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Ancient Greek mathematics
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=== Applied mathematics === Astronomy was considered one of the {{tlit|grc|mathΔmatΓ‘}}, and accordingly many mathematicians devoted time to astronomy. The ''[[Little Astronomy]]'' is a collection of short works, including [[Theodosius of Bithynia|Theodosius]]'s [[Theodosius' Spherics|''Spherics'']], [[Autolycus of Pitane|Autolycus]]'s ''On the Moving Sphere'', Euclid's ''Optics'' and ''Phaenomena'', [[Aristarchus of Samos|Aristarchus]]'s ''[[On the Sizes and Distances (Aristarchus)|On the Sizes and Distances]]'', that were part of an astronomy curriculum beginning in the 2nd century AD and transmitted as a group. The collection was translated into Arabic with a few additions such as Euclid's ''Data'', [[Menelaus of Alexandria|Menelaus]]'s ''Spherics'' (extant in Arabic only), and various works by Archimedes as the ''Middle Books'', intermediate between Euclid's ''Elements'' and Ptolemy's ''[[Almagest]]''.<ref>{{cite book |last=Evans |first=James |url=https://archive.org/details/historypracticeo0000evan/page/89/mode/1up?q=%22little+astronomy%22 |title=The History & Practice of Ancient Astronomy |publisher=Oxford University Press |year=1998 |isbn=0-19-509539-1 |at="The ''Little Astronomy''", {{pgs|89β91}} |url-access=limited}} {{pb}} {{cite thesis |last=Roughan |first=Christine |title=The Little Astronomy and Middle Books between the 2nd and 13th Centuries CE: Transmissions of Astronomical Curricula |type=PhD thesis |publisher=New York University |url=https://archive.nyu.edu/handle/2451/64391 |year=2023}} </ref>{{sfn|Acerbi|2018|pp=284-285}} The development of [[trigonometry]] as a synthesis of Babylonian and Greek methods is commonly attributed to [[Hipparchus]], who made extensive astronomical observations and wrote several mathematical treatises, though only his ''Commentary on the Phaenomena of Eudoxus and Aratus'' survives.<ref name="10.1111_j.1600-0498.1974.tb00205.x" /><ref>{{Cite journal |last=Duke |first=D. |date=2011 |title=The very early history of trigonometry. |url=https://people.sc.fsu.edu/~dduke/earlytrig12.pdf |journal=DIO: The International Journal of Scientific History |volume=17 |pages=34β42}}</ref><ref name=":3">{{Cite web |last=Jones |first=A. |date=1994 |title=Greek mathematics to AD 300 |url=https://www.routledge.com/Companion-Encyclopedia-of-the-History-and-Philosophy-of-the-Mathematical/Grattan-Guiness/p/book/9781138688117 |access-date=2021-05-26 |website=Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences: Volume One |pages=46β57}}</ref> In the 2nd century AD, Ptolemy wrote a work now called the ''[[Almagest]]'' explaining the motions of the stars and planets according to a geocentric model, and calculated out chord tables to a higher degree of precision than had been done previously, along with an instruction manual, ''[[Handy Tables]]''.<ref>{{Cite web |last=Lambrou |first=M. |date=2003 |title=Theon of Alexandria and Hypatia |url=https://www.historyoftheancientworld.com/2012/01/theon-of-alexandria-and-hypatia/ |access-date=2021-05-26 |website=History of the Ancient World}}</ref><ref>{{Cite book |last=Tihon |url=https://books.google.com/books?id=r1QazgEACAAJ |title=Ptolemaiou Procheiroi Kanones. Ptolemy's Handy Tables. Volume 1b: Tables A1-A2. Transcription and Commentary |date=2011 |publisher=Peeters |isbn=978-2-7584-0117-9}}</ref> Ancient Greeks often considered the study of optics to be a part of applied geometry.{{sfn|Acerbi|2018|pp=281β282}} An extant work on [[catoptrics]] is dubiously attributed to Euclid. Archimedes is known to have written a now lost work on catoptrics, while [[Diocles (mathematician)|Diocles]]' ''On Burning Mirrors'' is extant in an Arabic translation.{{sfn|Acerbi|2018}} Other examples of [[applied mathematics]] around this time include the construction of analogue computers like the [[Antikythera mechanism]], the accurate measurement of the [[circumference of the Earth]] by [[Eratosthenes]], and the mathematical and mechanical works of [[Heron of Alexandria|Heron]].<ref>{{Cite journal |last=Edmunds |first=M. G. |date=2014-10-02 |title=The Antikythera mechanism and the mechanical universe |journal=Contemporary Physics |volume=55 |issue=4 |pages=263β285 |doi=10.1080/00107514.2014.927280}}</ref><ref>Russo, Lucio (2004). ''The Forgotten Revolution''. Berlin: Springer. pp. 273β277.</ref><ref>{{Cite journal |last=Tybjerg |first=Karin |date=2004-12-01 |title=Hero of Alexandria's Mechanical Geometry |journal=Apeiron |volume=37 |issue=4 |pages=29β56 |doi=10.1515/APEIRON.2004.37.4.29}}</ref>
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