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Dionysodorus - Wikipedia

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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Dionysodorus</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. 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<div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Ancient Greek mathematician (c. 250 BC – 190 BC)</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about the 3rd century BC mathematician. For the 5th century sophist, see <a href="/wiki/Dionysodorus_(sophist)" title="Dionysodorus (sophist)">Dionysodorus (sophist)</a>. For the 1st century AD mathematician, see <a href="/wiki/Dionysodorus_of_Amaseia" title="Dionysodorus of Amaseia">Dionysodorus of Amaseia</a>.</div> <p><b>Dionysodorus of Caunus</b> (<a href="/wiki/Ancient_Greek_language" class="mw-redirect" title="Ancient Greek language">Ancient Greek</a>: <span lang="grc">Διονυσόδωρος ὁ Καύνειος</span>, c. 250 BC – c. 190 BC) was an ancient <a href="/wiki/List_of_Greek_mathematicians" title="List of Greek mathematicians">Greek mathematician</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Life_and_work">Life and work</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dionysodorus&amp;action=edit&amp;section=1" title="Edit section: Life and work"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Little is known about the life of Dionysodorus. <a href="/wiki/Pliny_the_Elder" title="Pliny the Elder">Pliny the Elder</a> writes about a Dionysodorus who measured the Earth's circumference, however he is probably the one from <a href="/wiki/Pontus_(region)" title="Pontus (region)">Pontus</a> and different from the one from <a href="/wiki/Kaunos" title="Kaunos">Caunus</a> as <a href="/wiki/Strabo" title="Strabo">Strabo</a> differentiates between the two mathematicians.<sup id="cite_ref-:0_1-0" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">&#91;</span>1<span class="cite-bracket">&#93;</span></a></sup> </p><p>Dionysodorus is remembered for solving the <a href="/wiki/Cubic_equation" title="Cubic equation">cubic equation</a> by means of the intersection of a rectangular <a href="/wiki/Hyperbola" title="Hyperbola">hyperbola</a> and a <a href="/wiki/Parabola" title="Parabola">parabola</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">&#91;</span>2<span class="cite-bracket">&#93;</span></a></sup> <a href="/wiki/Eutocius" class="mw-redirect" title="Eutocius">Eutocius</a> credits Dionysodorus with the method of cutting a sphere into a given ratio, as described by him.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">&#91;</span>3<span class="cite-bracket">&#93;</span></a></sup> <a href="/wiki/Hero_of_Alexandria" title="Hero of Alexandria">Heron</a> mentions a work by Dionysauras entitled <i>On the Tore</i>, in which the volume of a <a href="/wiki/Torus" title="Torus">torus</a> is calculated and found to be equal to the area of the generating circle multiplied by the circumference of the circle created by tracing the center of the generating circle as it rotates about the torus's axis of revolution. Dionysodorus used <a href="/wiki/Archimedes" title="Archimedes">Archimedes</a>' methods to prove this result.<sup id="cite_ref-:0_1-1" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">&#91;</span>1<span class="cite-bracket">&#93;</span></a></sup> </p><p>It is also likely that this Dionysodorus was the inventor of a conical <a href="/wiki/Sundial" title="Sundial">sundial</a>.<sup id="cite_ref-:0_1-2" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">&#91;</span>1<span class="cite-bracket">&#93;</span></a></sup> Pliny's mentioning tells of an inscription placed on his tomb, addressed to the world above, stating that he had been to the centre of the Earth and found it 42 thousand <a href="/wiki/Stadion_(unit_of_length)" class="mw-redirect" title="Stadion (unit of length)">stadia</a> distant.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">&#91;</span>4<span class="cite-bracket">&#93;</span></a></sup> Pliny calls this a striking instance of Greek vanity; but this figure compares well with the modern measurement. </p> <div class="mw-heading mw-heading2"><h2 id="Citations_and_footnotes">Citations and footnotes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dionysodorus&amp;action=edit&amp;section=2" title="Edit section: Citations and footnotes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-:0-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:0_1-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Dionysodorus">"Dionysodorus biography"</a>. <i>mathshistory.st-andrews.ac.uk</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2023-04-13</span></span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=mathshistory.st-andrews.ac.uk&amp;rft.atitle=Dionysodorus+biography&amp;rft_id=https%3A%2F%2Fmathshistory.st-andrews.ac.uk%2FBiographies%2FDionysodorus&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3ADionysodorus" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Heath (1921)</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">Eutocius, Comment on book ii. prop. 5, of the <i>Sphere and Cylinder</i> of <a href="/wiki/Archimedes" title="Archimedes">Archimedes</a></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">Pliny, <i>Hist. Nat.</i> ii. 109</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dionysodorus&amp;action=edit&amp;section=3" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/T._L._Heath" class="mw-redirect" title="T. L. Heath">T. L. Heath</a>, <a href="//archive.org/details/cu31924008704219" class="extiw" title="iarchive:cu31924008704219">A History of Greek Mathematics II</a> (Oxford, 1921).</li> <li>Netz, Reviel. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=kTDRJwCCMecC"><i>The Transformations of Mathematics in the Early Mediterranean World</i></a>. Cambridge University Press, 2004. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a>&#160;<a href="/wiki/Special:BookSources/0-521-82996-8" title="Special:BookSources/0-521-82996-8">0-521-82996-8</a>. Pags. 29-39.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dionysodorus&amp;action=edit&amp;section=4" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO&#39;ConnorRobertson" class="citation cs2">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" class="mw-redirect" title="Edmund F. Robertson">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Dionysodorus.html">"Dionysodorus"</a>, <i><a href="/wiki/MacTutor_History_of_Mathematics_Archive" title="MacTutor History of Mathematics Archive">MacTutor History of Mathematics Archive</a></i>, <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a></cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=bookitem&amp;rft.atitle=Dionysodorus&amp;rft.btitle=MacTutor+History+of+Mathematics+Archive&amp;rft.pub=University+of+St+Andrews&amp;rft.aulast=O%27Connor&amp;rft.aufirst=John+J.&amp;rft.au=Robertson%2C+Edmund+F.&amp;rft_id=https%3A%2F%2Fmathshistory.st-andrews.ac.uk%2FBiographies%2FDionysodorus.html&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3ADionysodorus" class="Z3988"></span></li></ul> <div class="navbox-styles"><style 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mathematics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_Greek_mathematicians" title="List of Greek mathematicians">Mathematicians</a><br /><a href="/wiki/Timeline_of_ancient_Greek_mathematicians" title="Timeline of ancient Greek mathematicians">(timeline)</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anaxagoras" title="Anaxagoras">Anaxagoras</a></li> <li><a href="/wiki/Anthemius_of_Tralles" title="Anthemius of Tralles">Anthemius</a></li> <li><a href="/wiki/Archytas" title="Archytas">Archytas</a></li> <li><a href="/wiki/Aristaeus_the_Elder" title="Aristaeus the Elder">Aristaeus the Elder</a></li> <li><a href="/wiki/Aristarchus_of_Samos" title="Aristarchus of Samos">Aristarchus</a></li> <li><a href="/wiki/Aristotle" title="Aristotle">Aristotle</a></li> <li><a href="/wiki/Apollonius_of_Perga" title="Apollonius of Perga">Apollonius</a></li> <li><a href="/wiki/Archimedes" title="Archimedes">Archimedes</a></li> <li><a href="/wiki/Autolycus_of_Pitane" title="Autolycus of Pitane">Autolycus</a></li> <li><a href="/wiki/Bion_of_Abdera" title="Bion of Abdera">Bion</a></li> <li><a href="/wiki/Bryson_of_Heraclea" title="Bryson of Heraclea">Bryson</a></li> <li><a href="/wiki/Callippus" title="Callippus">Callippus</a></li> <li><a href="/wiki/Carpus_of_Antioch" title="Carpus of Antioch">Carpus</a></li> <li><a href="/wiki/Chrysippus" title="Chrysippus">Chrysippus</a></li> <li><a href="/wiki/Cleomedes" title="Cleomedes">Cleomedes</a></li> <li><a href="/wiki/Conon_of_Samos" title="Conon of Samos">Conon</a></li> <li><a href="/wiki/Ctesibius" title="Ctesibius">Ctesibius</a></li> <li><a href="/wiki/Democritus" title="Democritus">Democritus</a></li> <li><a href="/wiki/Dicaearchus" title="Dicaearchus">Dicaearchus</a></li> <li><a href="/wiki/Diocles_(mathematician)" title="Diocles (mathematician)">Diocles</a></li> <li><a href="/wiki/Diophantus" title="Diophantus">Diophantus</a></li> <li><a href="/wiki/Dinostratus" title="Dinostratus">Dinostratus</a></li> <li><a class="mw-selflink selflink">Dionysodorus</a></li> <li><a href="/wiki/Domninus_of_Larissa" title="Domninus of Larissa">Domninus</a></li> <li><a href="/wiki/Eratosthenes" title="Eratosthenes">Eratosthenes</a></li> <li><a href="/wiki/Eudemus_of_Rhodes" title="Eudemus of Rhodes">Eudemus</a></li> <li><a href="/wiki/Euclid" title="Euclid">Euclid</a></li> <li><a href="/wiki/Eudoxus_of_Cnidus" title="Eudoxus of Cnidus">Eudoxus</a></li> <li><a href="/wiki/Eutocius_of_Ascalon" title="Eutocius of Ascalon">Eutocius</a></li> <li><a href="/wiki/Geminus" title="Geminus">Geminus</a></li> <li><a href="/wiki/Heliodorus_of_Larissa" title="Heliodorus of Larissa">Heliodorus</a></li> <li><a href="/wiki/Hero_of_Alexandria" title="Hero of Alexandria">Heron</a></li> <li><a href="/wiki/Hipparchus" title="Hipparchus">Hipparchus</a></li> <li><a href="/wiki/Hippasus" title="Hippasus">Hippasus</a></li> <li><a href="/wiki/Hippias" title="Hippias">Hippias</a></li> <li><a href="/wiki/Hippocrates_of_Chios" title="Hippocrates of Chios">Hippocrates</a></li> <li><a href="/wiki/Hypatia" title="Hypatia">Hypatia</a></li> <li><a href="/wiki/Hypsicles" title="Hypsicles">Hypsicles</a></li> <li><a href="/wiki/Isidore_of_Miletus" title="Isidore of Miletus">Isidore of Miletus</a></li> <li><a href="/wiki/Leon_(mathematician)" title="Leon (mathematician)">Leon</a></li> <li><a href="/wiki/Marinus_of_Neapolis" title="Marinus of Neapolis">Marinus</a></li> <li><a href="/wiki/Menaechmus" title="Menaechmus">Menaechmus</a></li> <li><a href="/wiki/Menelaus_of_Alexandria" title="Menelaus of Alexandria">Menelaus</a></li> <li><a href="/wiki/Metrodorus_(grammarian)" title="Metrodorus (grammarian)">Metrodorus</a></li> <li><a href="/wiki/Nicomachus" title="Nicomachus">Nicomachus</a></li> <li><a href="/wiki/Nicomedes_(mathematician)" title="Nicomedes (mathematician)">Nicomedes</a></li> <li><a href="/wiki/Nicoteles_of_Cyrene" title="Nicoteles of Cyrene">Nicoteles</a></li> <li><a href="/wiki/Oenopides" title="Oenopides">Oenopides</a></li> <li><a href="/wiki/Pappus_of_Alexandria" title="Pappus of Alexandria">Pappus</a></li> <li><a href="/wiki/Perseus_(geometer)" title="Perseus (geometer)">Perseus</a></li> <li><a href="/wiki/Philolaus" title="Philolaus">Philolaus</a></li> <li><a href="/wiki/Philon" title="Philon">Philon</a></li> <li><a href="/wiki/Philonides_of_Laodicea" title="Philonides of Laodicea">Philonides</a></li> <li><a href="/wiki/Plato" title="Plato">Plato</a></li> <li><a href="/wiki/Porphyry_(philosopher)" title="Porphyry (philosopher)">Porphyry</a></li> <li><a href="/wiki/Posidonius" title="Posidonius">Posidonius</a></li> <li><a href="/wiki/Proclus" title="Proclus">Proclus</a></li> <li><a href="/wiki/Ptolemy" title="Ptolemy">Ptolemy</a></li> <li><a href="/wiki/Pythagoras" title="Pythagoras">Pythagoras</a></li> <li><a href="/wiki/Serenus_of_Antino%C3%B6polis" title="Serenus of Antinoöpolis">Serenus </a></li> <li><a href="/wiki/Simplicius_of_Cilicia" title="Simplicius of Cilicia">Simplicius</a></li> <li><a href="/wiki/Sosigenes_of_Alexandria" class="mw-redirect" title="Sosigenes of Alexandria">Sosigenes</a></li> <li><a href="/wiki/Sporus_of_Nicaea" title="Sporus of Nicaea">Sporus</a></li> <li><a href="/wiki/Thales_of_Miletus" title="Thales of Miletus">Thales</a></li> <li><a href="/wiki/Theaetetus_(mathematician)" title="Theaetetus (mathematician)">Theaetetus</a></li> <li><a href="/wiki/Theano_(philosopher)" title="Theano (philosopher)">Theano</a></li> <li><a href="/wiki/Theodorus_of_Cyrene" title="Theodorus of Cyrene">Theodorus</a></li> <li><a href="/wiki/Theodosius_of_Bithynia" title="Theodosius of Bithynia">Theodosius</a></li> <li><a href="/wiki/Theon_of_Alexandria" title="Theon of Alexandria">Theon of Alexandria</a></li> <li><a href="/wiki/Theon_of_Smyrna" title="Theon of Smyrna">Theon of Smyrna</a></li> <li><a href="/wiki/Thymaridas" title="Thymaridas">Thymaridas</a></li> <li><a href="/wiki/Xenocrates" title="Xenocrates">Xenocrates</a></li> <li><a href="/wiki/Zeno_of_Elea" title="Zeno of Elea">Zeno of Elea</a></li> <li><a href="/wiki/Zeno_of_Sidon" title="Zeno of Sidon">Zeno of Sidon</a></li> <li><a href="/wiki/Zenodorus_(mathematician)" title="Zenodorus (mathematician)">Zenodorus</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Treatises</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Almagest" title="Almagest">Almagest</a></i></li> <li><a href="/wiki/Archimedes_Palimpsest" title="Archimedes Palimpsest">Archimedes Palimpsest</a></li> <li><i><a href="/wiki/Arithmetica" title="Arithmetica">Arithmetica</a></i></li> <li><a href="/wiki/Apollonius_of_Perga#Conics" title="Apollonius of Perga"><i>Conics</i> <span style="font-size:85%;">(Apollonius)</span></a></li> <li><i><a href="/wiki/Catoptrics" title="Catoptrics">Catoptrics</a></i></li> <li><a href="/wiki/Data_(Euclid)" class="mw-redirect" title="Data (Euclid)"><i>Data</i> <span style="font-size:85%;">(Euclid)</span></a></li> <li><a href="/wiki/Euclid%27s_Elements" title="Euclid&#39;s Elements"><i>Elements</i> <span style="font-size:85%;">(Euclid)</span></a></li> <li><i><a href="/wiki/Measurement_of_a_Circle" title="Measurement of a Circle">Measurement of a Circle</a></i></li> <li><i><a href="/wiki/On_Conoids_and_Spheroids" title="On Conoids and Spheroids">On Conoids and Spheroids</a></i></li> <li><a href="/wiki/On_the_Sizes_and_Distances_(Aristarchus)" title="On the Sizes and Distances (Aristarchus)"><i>On the Sizes and Distances</i> <span style="font-size:85%;">(Aristarchus)</span></a></li> <li><a href="/wiki/On_Sizes_and_Distances_(Hipparchus)" title="On Sizes and Distances (Hipparchus)"><i>On Sizes and Distances</i> <span style="font-size:85%;">(Hipparchus)</span></a></li> <li><a href="/wiki/Autolycus_of_Pitane" title="Autolycus of Pitane"><i>On the Moving Sphere</i> <span style="font-size:85%;">(Autolycus)</span></a></li> <li><a href="/wiki/Euclid%27s_Optics" title="Euclid&#39;s Optics"><i>Optics</i> <span style="font-size:85%;">(Euclid)</span></a></li> <li><i><a href="/wiki/On_Spirals" title="On Spirals">On Spirals</a></i></li> <li><i><a href="/wiki/On_the_Sphere_and_Cylinder" title="On the Sphere and Cylinder">On the Sphere and Cylinder</a></i></li> <li><i><a href="/wiki/Ostomachion" title="Ostomachion">Ostomachion</a></i></li> <li><i><a href="/wiki/Planisphaerium" title="Planisphaerium">Planisphaerium</a></i></li> <li><a href="/wiki/Theodosius%27_Spherics" title="Theodosius&#39; Spherics"><i>Spherics</i> <span style="font-size:85%;">(Theodosius)</span></a></li> <li><a href="/wiki/Menelaus_of_Alexandria" title="Menelaus of Alexandria"><i>Spherics</i> <span style="font-size:85%;">(Menelaus)</span></a></li> <li><i><a href="/wiki/The_Quadrature_of_the_Parabola" class="mw-redirect" title="The Quadrature of the Parabola">The Quadrature of the Parabola</a></i></li> <li><i><a href="/wiki/The_Sand_Reckoner" title="The Sand Reckoner">The Sand Reckoner</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Problems</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Constructible_number" title="Constructible number">Constructible numbers</a> <ul><li><a href="/wiki/Angle_trisection" title="Angle trisection">Angle trisection</a></li> <li><a href="/wiki/Doubling_the_cube" title="Doubling the cube">Doubling the cube</a></li> <li><a href="/wiki/Squaring_the_circle" title="Squaring the circle">Squaring the circle</a></li></ul></li> <li><a href="/wiki/Problem_of_Apollonius" title="Problem of Apollonius">Problem of Apollonius</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts<br />and definitions</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Angle" title="Angle">Angle</a> <ul><li><a href="/wiki/Central_angle" title="Central angle">Central</a></li> <li><a href="/wiki/Inscribed_angle" title="Inscribed angle">Inscribed</a></li></ul></li> <li><a href="/wiki/Axiomatic_system" title="Axiomatic system">Axiomatic system</a> <ul><li><a href="/wiki/Axiom" title="Axiom">Axiom</a></li></ul></li> <li><a href="/wiki/Chord_(geometry)" title="Chord (geometry)">Chord</a></li> <li><a href="/wiki/Circles_of_Apollonius" title="Circles of Apollonius">Circles of Apollonius</a> <ul><li><a href="/wiki/Apollonian_circles" title="Apollonian circles">Apollonian circles</a></li> <li><a href="/wiki/Apollonian_gasket" title="Apollonian gasket">Apollonian gasket</a></li></ul></li> <li><a href="/wiki/Circumscribed_circle" title="Circumscribed circle">Circumscribed circle</a></li> <li><a href="/wiki/Commensurability_(mathematics)" title="Commensurability (mathematics)">Commensurability</a></li> <li><a href="/wiki/Diophantine_equation" title="Diophantine equation">Diophantine equation</a></li> <li><a href="https://en.wikiquote.org/wiki/Doctrine_of_proportion_(mathematics)" class="extiw" title="wikiquote:Doctrine of proportion (mathematics)">Doctrine of proportionality</a></li> <li><a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean geometry</a></li> <li><a href="/wiki/Golden_ratio" title="Golden ratio">Golden ratio</a></li> <li><a href="/wiki/Greek_numerals" title="Greek numerals">Greek numerals</a></li> <li><a href="/wiki/Incircle_and_excircles_of_a_triangle" class="mw-redirect" title="Incircle and excircles of a triangle">Incircle and excircles of a triangle</a></li> <li><a href="/wiki/Method_of_exhaustion" title="Method of exhaustion">Method of exhaustion</a></li> <li><a href="/wiki/Parallel_postulate" title="Parallel postulate">Parallel postulate</a></li> <li><a href="/wiki/Platonic_solid" title="Platonic solid">Platonic solid</a></li> <li><a href="/wiki/Lune_of_Hippocrates" title="Lune of Hippocrates">Lune of Hippocrates</a></li> <li><a href="/wiki/Quadratrix_of_Hippias" title="Quadratrix of Hippias">Quadratrix of Hippias</a></li> <li><a href="/wiki/Regular_polygon" title="Regular polygon">Regular polygon</a></li> <li><a href="/wiki/Straightedge_and_compass_construction" title="Straightedge and compass construction">Straightedge and compass construction</a></li> <li><a href="/wiki/Triangle_center" title="Triangle center">Triangle center</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Results</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">In <a href="/wiki/Euclid%27s_elements" class="mw-redirect" title="Euclid&#39;s elements"><i>Elements</i></a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Angle_bisector_theorem" title="Angle bisector theorem">Angle bisector theorem</a></li> <li><a href="/wiki/Exterior_angle_theorem" title="Exterior angle theorem">Exterior angle theorem</a></li> <li><a href="/wiki/Euclidean_algorithm" title="Euclidean algorithm">Euclidean algorithm</a></li> <li><a href="/wiki/Euclid%27s_theorem" title="Euclid&#39;s theorem">Euclid's theorem</a></li> <li><a href="/wiki/Geometric_mean_theorem" title="Geometric mean theorem">Geometric mean theorem</a></li> <li><a href="/wiki/Greek_geometric_algebra" class="mw-redirect" title="Greek geometric algebra">Greek geometric algebra</a></li> <li><a href="/wiki/Hinge_theorem" title="Hinge theorem">Hinge theorem</a></li> <li><a href="/wiki/Inscribed_angle_theorem" class="mw-redirect" title="Inscribed angle theorem">Inscribed angle theorem</a></li> <li><a href="/wiki/Intercept_theorem" title="Intercept theorem">Intercept theorem</a></li> <li><a href="/wiki/Intersecting_chords_theorem" title="Intersecting chords theorem">Intersecting chords theorem</a></li> <li><a href="/wiki/Intersecting_secants_theorem" title="Intersecting secants theorem">Intersecting secants theorem</a></li> <li><a href="/wiki/Law_of_cosines" title="Law of cosines">Law of cosines</a></li> <li><a href="/wiki/Pons_asinorum" title="Pons asinorum">Pons asinorum</a></li> <li><a href="/wiki/Pythagorean_theorem" title="Pythagorean theorem">Pythagorean theorem</a></li> <li><a href="/wiki/Tangent-secant_theorem" class="mw-redirect" title="Tangent-secant theorem">Tangent-secant theorem</a></li> <li><a href="/wiki/Thales%27s_theorem" title="Thales&#39;s theorem">Thales's theorem</a></li> <li><a href="/wiki/Theorem_of_the_gnomon" title="Theorem of the gnomon">Theorem of the gnomon</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Apollonius_of_Tyana" title="Apollonius of Tyana">Apollonius</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Apollonius%27s_theorem" title="Apollonius&#39;s theorem">Apollonius's theorem</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aristarchus%27s_inequality" title="Aristarchus&#39;s inequality">Aristarchus's inequality</a></li> <li><a href="/wiki/Crossbar_theorem" title="Crossbar theorem">Crossbar theorem</a></li> <li><a href="/wiki/Heron%27s_formula" title="Heron&#39;s formula">Heron's formula</a></li> <li><a href="/wiki/Irrational_number" title="Irrational number">Irrational numbers</a></li> <li><a href="/wiki/Law_of_sines" title="Law of sines">Law of sines</a></li> <li><a href="/wiki/Menelaus%27s_theorem" title="Menelaus&#39;s theorem">Menelaus's theorem</a></li> <li><a href="/wiki/Pappus%27s_area_theorem" title="Pappus&#39;s area theorem">Pappus's area theorem</a></li> <li><a href="/wiki/Diophantus_II.VIII" title="Diophantus II.VIII">Problem II.8 of <i>Arithmetica</i></a></li> <li><a href="/wiki/Ptolemy%27s_inequality" title="Ptolemy&#39;s inequality">Ptolemy's inequality</a></li> <li><a href="/wiki/Ptolemy%27s_table_of_chords" title="Ptolemy&#39;s table of chords">Ptolemy's table of chords</a></li> <li><a href="/wiki/Ptolemy%27s_theorem" title="Ptolemy&#39;s theorem">Ptolemy's theorem</a></li> <li><a href="/wiki/Spiral_of_Theodorus" title="Spiral of Theodorus">Spiral of Theodorus</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Centers</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cyrene,_Libya" title="Cyrene, Libya">Cyrene</a></li> <li><a href="/wiki/Musaeum" class="mw-redirect" title="Musaeum">Mouseion of Alexandria</a></li> <li><a href="/wiki/Platonic_Academy" title="Platonic Academy">Platonic Academy</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ancient_Greek_astronomy" title="Ancient Greek astronomy">Ancient Greek astronomy</a></li> <li><a href="/wiki/Attic_numerals" title="Attic numerals">Attic numerals</a></li> <li><a href="/wiki/Greek_numerals" title="Greek numerals">Greek numerals</a></li> <li><a href="/wiki/Latin_translations_of_the_12th_century" title="Latin translations of the 12th century">Latin translations of the 12th century</a></li> <li><a href="/wiki/Non-Euclidean_geometry" title="Non-Euclidean geometry">Non-Euclidean geometry</a></li> <li><a href="/wiki/Philosophy_of_mathematics" title="Philosophy of mathematics">Philosophy of mathematics</a></li> <li><a href="/wiki/Neusis_construction" title="Neusis construction">Neusis construction</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">History of</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/A_History_of_Greek_Mathematics" title="A History of Greek Mathematics">A History of Greek Mathematics</a></i> <ul><li>by <a href="/wiki/Thomas_Heath_(classicist)" title="Thomas Heath (classicist)">Thomas Heath</a></li></ul></li> <li><a href="/wiki/History_of_algebra" title="History of algebra">algebra</a> <ul><li><a href="/wiki/Timeline_of_algebra" title="Timeline of algebra">timeline</a></li></ul></li> <li><a href="/wiki/History_of_arithmetic" class="mw-redirect" title="History of arithmetic">arithmetic</a> <ul><li><a href="/wiki/Timeline_of_numerals_and_arithmetic" title="Timeline of numerals and arithmetic">timeline</a></li></ul></li> <li><a href="/wiki/History_of_calculus" title="History of calculus">calculus</a> <ul><li><a href="/wiki/Timeline_of_calculus_and_mathematical_analysis" title="Timeline of calculus and mathematical analysis">timeline</a></li></ul></li> <li><a href="/wiki/History_of_geometry" title="History of geometry">geometry</a> <ul><li><a href="/wiki/Timeline_of_geometry" title="Timeline of geometry">timeline</a></li></ul></li> <li><a href="/wiki/History_of_logic" title="History of logic">logic</a> <ul><li><a href="/wiki/Timeline_of_mathematical_logic" title="Timeline of mathematical logic">timeline</a></li></ul></li> <li><a href="/wiki/History_of_mathematics" title="History of mathematics">mathematics</a> <ul><li><a href="/wiki/Timeline_of_mathematics" title="Timeline of mathematics">timeline</a></li></ul></li> <li><a href="/wiki/History_of_numbers" class="mw-redirect" title="History of numbers">numbers</a> <ul><li><a href="/wiki/Prehistoric_counting" class="mw-redirect" title="Prehistoric counting">prehistoric counting</a></li></ul></li> <li><a href="/wiki/History_of_ancient_numeral_systems" title="History of ancient numeral systems">numeral systems</a> <ul><li><a href="/wiki/List_of_numeral_systems" title="List of numeral systems">list</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other cultures</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mathematics_in_the_medieval_Islamic_world" title="Mathematics in the medieval Islamic world">Arabian/Islamic</a></li> <li><a href="/wiki/Babylonian_mathematics" title="Babylonian mathematics">Babylonian</a></li> <li><a href="/wiki/Chinese_mathematics" title="Chinese mathematics">Chinese</a></li> <li><a href="/wiki/Ancient_Egyptian_mathematics" title="Ancient Egyptian mathematics">Egyptian</a></li> <li><a href="/wiki/Mathematics_of_the_Incas" title="Mathematics of the Incas">Incan</a></li> <li><a href="/wiki/Indian_mathematics" title="Indian mathematics">Indian</a></li> <li><a href="/wiki/Japanese_mathematics" title="Japanese mathematics">Japanese</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><b><span class="nowrap"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Parthenon_from_west.jpg/16px-Parthenon_from_west.jpg" decoding="async" width="16" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Parthenon_from_west.jpg/24px-Parthenon_from_west.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Parthenon_from_west.jpg/32px-Parthenon_from_west.jpg 2x" data-file-width="2048" data-file-height="1536" /></span></span> </span><a href="/wiki/Portal:Ancient_Greece" title="Portal:Ancient Greece">Ancient Greece&#32;portal</a></b>&#160;&#8226;&#32; <b><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/16px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="16" height="16" class="mw-file-element" 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