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Ancient Greek mathematics
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=== Geometry === {{main|Straightedge and compass construction}} [[File:Platonic Solids Transparent.svg|thumb|The construction of the [[Platonic solids]], from Book XIII of the ''Elements'', is often credited to Theaetetus, who was active around the time of Plato]] During the Hellenistic age, three construction problems in geometry became famous: [[doubling the cube]], [[angle trisection|trisecting an angle]], and [[squaring the circle]], all of which are now known to be impossible with a straight edge and compass. Many attempts were made using [[neusis]] constructions including the [[Cissoid of Diocles]], [[Quadratrix]], and the [[Conchoid (mathematics)|Conchoid]] of Nicomedes.{{sfn|Knorr|1986}} Regular polygons and polyhedra had already been known before Euclid's ''Elements'', but Archimedes extended their study to include semiregular polyhedra, also known as [[Archimedean solid]]s. A work transmitted as Book XIV of Euclid's ''Elements'', likely written a few centuries later by [[Hypsicles]], lists other works on the topic, such [[Aristaeus the Elder]]'s ''Comparison of Five Figures'' and Apollonius of Perga's ''Comparison of the Dodecahedron and the Icosahedron''.{{sfn|Acerbi|2018}} Another book, transmitted as Book XV of Euclid's ''Elements'', which was compiled in the 6th century AD, provides further developments.{{sfn|Acerbi|2018}} Most of the works that became part of a standard mathematical curriculum in late antiquity were composed during the Hellenistic period: ''[[Data (Euclid)|Data]]'' and ''[[Porisms]]'' by Euclid, several works by Apollonius of Perga including ''Cutting off a ratio'', ''Cutting off an area'', ''Determinate section'', ''Tangencies'', and ''Neusis'', and several works dealing with [[Locus (mathematics)|loci]], including ''Plane Loci'' and ''Conics'' by Apollonius, ''Solid Loci'' by [[Aristaeus the Elder]], ''Loci on a Surface'' by Euclid, and ''On Means'' by [[Eratosthenes of Cyrene]]. All of these works other than ''Data'', ''Conics'' Books IβVII, and ''Cutting off a ratio'' are lost but are known from Book 7 of [[Pappus of Alexandria|Pappus]]' ''Collection''.<ref>{{cite book |last1=Pappus |first1=of Alexandria |title=Book 7 of the Collection |date=1986 |location=New York |publisher=Springer |isbn=978-0-387-96257-3 |url=https://archive.org/details/book7ofcollectio0000papp |access-date=4 May 2025}}</ref>
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