{"id":3073,"date":"2024-02-27T07:02:09","date_gmt":"2024-02-27T06:02:09","guid":{"rendered":"https:\/\/lesminis.fr\/blog\/?p=3073"},"modified":"2024-02-25T18:48:25","modified_gmt":"2024-02-25T17:48:25","slug":"euclide-et-les-elements-la-bible-de-la-geometrie","status":"publish","type":"post","link":"https:\/\/lesminis.fr\/blog\/euclide-et-les-elements-la-bible-de-la-geometrie\/","title":{"rendered":"Euclide et les \u00c9l\u00e9ments, la bible de la g\u00e9om\u00e9trie"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_83 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/lesminis.fr\/blog\/euclide-et-les-elements-la-bible-de-la-geometrie\/#Introduction\" >Introduction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/lesminis.fr\/blog\/euclide-et-les-elements-la-bible-de-la-geometrie\/#Qui_etait_Euclide\" >Qui \u00e9tait Euclide ?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/lesminis.fr\/blog\/euclide-et-les-elements-la-bible-de-la-geometrie\/#La_geometrie_chez_les_Grecs\" >La g\u00e9om\u00e9trie chez les Grecs<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/lesminis.fr\/blog\/euclide-et-les-elements-la-bible-de-la-geometrie\/#Lorganisation_des_Elements\" >L\u2019organisation des \u00c9l\u00e9ments<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/lesminis.fr\/blog\/euclide-et-les-elements-la-bible-de-la-geometrie\/#La_methode_dEuclide\" >La m\u00e9thode d&rsquo;Euclide<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/lesminis.fr\/blog\/euclide-et-les-elements-la-bible-de-la-geometrie\/#Limpact_des_%C2%AB_Elements_%C2%BB\" >L&rsquo;impact des \u00ab\u00a0\u00c9l\u00e9ments\u00a0\u00bb<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/lesminis.fr\/blog\/euclide-et-les-elements-la-bible-de-la-geometrie\/#La_rigueur_dEuclide\" >La rigueur d\u2019Euclide<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/lesminis.fr\/blog\/euclide-et-les-elements-la-bible-de-la-geometrie\/#Linfluence_des_Elements\" >L\u2019influence des \u00c9l\u00e9ments<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/lesminis.fr\/blog\/euclide-et-les-elements-la-bible-de-la-geometrie\/#Euclide_et_la_geometrie_moderne\" >Euclide et la g\u00e9om\u00e9trie moderne<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Introduction\"><\/span>Introduction<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"whitespace-pre-wrap\">Il y a environ 2300 ans vivait un grand math\u00e9maticien grec nomm\u00e9 <strong>Euclide<\/strong>. Son \u0153uvre la plus c\u00e9l\u00e8bre, les <em>\u00c9l\u00e9ments<\/em>, est un des livres les plus lus et \u00e9tudi\u00e9s de tous les temps !<\/p>\n<p class=\"whitespace-pre-wrap\">Les \u00c9l\u00e9ments rassemblent les connaissances de g\u00e9om\u00e9trie et de math\u00e9matiques de l\u2019\u00e9poque. C&rsquo;est un peu la \u00ab\u00a0bible\u00a0\u00bb des math\u00e9maticiens, leur livre de r\u00e9f\u00e9rence. Pendant des si\u00e8cles, c&rsquo;\u00e9tait LE manuel par excellence pour apprendre la g\u00e9om\u00e9trie.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Qui_etait_Euclide\"><\/span>Qui \u00e9tait Euclide ?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Euclide vivait \u00e0 Alexandrie, une des plus grandes villes de l&rsquo;\u00c9gypte ancienne, autour de 300 avant J.-C. C&rsquo;\u00e9tait un temps o\u00f9 la connaissance et la science fleurissaient, et Euclide se trouvait au c\u0153ur de cette effervescence intellectuelle. Bien que nous ne sachions pas beaucoup sur sa vie personnelle, son \u0153uvre a travers\u00e9 les si\u00e8cles pour arriver jusqu&rsquo;\u00e0 nous.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"La_geometrie_chez_les_Grecs\"><\/span>La g\u00e9om\u00e9trie chez les Grecs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"whitespace-pre-wrap\">\u00c0 l\u2019\u00e9poque d\u2019Euclide, entre -300 et -200, les Grecs \u00e9taient fascin\u00e9s par la g\u00e9om\u00e9trie. Pour eux, comprendre les figures g\u00e9om\u00e9triques comme les triangles, les cercles ou les polygones, \u00e9tait une qu\u00eate intellectuelle importante.<\/p>\n<p class=\"whitespace-pre-wrap\">Ils cherchaient la connaissance pure par la pens\u00e9e et le raisonnement, sans besoin de v\u00e9rifier sur le terrain. C\u2019est ce qu\u2019on appelle la <strong>g\u00e9om\u00e9trie th\u00e9orique<\/strong> : \u00e0 partir de quelques v\u00e9rit\u00e9s de base qu\u2019on admet, appel\u00e9es \u00ab\u00a0axiomes\u00a0\u00bb, on construit des raisonnements logiques pour d\u00e9couvrir de nouvelles v\u00e9rit\u00e9s.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Lorganisation_des_Elements\"><\/span>L\u2019organisation des \u00c9l\u00e9ments<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"whitespace-pre-wrap\">Les \u00c9l\u00e9ments sont organis\u00e9s en 13 livres ou chapitres. Les 5 premiers concernent la g\u00e9om\u00e9trie plane, par exemple sur les triangles, les parall\u00e8les ou les pyramides. Puis on trouve des livres sur les nombres, ou la division des figures.<\/p>\n<p class=\"whitespace-pre-wrap\">Chaque livre commence par des \u00ab\u00a0d\u00e9finitions\u00a0\u00bb : par exemple Euclide d\u00e9finit ce qu\u2019est un point, une ligne, un triangle etc. Puis suivent les \u00ab\u00a0axiomes\u00a0\u00bb, ces fameuses v\u00e9rit\u00e9s admises sans d\u00e9monstration.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"La_methode_dEuclide\"><\/span>La m\u00e9thode d&rsquo;Euclide<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Ce qui rend les \u00ab\u00a0\u00c9l\u00e9ments\u00a0\u00bb si sp\u00e9ciaux, c&rsquo;est la m\u00e9thode utilis\u00e9e par Euclide pour pr\u00e9senter la g\u00e9om\u00e9trie. Il commence par d\u00e9finir les concepts de base, comme le point, la ligne et le cercle. Puis, il \u00e9nonce des axiomes, ou postulats, qui sont des affirmations consid\u00e9r\u00e9es comme \u00e9videntes et accept\u00e9es sans preuve.<\/p>\n<p>\u00c0 partir de l\u00e0, Euclide construit, \u00e9tape par \u00e9tape, des propositions et des th\u00e9or\u00e8mes, prouvant chaque nouvel \u00e9nonc\u00e9 \u00e0 partir des pr\u00e9c\u00e9dents. Cette m\u00e9thode logique et rigoureuse \u00e9tait r\u00e9volutionnaire et a \u00e9tabli un standard pour la pens\u00e9e scientifique.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Limpact_des_%C2%AB_Elements_%C2%BB\"><\/span>L&rsquo;impact des \u00ab\u00a0\u00c9l\u00e9ments\u00a0\u00bb<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Les \u00ab\u00a0\u00c9l\u00e9ments\u00a0\u00bb d&rsquo;Euclide n&rsquo;ont pas seulement pos\u00e9 les bases de la g\u00e9om\u00e9trie. Ils ont aussi influenc\u00e9 de mani\u00e8re profonde le d\u00e9veloppement de la logique, de la philosophie et des sciences. Son \u0153uvre a enseign\u00e9 \u00e0 des g\u00e9n\u00e9rations de penseurs comment aborder un probl\u00e8me de mani\u00e8re syst\u00e9matique, comment construire un argument solide et comment chercher la v\u00e9rit\u00e9 dans la structure m\u00eame du monde.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-3075 size-full\" src=\"https:\/\/lesminis.fr\/blog\/wp-content\/uploads\/2024\/02\/2-6.jpg\" alt=\"Euclide histoire geometrie ecole coll\u00e8ge collectivit\u00e9\" width=\"1000\" height=\"1000\" srcset=\"https:\/\/lesminis.fr\/blog\/wp-content\/uploads\/2024\/02\/2-6.jpg 1000w, https:\/\/lesminis.fr\/blog\/wp-content\/uploads\/2024\/02\/2-6-300x300.jpg 300w, https:\/\/lesminis.fr\/blog\/wp-content\/uploads\/2024\/02\/2-6-150x150.jpg 150w, https:\/\/lesminis.fr\/blog\/wp-content\/uploads\/2024\/02\/2-6-768x768.jpg 768w, https:\/\/lesminis.fr\/blog\/wp-content\/uploads\/2024\/02\/2-6-696x696.jpg 696w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/p>\n<p>Pendant des si\u00e8cles, les \u00ab\u00a0\u00c9l\u00e9ments\u00a0\u00bb ont \u00e9t\u00e9 le livre de math\u00e9matiques le plus publi\u00e9 apr\u00e8s la Bible. Ils ont \u00e9t\u00e9 \u00e9tudi\u00e9s par des scientifiques, des math\u00e9maticiens, des philosophes et m\u00eame des artistes, chacun y trouvant une source d&rsquo;inspiration et un guide vers la compr\u00e9hension des lois de l&rsquo;univers.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"La_rigueur_dEuclide\"><\/span>La rigueur d\u2019Euclide<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"whitespace-pre-wrap\">Ce qui a fait la r\u00e9putation d\u2019Euclide, c\u2019est l\u2019extr\u00eame <strong>rigueur de ses raisonnements<\/strong>. Il d\u00e9duit toutes ses propositions \u00e0 partir d\u2019un petit nombre d\u2019axiomes simples, de d\u00e9finitions, et de propositions d\u00e9j\u00e0 d\u00e9montr\u00e9es.<\/p>\n<p class=\"whitespace-pre-wrap\">Par exemple, sa toute premi\u00e8re proposition est : \u00ab\u00a0Construire un triangle \u00e9quilat\u00e9ral sur un segment donn\u00e9\u00a0\u00bb. Et il le d\u00e9montre en quelques \u00e9tapes logiques.<\/p>\n<p class=\"whitespace-pre-wrap\">Cette fa\u00e7on si rigoureuse de proc\u00e9der a servi de mod\u00e8le jusqu\u2019\u00e0 aujourd\u2019hui. En math\u00e9matiques, quand on dit qu\u2019une d\u00e9monstration est \u00ab\u00a0euclidienne\u00a0\u00bb, \u00e7a veut dire qu\u2019elle est irr\u00e9prochable !<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Linfluence_des_Elements\"><\/span>L\u2019influence des \u00c9l\u00e9ments<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"whitespace-pre-wrap\">Les \u00c9l\u00e9ments ont \u00e9t\u00e9 LE manuel de g\u00e9om\u00e9trie pendant des si\u00e8cles. D\u2019abord chez les Grecs, puis au Moyen \u00c2ge, et m\u00eame de grands scientifiques comme Galil\u00e9e ou Newton ont \u00e9t\u00e9 nourris \u00e0 l\u2019ouvrage d\u2019Euclide !<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-3076 size-full\" src=\"https:\/\/lesminis.fr\/blog\/wp-content\/uploads\/2024\/02\/3-6.jpg\" alt=\"L'influence des \u00e9l\u00e9ment salle de classe math\u00e9matiques g\u00e9om\u00e9trie\" width=\"1000\" height=\"1000\" srcset=\"https:\/\/lesminis.fr\/blog\/wp-content\/uploads\/2024\/02\/3-6.jpg 1000w, https:\/\/lesminis.fr\/blog\/wp-content\/uploads\/2024\/02\/3-6-300x300.jpg 300w, https:\/\/lesminis.fr\/blog\/wp-content\/uploads\/2024\/02\/3-6-150x150.jpg 150w, https:\/\/lesminis.fr\/blog\/wp-content\/uploads\/2024\/02\/3-6-768x768.jpg 768w, https:\/\/lesminis.fr\/blog\/wp-content\/uploads\/2024\/02\/3-6-696x696.jpg 696w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/p>\n<p class=\"whitespace-pre-wrap\">Bien s\u00fbr, les math\u00e9matiques ont beaucoup progress\u00e9 depuis l&rsquo;Antiquit\u00e9. Mais de nombreux th\u00e9or\u00e8mes et raisonnements vus au coll\u00e8ge viennent directement des \u00c9l\u00e9ments.<\/p>\n<p class=\"whitespace-pre-wrap\">Alors la prochaine fois que tu \u00e9tudies un polygone ou calcules une aire, n\u2019oublie pas que c&rsquo;est Gr\u00e2ce \u00e0 Euclide que la g\u00e9om\u00e9trie est devenue beaucoup plus facile.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Euclide_et_la_geometrie_moderne\"><\/span>Euclide et la g\u00e9om\u00e9trie moderne<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Tu te demandes peut-\u00eatre : \u00ab\u00a0Mais en quoi tout cela est-il important pour moi ?\u00a0\u00bb Eh bien, chaque fois que tu observes un objet, que tu mesures une distance ou que tu regardes une carte, tu utilises des principes \u00e9tablis par Euclide il y a plus de 2000 ans. Ses th\u00e9ories sur les propri\u00e9t\u00e9s des formes et des espaces sont \u00e0 la base de tout, de l&rsquo;architecture \u00e0 la navigation, en passant par la technologie et l&rsquo;art.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduction Il y a environ 2300 ans vivait un grand math\u00e9maticien grec nomm\u00e9 Euclide. Son \u0153uvre la plus c\u00e9l\u00e8bre, les \u00c9l\u00e9ments, est un des livres les plus lus et \u00e9tudi\u00e9s de tous les temps ! Les \u00c9l\u00e9ments rassemblent les connaissances de g\u00e9om\u00e9trie et de math\u00e9matiques de l\u2019\u00e9poque. C&rsquo;est un peu la \u00ab\u00a0bible\u00a0\u00bb des math\u00e9maticiens, leur [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":3074,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[105],"tags":[],"class_list":["post-3073","post","type-post","status-publish","format-standard","has-post-thumbnail","category-minispedago-predagogie-montessori-activites-developpement"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.6 (Yoast SEO v27.6) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Euclide et les \u00c9l\u00e9ments, la bible de la g\u00e9om\u00e9trie<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/lesminis.fr\/blog\/euclide-et-les-elements-la-bible-de-la-geometrie\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Euclide et les \u00c9l\u00e9ments, la bible de la g\u00e9om\u00e9trie\" \/>\n<meta property=\"og:description\" content=\"Introduction Il y a environ 2300 ans vivait un grand math\u00e9maticien grec nomm\u00e9 Euclide. Son \u0153uvre la plus c\u00e9l\u00e8bre, les \u00c9l\u00e9ments, est un des livres les plus lus et \u00e9tudi\u00e9s de tous les temps ! Les \u00c9l\u00e9ments rassemblent les connaissances de g\u00e9om\u00e9trie et de math\u00e9matiques de l\u2019\u00e9poque. 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