid gx-0 h-100 justify-content-between align-items-center container-lg mx-auto p-0 position-relative"> <div class="d-flex align-items-center"> <button class="d-flex align-items-center justify-self-start js-toggle js-toggle-hamburger btn btn-link link-white btn-sm rounded-0 p-10"> <div class="hamburger-tooltip"> <em class="material-icons d-inline-block font-24" id="nav-toggle" data-icon="menu"></em> </div> <em class="material-icons d-inline-block font-24 global-nav-search-icon" id="nav-search-icon" data-icon="search" ></em> </button> <a href="/" class="d-flex align-items-center justify-content-center ml-10"> <img loading="lazy" src="https://cdn.britannica.com/mendel/eb-logo/MendelNewThistleLogo.png" alt="Encyclopedia Britannica" class="global-nav-logo global-nav-logo-left" /> </a> <div class="global-nav-top-search-bar global-nav-top-search-container global-nav-search-container" id="global-nav-top-search-bar"> <form method="get" action="/search" id="global-nav-search" class="md-search-form m-0 global-nav-search-bar-small"> <div class="search-box position-relative col-100"> <label class="sr-only" for="global-nav-search-query">Search Britannica</label> <input name="query" id="global-nav-search-query" placeholder="Search Britannica..." class="form-control form-control-lg rounded-lg font-16 search-query pl-20 pr-70 shadow-sm" maxlength="200" autocomplete="off" aria-label="Search Britannica" /> <button class="search-reset-btn btn btn-link px-10 position-absolute top-0 h-100 d-none" type="reset"> <em class="material-icons" data-icon="close"></em> </button> <button class="search-submit btn btn-link text-blue px-10 position-absolute top-0 right-0 h-100" type="submit" disabled> <span class="sr-only">Click here to search</span> <em class="material-icons search-icon" data-icon="search"></em> </button> </div> </form> </div> </div> <a href="/" class="d-flex align-items-center justify-content-center"> <img loading="lazy" src="https://cdn.britannica.com/mendel/eb-logo/MendelNewThistleLogo.png" alt="Encyclopedia Britannica" class="global-nav-center global-nav-logo non-homepage-logo" /> </a> <form method="get" action="/search" id="global-nav-search" class="md-search-form m-0 global-nav-search-bar-small global-nav-center search global-nav-center-search-container"> <div class="search-box position-relative col-100"> <label class="sr-only" for="global-nav-search-query">Search Britannica</label> <input name="query" id="global-nav-search-query" placeholder="Search Britannica..." class="form-control form-control-lg rounded-lg font-16 search-query pl-20 pr-70 shadow-sm" maxlength="200" autocomplete="off" aria-label="Search Britannica" /> <button class="search-reset-btn btn btn-link px-10 position-absolute top-0 h-100 d-none" type="reset"> <em class="material-icons" data-icon="close"></em> </button> <button class="search-submit btn btn-link text-blue px-10 position-absolute top-0 right-0 h-100" type="submit" disabled> <span class="sr-only">Click here to search</span> <em class="material-icons search-icon" data-icon="search"></em> </button> </div> </form> <div class="col-35 col-sm-auto text-right order-3 mr-lg-15 align-items-center d-flex justify-content-end"> <div class="d-none d-md-inline-block"> <SPAN class="marketing-HEADER_SUBSCRIPTION_DESKTOP2 marketing-content" data-marketing-id="HEADER_SUBSCRIPTION_DESKTOP2"><a href="https://subscription.britannica.com/subscribe?partnerCode=BP_Black_Friday_AUUS" class="subscribe-link btn btn-sm btn-outline-white-orange py-5 mr-10" target="_blank" rel="noopener"> Subscribe </a></SPAN></div> <div class="d-inline-block d-md-none mr-5 mr-sm-10"> <SPAN class="marketing-HEADER_SUBSCRIPTION_MOBILE marketing-content" data-marketing-id="HEADER_SUBSCRIPTION_MOBILE"><a href="https://subscription.britannica.com/subscribe?partnerCode=BP_Black_Friday_AUUS" class="subscribe-link btn btn-xs btn-orange-dark p-5" target="_blank" rel="noopener"> Subscribe </a></SPAN></div> <button class="js-toggle-user-dropdown js-toggle btn btn-sm btn-link link-white rounded-0 px-md-15 pl-5 pr-5"> <span class="d-none d-md-inline-block mr-5">Login</span> <em class="material-icons d-inline-block d-md-none font-16 font-sm-20" data-icon="account_circle"></em> <div class="d-none dropdown-menu-subscription-link">https://subscription.britannica.com/subscribe?partnerCode=BP_Black_Friday_AUUS</div> <em class="material-icons inactive-icon d-inline-block font-18" data-icon="keyboard_arrow_down"></em> <em class="material-icons active-icon d-inline-block font-18" data-icon="keyboard_arrow_up"></em> </button> </div> </div> </div> <div class="d-none hamburger-menu-subscription-link"><DIV class="marketing-HAMBURGER_MENU_CTA marketing-content" data-marketing-id="HAMBURGER_MENU_CTA"><a href="https://premium.britannica.com/premium-membership/?utm_source=premium&utm_medium=hamburger-menu&utm_campaign=black-friday-2024" class="subscribe-link btn btn-sm btn-orange py-5" target="_blank"> Subscribe <span class="d-none d-md-inline"> Now</span> </a></DIV></div> <div id="global-nav-react"> <div class="d-none"> <ul> <li><a href="/">Home</a></li> <li><a href="/procon">ProCon</a></li> <li><a href="/History-Society">History & Society</a></li> <li><a href="/Science-Tech">Science & Tech</a></li> <li><a href="/Biographies">Biographies</a></li> <li><a href="/Animals-Nature">Animals & Nature</a></li> <li><a href="/Geography-Travel">Geography & Travel</a></li> <li><a href="/Arts-Culture">Arts & Culture</a></li> <li><a href="/money">Money</a></li> </ul> <ul> <li><a href="/quiz/browse">Games & Quizzes</a></li> <li><a href="/videos">Videos</a></li> <li><a href="/on-this-day">On This Day</a></li> <li><a href="/one-good-fact">One Good Fact</a></li> <li><a href="/dictionary">Dictionary</a></li> <li><a href="/new-articles">New Articles</a></li> </ul> <a href="/History-Society">History & Society</a> <ul> <li><a href="/browse/Lifestyles-Social-Issues">Lifestyles & Social Issues</a></li> <li><a href="/browse/Philosophy-Religion">Philosophy & Religion</a></li> <li><a href="/browse/Politics-Law-Government">Politics, Law & Government</a></li> <li><a href="/browse/World-History">World History</a></li> </ul> <a href="/Science-Tech">Science & Tech</a> <ul> <li><a href="/browse/Health-Medicine">Health & Medicine</a></li> <li><a href="/browse/Science">Science</a></li> <li><a href="/browse/Technology">Technology</a></li> </ul> <a href="/Biographies">Biographies</a> <ul> <li><a href="/browse/biographies">Browse Biographies</a></li> </ul> <a href="/Animals-Nature">Animals & Nature</a> <ul> <li><a href="/browse/Birds-Reptiles-Vertebrates">Birds, Reptiles & Other Vertebrates</a></li> <li><a href="/browse/Bugs-Mollusks-Invertebrates">Bugs, Mollusks & Other Invertebrates</a></li> <li><a href="/browse/Environment">Environment</a></li> <li><a href="/browse/Fossil-Geologic-Time">Fossils & Geologic Time</a></li> <li><a href="/browse/Mammals">Mammals</a></li> <li><a href="/browse/Plants">Plants</a></li> </ul> <a href="/Geography-Travel">Geography & Travel</a> <ul> <li><a href="/browse/Geography-Travel">Geography & Travel</a></li> </ul> <a href="/Arts-Culture">Arts & Culture</a> <ul> <li><a href="/browse/Entertainment-Pop-Culture">Entertainment & Pop Culture</a></li> <li><a href="/browse/Literature">Literature</a></li> <li><a href="/browse/Sports-Recreation">Sports & Recreation</a></li> <li><a href="/browse/Visual-Arts">Visual Arts</a></li> </ul> <ul> <li><a href="/stories/companion">Companions</a></li> <li><a href="/stories/demystified">Demystified</a></li> <li><a href="/gallery/browse">Image Galleries</a></li> <li><a href="/list/browse">Lists</a></li> <li><a href="/podcasts">Podcasts</a></li> <li><a href="/stories/spotlight">Spotlight</a></li> <li><a href="/summary">Summaries</a></li> <li><a href="/stories/the-forum">The Forum</a></li> <li><a href="/question">Top Questions</a></li> <li><a href="/stories/wtfact">#WTFact</a></li> </ul> <ul> <li><a href="https://kids.britannica.com/">Britannica Kids</a></li> </ul> </div> </div> </header> <div class="bg-navy-dark"> <div class="container-lg p-0 d-flex justify-content-center global-nav-categories-bar overflow-hidden"> <div class="slider js-slider position-relative d-inline-flex align-items-center mw-100 global-nav-slider category-snap-slider"> <div class="slider-container js-slider-container overflow-hidden d-flex font-14 overflow-hidden text-nowrap mx-5"> <a class="nav-bar-category mx-5 category-link-CHATBOT " href="/chatbot">Ask the Chatbot</a> <a class="nav-bar-category mx-5 category-link-QUIZZES " href="/quiz/browse">Games & Quizzes</a> <a class="nav-bar-category mx-5 category-link-PROCON " href="/procon">ProCon</a> <a class="nav-bar-category mx-5 category-link-HISTORY " href="/History-Society">History & Society</a> <a class="nav-bar-category mx-5 category-link-SCIENCE " href="/Science-Tech">Science & Tech</a> <a class="nav-bar-category mx-5 category-link-BIOS " href="/Biographies">Biographies</a> <a class="nav-bar-category mx-5 category-link-ANIMALS " href="/Animals-Nature">Animals & Nature</a> <a class="nav-bar-category mx-5 category-link-GEOGRAPHY selected selected" href="/Geography-Travel">Geography & Travel</a> <a class="nav-bar-category mx-5 category-link-ART " href="/Arts-Culture">Arts & Culture</a> <a class="nav-bar-category mx-5 category-link-MONEY " href="/money">Money</a> <a class="nav-bar-category mx-5 category-link-VIDEOS " href="/videos">Videos</a> </div> <button disabled class="prev-button js-prev-button position-absolute btn btn-circle shadow btn-blue " aria-label="Previous"> <span class="material-icons md-24" data-icon="keyboard_arrow_left"></span> </button> <button disabled class="next-button js-next-button position-absolute btn btn-circle shadow btn-blue " aria-label="Next"> <span class="material-icons md-24" data-icon="keyboard_arrow_right"></span> </button> </div> </div> </div> <main> <div class="md-page-wrapper"> <div id="content" class="md-content"> <div class="md-article-container template-desktop"> <div class="infinite-scroll-container article last"> <article class="article-content container-lg qa-content px-0 pt-0 pb-40 py-lg-20 content " data-topic-id="54184"> <div class="grid gx-0"> <div class="col-auto"> <div class="topic-left-rail md-article-drawer position-relative d-flex border-right-sm border-left-sm open"> <div class="drawer d-flex flex-column open"> <div class="left-rail-section-content"> <div class="topic-left-rail-header text-truncate bg-gray-50 position-relative text-right d-flex align-items-center"> <div class="tlr-title px-20 py-15 text-left"> <em class="material-icons text-gray-400 d-lg-none" data-icon="toc"></em> <a class="font-serif font-weight-bold text-black link-blue" href="https://www.britannica.com/biography/Isaac-Barrow">Isaac Barrow</a> </div> <button aria-label="Close" class="js-sections-close-button btn-link btn-sm btn d-lg-none position-absolute top-0 p-10 right-0" > <em class="material-icons font-26" data-icon="close"></em> </button> </div> <div class="section-content pl-10 pr-20 pl-sm-50 pr-sm-60 pl-lg-5 pr-lg-10 pt-10 pt-lg-0 bg-gray-50 clear-catfish-ad"> <div class="toc mb-20"> <div class="font-serif font-14 font-weight-bold mx-15 mb-15 mt-20"> Table of Contents </div> <span class="toc-extra-link selected link-gray-900 mt-15"> Introduction </span> <a class="toc-extra-link link-gray-900" href="https://www.britannica.com/biography/Isaac-Barrow/additional-info">References & Edit History</a> <a class="toc-extra-link link-gray-900" href="/facts/Isaac-Barrow">Quick Facts & Related Topics</a> </div> <div class="tlr-media-slider pb-10 mb-30"> <a class="section-header link-gray-900 font-serif font-14 font-weight-bold mb-10 mx-10" href="https://www.britannica.com/biography/Isaac-Barrow/images-videos">Images</a> <div class="slider js-slider position-relative d-inline-flex align-items-center mw-100 "> <div class="slider-container js-slider-container overflow-hidden d-flex overflow-hidden text-nowrap ml-15"> <a href="https://cdn.britannica.com/87/29787-004-A22485F7/Isaac-Barrow-pencil-drawing-David-Loggan-National.jpg" data-href="/media/1/54184/22361" class="media-overlay-link d-inline-block mr-5"> <img loading="lazy" src="https://cdn.britannica.com/87/29787-004-A22485F7/Isaac-Barrow-pencil-drawing-David-Loggan-National.jpg" alt="Isaac Barrow, pencil drawing by David Loggan, 1676; in the National Portrait Gallery, London" height="50" /> </a> </div> <button disabled class="prev-button js-prev-button position-absolute btn btn-circle shadow btn-blue " aria-label="Previous"> <span class="material-icons md-24" data-icon="keyboard_arrow_left"></span> </button> <button disabled class="next-button js-next-button position-absolute btn btn-circle shadow btn-blue " aria-label="Next"> <span class="material-icons md-24" data-icon="keyboard_arrow_right"></span> </button> </div> </div> <div class="mb-30 tlr-related-quizzes"> <div class="text-gray-900 p-5 font-serif font-14 font-weight-bold mx-10 mb-10"> Quizzes </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/quiz/Numbers-and-mathematics"> <img loading="lazy" src="https://cdn.britannica.com/86/94086-131-0BAE374D/Equations-blackboard.jpg?w=200&h=200&c=crop" alt="Equations written on blackboard" width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/quiz/Numbers-and-mathematics" >Numbers and Mathematics</a> </div> </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/quiz/all-about-math-quiz"> <img loading="lazy" src="https://cdn.britannica.com/86/94086-131-0BAE374D/Equations-blackboard.jpg?w=200&h=200&c=crop" alt="Equations written on blackboard" width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/quiz/all-about-math-quiz" >All About Math Quiz</a> </div> </div> </div> <div class="mb-30 tlr-related-questions"> <div class="text-gray-900 p-5 pb-0 font-serif font-14 font-weight-bold mx-10 mb-15"> Related Questions </div> <ul> <li class="link-gray-900 mb-15"><a class="" href="/question/When-was-London-founded">When was London founded?</a> </li> <li class="link-gray-900 mb-15"><a class="" href="/question/Was-London-bombed-during-World-War-II">Was London bombed during World War II?</a> </li> <li class="link-gray-900 mb-15"><a class="" href="/question/What-is-London-known-for">What is London known for?</a> </li> </ul> </div> <div class="mb-30 tlr-read-next"> <div class="text-gray-900 p-5 font-serif font-14 font-weight-bold mx-10 mb-10"> Read Next </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/story/whats-the-difference-between-great-britain-and-the-united-kingdom"> <img loading="lazy" src="https://cdn.britannica.com/43/193443-131-17ABE1C9/Union-Jack-flag-Great-Britain-united-kingdom.jpg?w=200&h=200&c=crop" alt="Union Jack flag of Great Britain, united kingdom" width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/story/whats-the-difference-between-great-britain-and-the-united-kingdom" >What’s the Difference Between Great Britain and the United Kingdom?</a> </div> </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/story/unusual-counting-systems"> <img loading="lazy" src="https://cdn.britannica.com/41/191041-131-7ECE668A/bunch-numbers.jpg?w=200&h=200&c=crop" alt="bunch of numbers" width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/story/unusual-counting-systems" >Unusual Counting Systems</a> </div> </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/story/is-zero-an-even-or-an-odd-number"> <img loading="lazy" src="https://cdn.britannica.com/49/191949-131-3E2AC277/balloon.jpg?w=200&h=200&c=crop" alt="number zero, 0 balloon" width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/story/is-zero-an-even-or-an-odd-number" >Is Zero an Even or an Odd Number?</a> </div> </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/list/11-lesser-known-mostly-contemporary-paintings-you-should-hunt-down-the-next-time-youre-in-london"> <img loading="lazy" src="https://cdn.britannica.com/34/231634-050-3F7B39B1/London-Big-Ben-from-Trafalgar-Square-traffic-in-UK.jpg?w=200&h=200&c=crop" alt="London Big Ben from Trafalgar Square traffic in UK" width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/list/11-lesser-known-mostly-contemporary-paintings-you-should-hunt-down-the-next-time-youre-in-london" >11 Lesser-Known, Mostly Contemporary Paintings You Should Hunt Down the Next Time You’re in London</a> </div> </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/story/lay-lie-lied-lain-when-do-we-use-which"> <img loading="lazy" src="https://cdn.britannica.com/59/195959-131-01E0E29B/ginger-cat-bed-focus-floor-carpet.jpg?w=200&h=200&c=crop" alt="A ginger cat sleeps in his soft cozy bed on a floor carpet, soft focus" width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/story/lay-lie-lied-lain-when-do-we-use-which" >Lay, Lie, Lied, Lain: When Do We Use Which?</a> </div> </div> </div> <div class="mb-30 tlr-discover"> <div class="text-gray-900 p-5 font-serif font-14 font-weight-bold mx-10 mb-10"> Discover </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/list/10-famous-artworks-by-leonardo-da-vinci"> <img loading="lazy" src="https://cdn.britannica.com/06/200006-131-ABB681CF/Leonardo-da-Vinci-Italian-Renaissance-Florence-Engraving-1500.jpg?w=200&h=200&c=crop" alt="Leonardo da Vinci (1452-1519), Italian Renaissance painter from Florence. Engraving by Cosomo Colombini (d. 1812) after a Leonardo self portrait. Ca. 1500." width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/list/10-famous-artworks-by-leonardo-da-vinci" >10 Famous Artworks by Leonardo da Vinci</a> </div> </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/story/why-is-thanksgiving-in-the-us-celebrated-on-a-thursday"> <img loading="lazy" src="https://cdn.britannica.com/06/212906-131-C791368A/Thanksgiving-celebration-food-table-spread.jpg?w=200&h=200&c=crop" alt="Thanksgiving Celebration Traditional Dinner Setting Food Concept" width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/story/why-is-thanksgiving-in-the-us-celebrated-on-a-thursday" >Why Is Thanksgiving in the U.S. Celebrated on a Thursday?</a> </div> </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/story/the-rise-of-the-machines-pros-and-cons-of-the-industrial-revolution"> <img loading="lazy" src="https://cdn.britannica.com/17/167717-131-94C99B30/boys-mill-Macon-Georgia-1909.jpg?w=200&h=200&c=crop" alt="Young boys working in a thread spinning mill in Macon, Georgia, 1909. Boys are so small they have to climb onto the spinning frame to reach and fix broken threads and put back empty bobbins. Child labor. Industrial revolution" width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/story/the-rise-of-the-machines-pros-and-cons-of-the-industrial-revolution" >The Rise of the Machines: Pros and Cons of the Industrial Revolution</a> </div> </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/story/why-is-it-called-black-friday"> <img loading="lazy" src="https://cdn.britannica.com/73/218073-131-D8DF29B6/Macys-Herald-Square-New-York-Black-Friday-Thanksgiving-2018.jpg?w=200&h=200&c=crop" alt="New York NY/ USA- November 23, 2018 Hordes of shoppers throng the Macy's Herald Square flagship store in New York looking for bargains on the day after Thanksgiving, Black Friday." width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/story/why-is-it-called-black-friday" >Why Is It Called Black Friday?</a> </div> </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/list/7-of-historys-most-notorious-serial-killers"> <img loading="lazy" src="https://cdn.britannica.com/51/212551-131-CCA62CB1/Shadow-man-spooky-building-knife.jpg?w=200&h=200&c=crop" alt="Shadow of a man holding large knife in his hand inside of some dark, spooky buiding" width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/list/7-of-historys-most-notorious-serial-killers" >7 of History's Most Notorious Serial Killers</a> </div> </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/list/11-egyptian-gods-and-goddesses"> <img loading="lazy" src="https://cdn.britannica.com/52/196952-131-0665E4EE/Egyptians-hieroglyphics-carvings.jpg?w=200&h=200&c=crop" alt="An ancient egyptian hieroglyphic painted carving showing the falcon headed god Horus seated on a throne and holding a golden fly whisk. Before him are the Pharoah Seti and the goddess Isis. Interior wall of the temple to Osiris at Abydos, Egypt." width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/list/11-egyptian-gods-and-goddesses" >11 Egyptian Gods and Goddesses</a> </div> </div> <div class="imagelink-with-image-on-the-side card card-horizontal tlr-img-with-side-link ml-15 link-gray-900 mb-10" > <div class="position-relative card-media" style="flex: 0;"> <a class="ilf-image position-relative" href="/story/was-santa-claus-a-real-person"> <img loading="lazy" src="https://cdn.britannica.com/92/202092-131-ACFF5B40/Santa-Claus-sleigh.jpg?w=200&h=200&c=crop" alt="Santa Claus flying in his sleigh, christmas, reindeer" width="200" height="200" /> </a> </div> <div class="card-body ilf-content"> <a class="font-weight-semi-bold d-block mb-5 font-16 ilf-title" href="/story/was-santa-claus-a-real-person" >Was Santa Claus a Real Person?</a> </div> </div> </div> </div> </div> </div> <button class="drawerToggle btn position-sticky border btn-xs btn-white btn-circle rounded-sm d-none d-lg-flex " type="button" aria-label="Toggle Drawer"> <em class="material-icons font-18 text-blue" data-icon="keyboard_arrow_left"></em> </button> </div> </div> <div class="col"> <div class="h-100 ml-0 pr-lg-0 "> <div class="h-100 grid gx-0 gx-lg-20"> <div class="h-100 col-sm"> <div class="h-100 infinite-pagination-container d-flex flex-column position-relative"> <div class="position-absolute top-0 h-100 w-100"> <div class="toc-sticky-header d-none d-lg-none bg-gray-50 px-10 px-sm-30 position-sticky w-100 "> <div class="toc-sticky-header-inner-container align-items-center d-flex mx-auto h-100 w-100"> <button class="d-flex d-lg-none btn btn-sm btn-white text-blue border-2 border-gray-100 gtm-mobile-toc-header-button js-sections-button d-lg-none p-10"> <em class="material-icons my-n5 md-icon" data-icon="toc"></em> Contents </button> <div class="header-ai-ask-button-placeholder"></div> <div class="header-ai-summarize-button-placeholder"></div> </div> </div> </div> <div class="grey-box w-100 grey-box-top grey-box-bottom"> <div class="grey-box-content mx-auto w-100"> <script type="application/ld+json"> { "@context" : "https://schema.org", "@type" : "BreadcrumbList", "itemListElement" : [ { "@type" : "ListItem", "position" : 1, "item" : { "@id" : "https://www.britannica.com/browse/Geography-Travel", "name": "Geography & Travel" } } , { "@type" : "ListItem", "position" : 2, "item" : { "@id" : "https://www.britannica.com/browse/Languages", "name": "Languages" } } ] } </script> <nav class="breadcrumb mt-20"> <span class="breadcrumb-item "> <a class="link-gray-600" href="/browse/Geography-Travel">Geography & Travel</a> </span> <span class="breadcrumb-item "> <a class="link-gray-600" href="/browse/Languages">Languages</a> </span> </nav> <div class="page2ref-true topic-content topic-type-BIOGRAPHY" data-student-article="false"> <script class="page-description-json" type="application/json"> { "url": "/biography/Isaac-Barrow", "shareUrl": "https://www.britannica.com/biography/Isaac-Barrow", "browserTitle": "Isaac Barrow | English Mathematician & Philosopher", "firstTopicPage": true, "topicId":54184 } </script> <div class="reading-channel"> <div class="desktop-header-image module-spacing"> <figure class="md-assembly m-0 mb-20 mb-md-0 card card-borderless print-false" data-assembly-id="13684" data-asm-type="image"> <div class="md-assembly-wrapper card-media " data-type="image"> <a style="min-height: 160px;" href="https://cdn.britannica.com/87/29787-004-A22485F7/Isaac-Barrow-pencil-drawing-David-Loggan-National.jpg" class="gtm-assembly-link position-relative d-flex align-items-center justify-content-center media-overlay-link card-media" data-href="/media/1/54184/22361"> <picture> <source media="(min-width: 680px)" srcset="https://cdn.britannica.com/87/29787-004-A22485F7/Isaac-Barrow-pencil-drawing-David-Loggan-National.jpg?w=300"> <img src="https://cdn.britannica.com/87/29787-004-A22485F7/Isaac-Barrow-pencil-drawing-David-Loggan-National.jpg?w=400&h=300&c=crop" alt="Isaac Barrow, pencil drawing by David Loggan, 1676; in the National Portrait Gallery, London" loading="eager" /> </picture> <button class="magnifying-glass btn btn-circle position-absolute shadow btn-white top-10 right-10" aria-label="Zoom in"> <em class="material-icons link-blue" data-icon="zoom_in"></em> </button> </a> </div> <figcaption class="card-body"> <div class="md-assembly-caption text-muted font-14 font-serif line-clamp"> <span> <a class="gtm-assembly-link md-assembly-title font-weight-bold d-inline font-sans-serif mr-5 media-overlay-link" href="https://cdn.britannica.com/87/29787-004-A22485F7/Isaac-Barrow-pencil-drawing-David-Loggan-National.jpg" data-href="/media/1/54184/22361"></a> <span><span>Isaac Barrow, pencil drawing by David Loggan, 1676; in the National Portrait Gallery, London</span></span> <button class="js-more-btn d-none btn btn-unstyled font-12 bg-white js-content" aria-label="Toggle more/less fact data"> <span class="link-blue">(more)</span> </button> </span> </div> </figcaption> </figure> </div><div class="topic-header"> <div class="d-flex align-items-top justify-content-between"> <div class="d-flex flex-column"> <div> <div> <h1>Isaac Barrow</h1></div> </div> <div class="topic-identifier font-16 font-md-20">English mathematician</div> </div> </div> <div class="d-none d-sm-flex flex-row"> <div class="mr-10 mb-15"> <button class="ai-ask-button btn border-2 btn-sm js-inline-ai-ask-button btn-outline-red-400 border-red-400"> Ask the Chatbot a Question </button> </div> <div class="d-none d-sm-block md-topic-tools qa-action-buttons mb-15" data-topic-id="54184"> <button class="js-tooltip btn btn-sm btn-outline-blue border pr-10 border-2" > <em class="material-icons md-icon ml-n10 my-n5 mr-5" data-icon="more_vert"></em> More Actions </button> <div class="md-more-popover popover popover-sm p-0 font-14 z-1"> <div> <a class="js-modal btn btn-sm btn-link gtm-topic-tool font-weight-bold btn-link" href="/print/article/54184" target="_blank" > <em class="material-icons mr-5 ml-n10 my-n5 md-icon" data-icon="print"></em> Print </a> </div> <div> <button class="js-modal qa-cite-modal-button btn btn-sm btn-link gtm-topic-tool font-weight-bold btn-link" data-modal="[data-topic-id=54184] .md-cite-modal"> <em class="material-icons mr-5 ml-n10 my-n5 md-icon" data-icon="verified"></em> Cite </button> <div class="md-cite-modal size-lg d-none"> <div class="md-modal-body"> <div class="h2 font-serif d-flex align-items-center pb-15 border-bottom mb-15"> <em class="material-icons text-blue mr-10">verified</em>Cite </div> <div class="font-serif"> While every effort has been made to follow citation style rules, there may be some discrepancies. Please refer to the appropriate style manual or other sources if you have any questions. </div> <div class="label mt-20 mb-10">Select Citation Style</div> <select class="js-citation-format-select form-select"> <option selected value="mla">MLA</option> <option value="apa">APA</option> <option value="chicago">Chicago Manual of Style</option> </select> <div class="citation font-serif border rounded p-15 mt-20" data-authors="Mordechai Feingold" data-title="Isaac Barrow" data-published-date="27 Sep. 2024" data-url="https://www.britannica.com/biography/Isaac-Barrow" > <div class="citation-text"></div> </div> <button class="js-copy-citation-button mt-20 btn btn-xs btn-outline-blue border shadow-sm pr-10" > <em class="material-icons md-icon ml-n10 my-n5 mr-5" data-icon="file_copy"></em> <span class="js-citation-status-text">Copy Citation</span> </button> </div> </div> </div> <div> <button class="js-share-modal-button js-modal btn btn-sm btn-link gtm-topic-tool font-weight-bold btn-link" data-modal="[data-topic-id=54184] .md-share-modal"> <em class="material-icons mr-5 ml-n10 my-n5 md-icon" data-icon="share"></em> Share </button> <div class="md-share-modal size-lg d-none qa-share-modal"> <div class="md-modal-body"> <div class="h2 font-serif d-flex align-items-center pb-15 border-bottom"> <em class="material-icons text-blue mr-10" data-icon="share"></em> Share </div> <div class="label my-20">Share to social media</div> <div class="md-social-toolbar-circle d-flex align-items-start inverted" data-value="share" title="Isaac Barrow" data-url="https://www.britannica.com/biography/Isaac-Barrow" > <a class="social-icon facebook justify-content-center d-flex align-items-center align-self-center" data-provider="facebook" href="https://www.facebook.com/BRITANNICA/" target="_blank" rel="noopener"><span>Facebook</span></a> <a class="social-icon x justify-content-center d-flex align-items-center align-self-center" data-provider="x" href="https://x.com/britannica" target="_blank" rel="noopener"><span>X</span></a> </div> <div class="label pt-20 mt-20 mb-5 border-top">URL</div> <a class="font-serif text-truncate d-inline-block" href="https://www.britannica.com/biography/Isaac-Barrow">https://www.britannica.com/biography/Isaac-Barrow</a> </div> </div> </div> <div> <button class="js-feedback-modal-button js-modal btn btn-sm btn-link gtm-topic-tool font-weight-bold btn-link" data-modal=".md-feedback-modal"> <em class="material-icons mr-5 ml-n10 my-n5 md-icon" data-icon="message"></em> Feedback </button> </div> <div> <button class="qa-external-website-modal-button js-modal btn btn-sm btn-link gtm-topic-tool font-weight-bold btn-link" data-modal="[data-topic-id=54184] .md-websites-modal"> <em class="material-icons md-icon ml-n10 mr-5" data-icon="link"></em> External Websites </button> </div> </div> <div class="md-feedback-modal size-lg d-none"> <div class="md-modal-body"> <div class="h2 font-serif pb-15 border-bottom"> Feedback </div> <form method="post" action="/submission/feedback/54184"> <div class="my-20"> Corrections? Updates? Omissions? Let us know if you have suggestions to improve this article (requires login). </div> <div class="type-menu"> <label for="feedback-type" class="label mb-10">Feedback Type</label> <select id="feedback-type" class="form-select mb-30" name="feedbackTypeId" required> <option value="" selected="selected">Select a type (Required)</option> <option value="1">Factual Correction</option> <option value="2">Spelling/Grammar Correction</option> <option value="3">Link Correction</option> <option value="4">Additional Information</option> <option value="5">Other</option> </select> </div> <label for="feedback" class="label mb-10">Your Feedback</label> <textarea id="feedback" class="form-control mb-30" name="feedback" maxlength="3000" rows="7" required></textarea> <button class="btn btn-blue" type="submit">Submit Feedback</button> </form> <div class="success-messaging d-none mt-30"> <div class="title">Thank you for your feedback</div> <p>Our editors will review what you’ve submitted and determine whether to revise the article.</p> </div> </div> </div> <div class="md-websites-modal size-lg d-none"> <div class="md-modal-body"> <div class="h2 font-serif pb-15 border-bottom font-weight-bold"> External Websites </div> <div class="pb-20"> <ul class="list-unstyled mt-20 lh-lg"> <li><a class="external" href="http://galileo.rice.edu/Catalog/NewFiles/barrow.html" target="_blank" rel="noopener nofollow">The Galileo Project - Biography of Isaac Barrow</a></li> <li><a class="external" href="https://www.westminster-abbey.org/abbey-commemorations/commemorations/isaac-barrow" target="_blank" rel="noopener nofollow">Westminster Abbey - Biography of Isaac Barrow</a></li> </ul> </div> <div class="md-websites-ebk-title">Britannica Websites</div> <div class="md-websites-ebk-subtitle">Articles from Britannica Encyclopedias for elementary and high school students.</div> <ul class="list-unstyled bps-topic-web-sites lh-lg"> <li><a class="external" href="https://kids.britannica.com/students/article/Isaac-Barrow/310083" target="_blank" rel="noopener">Isaac Barrow - Student Encyclopedia (Ages 11 and up)</a></li> </ul> </div> </div> </div> </div> <div class="toc-header-marker"></div> <button class="ai-ask-button btn border-2 js-header-ai-ask-button d-none btn-sm btn-outline-red-400 border-red-400 mr-0 mr-lg-10 ml-5 ml-sm-10 ml-lg-0 p-10"> Ask the Chatbot a Question </button> <div class="md-byline module-spacing "> <div class="font-serif font-12"> <span class="written-by text-gray-700"> Written by </span> <div class="editor-popover popover p-0"> <a class="d-block p-20 gtm-byline font-12 byline-contributor" href="/contributor/Mordechai-Feingold/4479" > <div class="editor-title font-16 font-weight-bold">Mordechai Feingold</div> <div class="editor-description font-12 font-serif mt-5 clamp-description text-black">Professor of Science and Technology Studies, Virginia Polytechnic Institute and State University, Blacksburg, Virginia. Author of <i>Before Newton: The Life and Times of Isaac Barrow (1990).</i></div> </a> <div data-popper-arrow></div> </div> <span class="btn btn-link editor-link p-0 qa-byline-link gtm-byline font-12 byline-contributor text-decoration-underline"> Mordechai Feingold</span></div> <div class="font-serif font-12 text-gray-700"> <span class="qa-fact-checked-by">Fact-checked by</span> <div class="editor-popover popover p-0"> <a class="d-block p-20 font-12" href="/editor/The-Editors-of-Encyclopaedia-Britannica/4419" > <div class="editor-title font-16 font-weight-bold">The Editors of Encyclopaedia Britannica</div> <div class="editor-description font-12 font-serif mt-5 text-black">Encyclopaedia Britannica's editors oversee subject areas in which they have extensive knowledge, whether from years of experience gained by working on that content or via study for an advanced degree. They write new content and verify and edit content received from contributors.</div> </a> <div data-popper-arrow></div> </div> <span class="btn btn-link editor-link p-0 qa-byline-link font-12 "> The Editors of Encyclopaedia Britannica</span></div> <div class="last-updated font-12 font-serif"> <span class="text-gray-700"> Last Updated: <time datetime="2024-09-27T00:00:00CDT" >Sep 27, 2024</time> •</span> <a class="byline-edit-history" href="https://www.britannica.com/biography/Isaac-Barrow/additional-info#history" rel="nofollow">Article History</a> </div></div> </div> <button class="d-flex d-lg-none btn btn-outline-blue border rounded-sm shadow-sm mobile-toc-button gtm-mobile-toc-inline-button d-none d-sm-block js-sections-inline-button module-spacing btn d-lg-none"> <em class="material-icons mr-5 ml-n10 my-n5 md-icon" data-icon="toc"></em> Table of Contents </button> <div class="d-flex d-sm-none flex-row"> <button class="d-flex d-lg-none btn btn-outline-blue border rounded-sm shadow-sm mobile-toc-button gtm-mobile-toc-inline-button js-sections-inline-button module-spacing"> <em class="material-icons mr-5 ml-n10 my-n5 md-icon" data-icon="toc"></em> Table of Contents </button> <button class="ai-ask-button btn border-2 ai-ask-button btn border-2 module-spacing btn-sm js-inline-ai-ask-button btn-outline-red-400 border-red-400 p-10 ml-5"> Ask the Chatbot a Question </button> </div> <div class="js-qf-module qf-module px-40 px-sm-20 py-15 mx-auto module-spacing font-14 bg-gray-50 rounded"> <div class="qf-title font-weight-bold font-14 mb-10 text-center"> Quick Facts</div> <div class="facts-list mt-10"> <div class=""> <div class="js-fact mb-10 line-clamp clamp-3"> <dl> <dt>Born: </dt> <dd>October 1630, <a href="/place/London">London</a>, <a href="/place/England">England</a></dd> </dl> <button class="js-more-btn d-none btn btn-unstyled font-12 bg-gray-50" aria-label="Toggle more/less fact data"> <em class="js-content link-blue">(Show more)</em> </button> </div> </div> <div class=""> <div class="js-fact mb-10 line-clamp clamp-3"> <dl> <dt>Died: </dt> <dd>May 4, 1677, <a href="/place/London">London</a> (aged 46)</dd> </dl> <button class="js-more-btn d-none btn btn-unstyled font-12 bg-gray-50" aria-label="Toggle more/less fact data"> <em class="js-content link-blue">(Show more)</em> </button> </div> <div class="text-center"> <a class="btn btn-sm btn-link p-0" href="/facts/Isaac-Barrow"> See all related content </a> </div> </div> </div> </div><span class="marker before-article"></span><section data-level="1" id="ref1"><span class="marker PREMOD1 mod-inline"></span><p class="topic-paragraph"><strong><span id="ref128946"></span>Isaac Barrow</strong> (born October 1630, <a href="https://www.britannica.com/place/London" class="md-crosslink autoxref " data-show-preview="true">London</a>, England—died May 4, 1677, London) was an English classical scholar, theologian, and mathematician who was the teacher of <span id="ref721595"></span><a href="https://www.britannica.com/biography/Isaac-Newton" class="md-crosslink " data-show-preview="true">Isaac Newton</a>. He developed a method of determining <a class="md-dictionary-link md-dictionary-tt-off eb" data-term="tangents" href="https://www.britannica.com/dictionary/tangents" data-type="EB">tangents</a> that closely approached the methods of <a href="https://www.britannica.com/science/calculus-mathematics" class="md-crosslink " data-show-preview="true">calculus</a>, and he first recognized that what became known as the processes of <a href="https://www.britannica.com/science/integration-mathematics" class="md-crosslink " data-show-preview="true">integration</a> and <a href="https://www.britannica.com/science/differentiation-mathematics" class="md-crosslink " data-show-preview="true">differentiation</a> in calculus are inverse operations.</p><span class="marker MOD1 mod-inline"></span><span class="marker PREMOD2 mod-inline"></span><p class="topic-paragraph">Barrow entered <a href="https://www.britannica.com/topic/Trinity-College-Hartford-Connecticut" class="md-crosslink " data-show-preview="true">Trinity College</a>, <a href="https://www.britannica.com/topic/University-of-Cambridge" class="md-crosslink " data-show-preview="true">Cambridge</a>, in 1643. There he distinguished himself as a classical scholar as well as a mathematician, earning his <a href="https://www.britannica.com/topic/bachelors-degree" class="md-crosslink autoxref " data-show-preview="true">bachelor’s degree</a> in 1648. He was elected a fellow of the college in 1649 and received his <a href="https://www.britannica.com/topic/master-degree" class="md-crosslink autoxref " data-show-preview="true">master’s degree</a> in 1652. Such precociousness helped to shield him from <a href="https://www.britannica.com/topic/Puritanism" class="md-crosslink " data-show-preview="true">Puritan</a> rule, for Barrow was an outspoken Royalist and <a href="https://www.britannica.com/topic/Anglicanism" class="md-crosslink " data-show-preview="true">Anglican</a>. By the mid-1650s he contemplated the publication of a full and accurate Latin edition of the Greek mathematicians, yet in a concise manner that utilized symbols for <a class="md-dictionary-link md-dictionary-tt-off mw" data-term="brevity" href="https://www.merriam-webster.com/dictionary/brevity" data-type="MW">brevity</a>. However, only <a href="https://www.britannica.com/biography/Euclid-Greek-mathematician" class="md-crosslink " data-show-preview="true">Euclid</a>’s <em><span id="ref128948"></span><a href="https://www.britannica.com/topic/Elements-by-Euclid" class="md-crosslink " data-show-preview="true">Elements</a></em> and <em>Data</em> appeared in 1656 and 1657, respectively, while other texts that Barrow prepared at the time—by <a href="https://www.britannica.com/biography/Archimedes" class="md-crosslink " data-show-preview="true">Archimedes</a>, <a href="https://www.britannica.com/biography/Apollonius-of-Perga" class="md-crosslink " data-show-preview="true">Apollonius of Perga</a>, and Theodosius of Bythnia—were not published until 1675. Barrow embarked on a European tour before the <em>Elements</em> was published, as the political climate in <a href="https://www.britannica.com/place/England" class="md-crosslink autoxref " data-show-preview="true">England</a> deteriorated and the Regius professorship of Greek at the <a href="https://www.britannica.com/topic/University-of-Oxford" class="md-crosslink " data-show-preview="true">University of Oxford</a>, to which he had been elected, was given to another. He spent four years in France, Italy, and Constantinople, returning to England with the restoration of the <a href="https://www.britannica.com/topic/House-of-Stuart" class="md-crosslink " data-show-preview="true">Stuart</a> monarchy in 1660. On his return to England, <a class="md-dictionary-link md-dictionary-tt-off eb" data-term="Barrow" href="https://www.britannica.com/dictionary/Barrow" data-type="EB">Barrow</a> was ordained in the Anglican Church and appointed to a Greek professorship at Cambridge. In 1662 he was also elected professor of <a href="https://www.britannica.com/science/geometry" class="md-crosslink autoxref " data-show-preview="true">geometry</a>, but he resigned both positions after his election as Lucasian Professor of Mathematics at Cambridge in 1663.</p><span class="marker MOD2 mod-inline"></span><span class="marker PREMOD3 mod-inline"></span><p class="topic-paragraph">Barrow was instrumental in institutionalizing the study of <a href="https://www.britannica.com/science/mathematics" class="md-crosslink autoxref " data-show-preview="true">mathematics</a> at Cambridge. From 1664 to 1666, he delivered a set of mathematical lectures—predominantly on the <a href="https://www.britannica.com/science/foundations-of-mathematics" class="md-crosslink " data-show-preview="true">foundations of mathematics</a>—that were published posthumously as <em>Lectiones mathematicae</em> (1683). These lectures treated such basic concepts as number, magnitude, and proportion; delved into the relationship between the various branches of mathematics; and considered the relation between mathematics and natural philosophy—most notably the concept of space. Barrow followed these with a series of lectures on geometry, <em>Lectiones geometricae</em> (1669), that were far more technical and novel. In investigating the generation of curves by motion, Barrow recognized the inverse relationship between <a class="md-dictionary-link md-dictionary-tt-off mw" data-term="integration" href="https://www.merriam-webster.com/dictionary/integration" data-type="MW">integration</a> and differentiation and came close to enunciating the fundamental theorem of <a href="https://www.britannica.com/science/calculus-mathematics" class="md-crosslink " data-show-preview="true">calculus</a>. His last series of lectures, on <a href="https://www.britannica.com/science/optics" class="md-crosslink autoxref " data-show-preview="true">optics</a>, <em>Lectiones opticae</em> (1670), built on the work of <a href="https://www.britannica.com/biography/Johannes-Kepler" class="md-crosslink " data-show-preview="true">Johannes Kepler</a> (1571–1630), <a href="https://www.britannica.com/biography/Rene-Descartes" class="md-crosslink " data-show-preview="true">René Descartes</a> (1596–1650), and <a href="https://www.britannica.com/biography/Thomas-Hobbes" class="md-crosslink " data-show-preview="true">Thomas Hobbes</a> (1588–1679), among others. In these lectures Barrow made major contributions to determining image location after <a href="https://www.britannica.com/science/reflection-physics" class="md-crosslink " data-show-preview="true">reflection</a> or <a href="https://www.britannica.com/science/refraction" class="md-crosslink " data-show-preview="true">refraction</a>; opened new vistas for the study of <a href="https://www.britannica.com/science/astigmatism-eye-disorder" class="md-crosslink " data-show-preview="true">astigmatism</a> and caustics (a collection of rays that, emanating from a single point, are reflected or refracted by a curved surface); and made suggestions toward a theory of light and colours.</p><a class="link-module shadow-sm d-block qa-quiz-module" href="/quiz/all-about-math-quiz" data-link-module-iframe-link=""> <img loading="lazy" src="https://cdn.britannica.com/86/94086-131-0BAE374D/Equations-blackboard.jpg" alt="Equations written on blackboard" class="rounded-sm mr-15" width="70" /> <div class="line-clamp clamp-5"> <div class="module-title bg-green">Britannica Quiz</div> <div class="font-weight-semi-bold mt-5">All About Math Quiz</div> </div> </a><span class="marker MOD3 mod-inline"></span><span class="marker PREMOD4 mod-inline"></span><p class="topic-paragraph">Barrow’s <a class="md-dictionary-link md-dictionary-tt-off mw" data-term="tenure" href="https://www.merriam-webster.com/dictionary/tenure" data-type="MW">tenure</a> as mathematics professor coincided with the maturation of <a href="https://www.britannica.com/science/newton-unit-of-measurement" class="md-crosslink autoxref " data-show-preview="true">Newton’s</a> mathematical studies, and scholars often debate the exact nature of their relationship. Barrow was not Newton’s official tutor, though they were both members of Trinity College. Newton attended Barrow’s lectures, and it is clear that Barrow encouraged and furthered Newton’s studies. Fully <a class="md-dictionary-link md-dictionary-tt-off mw" data-term="cognizant" href="https://www.merriam-webster.com/dictionary/cognizant" data-type="MW">cognizant</a> of the young man’s talents, Barrow resigned his professorship in 1669 in Newton’s favour and accepted a position as royal chaplain in London. In 1673 Barrow was appointed master of Trinity College by King <a href="https://www.britannica.com/biography/Charles-II-king-of-Great-Britain-and-Ireland" class="md-crosslink " data-show-preview="true">Charles II</a>.</p><div class="one-good-fact-module"> </div><span class="marker MOD4 mod-inline"></span><span class="marker PREMOD5 mod-inline"></span><p class="topic-paragraph">Although Barrow was regarded by his mathematical contemporaries in England as second only to Newton, he was more widely esteemed for his sermons and other writings on behalf of the <a href="https://www.britannica.com/topic/Church-of-England" class="md-crosslink " data-show-preview="true">Church of England</a>, and these were often reprinted well into the 19th century.</p><span class="marker MOD5 mod-inline"></span></section> <span class="md-signature"><a href="/contributor/Mordechai-Feingold/4479">Mordechai Feingold</a></span><span class="marker end-of-content"></span><span class="marker after-article"></span></div> <div id="chatbot-root"></div> </div> </div> </div> <div class="ai-dialog-placeholder"></div> </div> </div> <aside class="col-md-da-320"></aside> </div> </div> </div> </div> </article></div> </div></div> </div> </main> <div id="md-footer"></div> <noscript><iframe src="//www.googletagmanager.com/ns.html?id=GTM-5W6NC8" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript> <script type="text/javascript" id="_informizely_script_tag"> var IzWidget = IzWidget || {}; (function (d) { var scriptElement = d.createElement('script'); scriptElement.type = 'text/javascript'; scriptElement.async = true; scriptElement.src = "https://insitez.blob.core.windows.net/site/f780f33e-a610-4ac2-af81-3eb184037547.js"; var node = d.getElementById('_informizely_script_tag'); node.parentNode.insertBefore(scriptElement, node); } )(document); </script>  <script> window.ap3c = window.ap3c || {}; var ap3c = window.ap3c; ap3c.cmd = ap3c.cmd || []; ap3c.cmd.push(function() { ap3c.init('ZO4siT4cLwnykPnzZWJtd3Byb2Q', 'https://engage.email.britannica.com/'); ap3c.track({v: 0}); }); ap3c.activity = function(act) { ap3c.act = (ap3c.act || []); ap3c.act.push(act); }; var s, t; s = document.createElement('script'); s.type = 'text/javascript'; s.src = "https://engage.email.britannica.com/app.js"; t = document.getElementsByTagName('script')[0]; t.parentNode.insertBefore(s, t); </script> <script class="marketing-page-info" type="application/json"> {"pageType":"Topic","templateName":"DESKTOP","pageNumber":1,"pagesTotal":1,"pageId":54184,"pageLength":680,"initialLoad":true,"lastPageOfScroll":false} </script> <script class="marketing-content-info" type="application/json"> [] </script> <script src="https://cdn.britannica.com/mendel-resources/3-130/js/libs/jquery-3.5.0.min.js?v=3.130.14"></script> <script type="text/javascript" data-type="Init Mendel Code Splitting"> (function() { $.ajax({ dataType: 'script', cache: true, url: 'https://cdn.britannica.com/mendel-resources/3-130/dist/topic-page.js?v=3.130.14' }); })(); </script> <script class="analytics-metadata" type="application/json"> {"leg":"A","adLeg":"A","userType":"ANONYMOUS","pageType":"Topic","pageSubtype":null,"articleTemplateType":"BIO_MEDIUM","gisted":false,"pageNumber":1,"hasSummarizeButton":false,"hasAskButton":false} </script> <script type="text/javascript"> EBStat={accountId:-1,hostnameOverride:'webstats.eb.com',domain:'www.britannica.com', json:''}; </script> <script type="text/javascript"> ( function() { $.ajax( { dataType: 'script', cache: true, url: '//www.britannica.com/webstats/mendelstats.js?v=1' } ) .done( function() { try {writeStat(null,EBStat);} catch(err){} } ); })(); </script> <div id="bc-fixed-dialogue"></div> </body> </html>

CINXE.COM

Isaac Barrow | English Mathematician & Philosopher | Britannica