{"id":85,"date":"2018-06-19T13:09:49","date_gmt":"2018-06-19T17:09:49","guid":{"rendered":"https:\/\/library.brown.edu\/create\/poetryofscience\/?page_id=85"},"modified":"2025-07-17T12:03:23","modified_gmt":"2025-07-17T16:03:23","slug":"infernal-geometry","status":"publish","type":"page","link":"https:\/\/library.brown.edu\/create\/poetryofscience\/infernal-geometry\/","title":{"rendered":"Infernal Geometry"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">Infernal Geometry<\/h1>\n\n\n<nav style=\"font-style:normal;font-weight:600;\" class=\"is-responsive wp-block-navigation is-layout-flex wp-container-core-navigation-is-layout-db721894 wp-block-navigation-is-layout-flex\" aria-label=\"sections\" \n\t\t data-wp-interactive=\"core\/navigation\" data-wp-context='{\"overlayOpenedBy\":{\"click\":false,\"hover\":false,\"focus\":false},\"type\":\"overlay\",\"roleAttribute\":\"\",\"ariaLabel\":\"Menu\"}'><button aria-haspopup=\"dialog\" aria-label=\"Open menu\" class=\"wp-block-navigation__responsive-container-open\" \n\t\t\t\tdata-wp-on--click=\"actions.openMenuOnClick\"\n\t\t\t\tdata-wp-on--keydown=\"actions.handleMenuKeydown\"\n\t\t\t><svg width=\"24\" height=\"24\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 24 24\" aria-hidden=\"true\" focusable=\"false\"><path d=\"M4 7.5h16v1.5H4z\"><\/path><path d=\"M4 15h16v1.5H4z\"><\/path><\/svg><\/button>\n\t\t\t\t<div class=\"wp-block-navigation__responsive-container\"  id=\"modal-1\" \n\t\t\t\tdata-wp-class--has-modal-open=\"state.isMenuOpen\"\n\t\t\t\tdata-wp-class--is-menu-open=\"state.isMenuOpen\"\n\t\t\t\tdata-wp-watch=\"callbacks.initMenu\"\n\t\t\t\tdata-wp-on--keydown=\"actions.handleMenuKeydown\"\n\t\t\t\tdata-wp-on--focusout=\"actions.handleMenuFocusout\"\n\t\t\t\ttabindex=\"-1\"\n\t\t\t>\n\t\t\t\t\t<div class=\"wp-block-navigation__responsive-close\" tabindex=\"-1\">\n\t\t\t\t\t\t<div class=\"wp-block-navigation__responsive-dialog\" \n\t\t\t\tdata-wp-bind--aria-modal=\"state.ariaModal\"\n\t\t\t\tdata-wp-bind--aria-label=\"state.ariaLabel\"\n\t\t\t\tdata-wp-bind--role=\"state.roleAttribute\"\n\t\t\t>\n\t\t\t\t\t\t\t<button aria-label=\"Close menu\" class=\"wp-block-navigation__responsive-container-close\" \n\t\t\t\tdata-wp-on--click=\"actions.closeMenuOnClick\"\n\t\t\t><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 24 24\" width=\"24\" height=\"24\" aria-hidden=\"true\" focusable=\"false\"><path d=\"m13.06 12 6.47-6.47-1.06-1.06L12 10.94 5.53 4.47 4.47 5.53 10.94 12l-6.47 6.47 1.06 1.06L12 13.06l6.47 6.47 1.06-1.06L13.06 12Z\"><\/path><\/svg><\/button>\n\t\t\t\t\t\t\t<div class=\"wp-block-navigation__responsive-container-content\" \n\t\t\t\tdata-wp-watch=\"callbacks.focusFirstElement\"\n\t\t\t id=\"modal-1-content\">\n\t\t\t\t\t\t\t\t<ul style=\"font-style:normal;font-weight:600;\" class=\"wp-block-navigation__container is-responsive wp-block-navigation\"><li class=\" wp-block-navigation-item  menu-item menu-item-type-post_type menu-item-object-page wp-block-navigation-link\"><a class=\"wp-block-navigation-item__content\"  href=\"https:\/\/library.brown.edu\/create\/poetryofscience\/crafting-a-cosmos\/\" title=\"\"><span class=\"wp-block-navigation-item__label\">Crafting a Cosmos<\/span><\/a><\/li><li class=\" wp-block-navigation-item  menu-item menu-item-type-post_type menu-item-object-page wp-block-navigation-link\"><a class=\"wp-block-navigation-item__content\"  href=\"https:\/\/library.brown.edu\/create\/poetryofscience\/mapping-hell-cartography-and-the-comedy\/\" title=\"\"><span class=\"wp-block-navigation-item__label\">Mapping Hell<\/span><\/a><\/li><li class=\" wp-block-navigation-item  menu-item menu-item-type-post_type menu-item-object-page wp-block-navigation-link\"><a class=\"wp-block-navigation-item__content\"  href=\"https:\/\/library.brown.edu\/create\/poetryofscience\/dante-and-the-new-world\/\" title=\"\"><span class=\"wp-block-navigation-item__label\">Dante &amp; the New World<\/span><\/a><\/li><li class=\" wp-block-navigation-item  menu-item menu-item-type-post_type menu-item-object-page wp-block-navigation-link\"><a class=\"wp-block-navigation-item__content\"  href=\"https:\/\/library.brown.edu\/create\/poetryofscience\/infernal-geometry\/\" title=\"\"><span class=\"wp-block-navigation-item__label\">Infernal Geometry<\/span><\/a><\/li><li class=\" wp-block-navigation-item  menu-item menu-item-type-post_type menu-item-object-page wp-block-navigation-link\"><a class=\"wp-block-navigation-item__content\"  href=\"https:\/\/library.brown.edu\/create\/poetryofscience\/stars-and-moonspots-dantes-astronomy\/\" title=\"\"><span class=\"wp-block-navigation-item__label\">Stars &amp; Moonspots<\/span><\/a><\/li><li class=\" wp-block-navigation-item  menu-item menu-item-type-post_type menu-item-object-page wp-block-navigation-link\"><a class=\"wp-block-navigation-item__content\"  href=\"https:\/\/library.brown.edu\/create\/poetryofscience\/envisioning-the-heavens-purgatory-and-paradise\/\" title=\"\"><span class=\"wp-block-navigation-item__label\">Envisioning the Heavens<\/span><\/a><\/li><li class=\" wp-block-navigation-item  menu-item menu-item-type-post_type menu-item-object-page wp-block-navigation-link\"><a class=\"wp-block-navigation-item__content\"  href=\"https:\/\/library.brown.edu\/create\/poetryofscience\/archeology-and-mathematics-dante-in-the-19th-century\/\" title=\"\"><span class=\"wp-block-navigation-item__label\">Archeology &amp; Mathematics<\/span><\/a><\/li><li class=\" wp-block-navigation-item  menu-item menu-item-type-post_type menu-item-object-page wp-block-navigation-link\"><a class=\"wp-block-navigation-item__content\"  href=\"https:\/\/library.brown.edu\/create\/poetryofscience\/hells-beasts-and-bodies-the-anatomy-of-hell\/\" title=\"\"><span class=\"wp-block-navigation-item__label\">Hell\u2019s Beasts &amp; Bodies<\/span><\/a><\/li><li class=\" wp-block-navigation-item  menu-item menu-item-type-post_type menu-item-object-page wp-block-navigation-link\"><a class=\"wp-block-navigation-item__content\"  href=\"https:\/\/library.brown.edu\/create\/poetryofscience\/women-authors-of-science-and-the-comedy\/\" title=\"\"><span class=\"wp-block-navigation-item__label\">Women Authors of Science &amp; the Comedy<\/span><\/a><\/li><\/ul>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/nav>\n\n\n<div style=\"height:32px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>Dante guides the reader as Apelles paints, who through his high genius, illustrated by a subtle mind and by mathematical knowledge, places before our eyes the form and measurements of Hell.<\/p>\n<\/blockquote>\n\n\n\n<p class=\"has-text-align-right\"><strong>\u2014Cristoforo Landino, 1481<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div style=\"height:17px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-group has-background is-layout-grid wp-container-core-group-is-layout-1a149459 wp-block-group-is-layout-grid\" style=\"background-color:#faf3e6\">\n<figure class=\"wp-block-image is-resized\" style=\"margin-top:var(--wp--preset--spacing--40);margin-right:var(--wp--preset--spacing--40);margin-bottom:var(--wp--preset--spacing--40);margin-left:var(--wp--preset--spacing--40)\"><a href=\"https:\/\/library.brown.edu\/create\/poetryofscience\/infernal-geometry\/d27_aeon0867_1s-b1578m\/\" rel=\"attachment wp-att-193\"><img loading=\"lazy\" decoding=\"async\" width=\"1706\" height=\"2500\" src=\"https:\/\/library.brown.edu\/create\/poetryofscience\/wp-content\/uploads\/sites\/63\/2018\/06\/D27_AEON0867_1S-B1578m.jpg\" alt=\"Dante con l'espositioni di Christoforo Landino et d'Alessandro Vellutello [Dante with the Commentaries of Cristoforo Landino and Alessandro Vellutello]\" class=\"wp-image-193\" style=\"width:200px\"\/><\/a><figcaption class=\"wp-element-caption\"><strong>1. <em>Dante con l&#8217;espositioni di Christoforo Landino et d&#8217;Alessandro Vellutello<\/em> [Dante with the Commentaries of Cristoforo Landino and Alessandro Vellutello]<\/strong><br>Dante Alighieri (1265\u20131321)<br>Venice: Giovanni Battista and Melchior Sessa and Brothers, 1578<br>Brown University Library, Chambers Dante Collection<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image is-resized\" style=\"margin-top:var(--wp--preset--spacing--40);margin-right:var(--wp--preset--spacing--40);margin-bottom:var(--wp--preset--spacing--40);margin-left:var(--wp--preset--spacing--40)\"><a href=\"https:\/\/library.brown.edu\/create\/poetryofscience\/infernal-geometry\/b-1595_902-cropped-s4\/\" rel=\"attachment wp-att-141\"><img loading=\"lazy\" decoding=\"async\" width=\"771\" height=\"1012\" src=\"https:\/\/library.brown.edu\/create\/poetryofscience\/wp-content\/uploads\/sites\/63\/2018\/06\/B-1595_902-cropped-s4.jpg\" alt=\"La divina commedia di Dante Alighieri Nobile Fiorentino ridotta a miglior lezione dagli Accademici della Crusca [The Divine Comedy of Dante Alighieri Noble Florentine Restored to Its Best Interpretation by the Academics of the Crusca]\" class=\"wp-image-141\" style=\"width:200px\"\/><\/a><figcaption class=\"wp-element-caption\"><strong>2. <em>La divina commedia di Dante Alighieri Nobile Fiorentino ridotta a miglior lezione dagli Accademici della Crusca<\/em> [The Divine Comedy of Dante Alighieri Noble Florentine Restored to Its Best Interpretation by the Academics of the Crusca]<\/strong><br>Dante Alighieri (1265\u20131321)<br>Florence, Italy: Domenico Manzani, 1595<br>Brown University Library, Chambers Dante Collection<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image is-resized\" style=\"margin-top:var(--wp--preset--spacing--40);margin-right:var(--wp--preset--spacing--40);margin-bottom:var(--wp--preset--spacing--40);margin-left:var(--wp--preset--spacing--40)\"><a href=\"https:\/\/library.brown.edu\/create\/poetryofscience\/infernal-geometry\/olio002132_2\/\" rel=\"attachment wp-att-136\"><img loading=\"lazy\" decoding=\"async\" width=\"1078\" height=\"1448\" src=\"https:\/\/library.brown.edu\/create\/poetryofscience\/wp-content\/uploads\/sites\/63\/2018\/06\/olio002132_2.jpg\" alt=\"Liber Elementorum [Elements]\" class=\"wp-image-136\" style=\"width:200px\"\/><\/a><figcaption class=\"wp-element-caption\"><strong>3. <em>Liber Elementorum<\/em> [Elements]<\/strong><br>Euclid (mid-fourth century BC\u2013mid-third century BC)<br>Venice, Italy: Erhard Ratdolt, 1482<br>Brown University Library, Lownes Science Collection<br>First printed illustrations of geometrical diagrams; some marginal annotations in an early hand, including mathematical notation and a few revisions to diagrams; possible note of ownership and arms in bottom border<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image is-resized\" style=\"margin-top:var(--wp--preset--spacing--40);margin-right:var(--wp--preset--spacing--40);margin-bottom:var(--wp--preset--spacing--40);margin-left:var(--wp--preset--spacing--40)\"><a href=\"https:\/\/library.brown.edu\/create\/poetryofscience\/infernal-geometry\/d22_aeon2316_qb41-s2x-1490m\/\" rel=\"attachment wp-att-138\"><img loading=\"lazy\" decoding=\"async\" width=\"1826\" height=\"2500\" src=\"https:\/\/library.brown.edu\/create\/poetryofscience\/wp-content\/uploads\/sites\/63\/2018\/06\/D22_AEON2316_QB41-S2x-1490m.jpg\" alt=\"Sphaera Mundi [Sphere of the World]\" class=\"wp-image-138\" style=\"width:200px\"\/><\/a><figcaption class=\"wp-element-caption\"><strong>4. <em>Sphaera Mundi<\/em> [Sphere of the World]<\/strong><br>Johannes de Sacrobosco (active 1230)<br>Venice, Italy: Bonetus Locatellus for Octavianus Scotus, 1490<br>Brown University Library, Lownes Science Collection<br>Many marginal annotations in brown ink; celestial spheres filled in by the reader<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image is-resized\" style=\"margin-top:var(--wp--preset--spacing--40);margin-right:var(--wp--preset--spacing--40);margin-bottom:var(--wp--preset--spacing--40);margin-left:var(--wp--preset--spacing--40)\"><a href=\"https:\/\/library.brown.edu\/create\/poetryofscience\/infernal-geometry\/d24-aeon2762_1s-qb215-c6-1581m\/\" rel=\"attachment wp-att-139\"><img loading=\"lazy\" decoding=\"async\" width=\"1712\" height=\"2500\" src=\"https:\/\/library.brown.edu\/create\/poetryofscience\/wp-content\/uploads\/sites\/63\/2018\/06\/D24-AEON2762_1S-QB215-C6-1581m.jpg\" alt=\"Gnomonices\" class=\"wp-image-139\" style=\"width:200px\"\/><\/a><figcaption class=\"wp-element-caption\"><strong>5. <em>Gnomonices<\/em><\/strong><br>Christopher Clavius (1538\u20131612)<br>Rome, Italy: Francesco Zanetti, 1581<br>Brown University Library, History of Science Collection<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-container-content-ec55e6f3\"><\/p>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>How far into Hell would you have to travel to reach the center of the earth? Approximately 3,400 miles, according to Antonio Manetti. Manetti\u2019s measurements of Hell went virtually unchallenged until Alessandro Vellutello proposed a radically different mathematical model in his 1544 commentary on the <em>Comedy<\/em> <strong>(1)<\/strong>. He proposed new figures for the height of Lucifer, which was triangulated from the circumference of the earth, the height of the giants (in Hell\u2019s ninth circle) and the distance of Hell\u2019s lowest circles. Manetti\u2019s calculations were eventually adopted, but only after 40 years of fierce debate among Dante scholars.<\/p>\n\n\n\n<p>Rendered in a spare style, the engraved map frontispiece of the Crusca Academy\u2019s edition of the <em>Comedy<\/em> <strong>(2)<\/strong> presents a more mathematical approach to representing the underworld. The three different projections represent the width, length and depth of Hell according to the measurements of Manetti. Although other mathematicians offered different models for the dimensions of Hell, Galileo confirmed Manetti\u2019s findings in his lectures on \u201cthe site, form, and measurements of the <em>Inferno<\/em>\u201d that he delivered to the Florentine Academy in 1588. In these lectures, Galileo used drawings to prove his calculations, which demonstrates how images played a significant role in sustaining mathematical arguments about the poem\u2019s structure. Indeed, some scholars argue that the 1595 engraving was based on Galileo\u2019s own drawings of Hell.<\/p>\n\n\n\n<p>The Crusca Academy, a group of Florentine intellectuals, was concerned with standardizing the Italian language. Its members were responsible for publishing the first modern dictionary of Italian. To prepare their edition of the <em>Comedy<\/em>, they collected almost 100 manuscripts and printed editions of Dante\u2019s poem in order to restore the poem to its original linguistic state. The Crusca text is considered to be the first critical edition of Dante\u2019s poem: Its frontispiece\u2019s notably flat and linear style perhaps reflects the rigorous and systematic approach to Dante\u2019s text.<\/p>\n\n\n\n<p>The Crusca\u2019s diagram of Hell engraving drew upon the visual tradition of infernal cartography, while in simultaneous conversation with illustrations of mathematical and astronomical books, such as Euclid\u2019s <em>Elements<\/em> <strong>(3)<\/strong>, Ptolemy\u2019s <em>Almagest<\/em> and Sacrobosco\u2019s <em>Sphere<\/em> <strong>(4)<\/strong>, the primary math and astronomy textbooks in the medieval and early modern periods. These books also laid the groundwork for innovative printing techniques of geometrical figures, mathematical models and planetary motion. In many cases, the diagrams were annotated, copied, colored or cut out to create instruments to help readers calculate the movement of the hours, planets and stars. The resemblance between the 1595 frontispiece and the instrument <strong>(5)<\/strong> depicted in Christopher Clavius\u2019s <em>Gnomonices<\/em> (referring to the part of the sundial that casts a shadow) suggests that the engraving also served as a tool for readers to calculate Hell\u2019s dimensions more precisely, and perhaps, to experiment with their own models of Hell.<\/p>\n\n\n\n<p>&nbsp;<\/p>\n\n\n\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Infernal Geometry Dante guides the reader as Apelles paints, who through his high genius, illustrated by a subtle mind and by mathematical knowledge, places before our eyes the form and measurements of Hell. \u2014Cristoforo Landino, 1481 How far into Hell would you have to travel to reach the center of the earth? Approximately 3,400 miles, <a href=\"https:\/\/library.brown.edu\/create\/poetryofscience\/infernal-geometry\/\" class=\"more-link\">&#8230;<span class=\"screen-reader-text\">  Infernal Geometry<\/span><\/a><\/p>\n","protected":false},"author":36,"featured_media":0,"parent":0,"menu_order":4,"comment_status":"closed","ping_status":"closed","template":"template-full-width-no-menu.php","meta":{"footnotes":""},"class_list":["post-85","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/library.brown.edu\/create\/poetryofscience\/wp-json\/wp\/v2\/pages\/85","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/library.brown.edu\/create\/poetryofscience\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/library.brown.edu\/create\/poetryofscience\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/library.brown.edu\/create\/poetryofscience\/wp-json\/wp\/v2\/users\/36"}],"replies":[{"embeddable":true,"href":"https:\/\/library.brown.edu\/create\/poetryofscience\/wp-json\/wp\/v2\/comments?post=85"}],"version-history":[{"count":15,"href":"https:\/\/library.brown.edu\/create\/poetryofscience\/wp-json\/wp\/v2\/pages\/85\/revisions"}],"predecessor-version":[{"id":407,"href":"https:\/\/library.brown.edu\/create\/poetryofscience\/wp-json\/wp\/v2\/pages\/85\/revisions\/407"}],"wp:attachment":[{"href":"https:\/\/library.brown.edu\/create\/poetryofscience\/wp-json\/wp\/v2\/media?parent=85"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}