Editing Thales of Miletus (section)

==== Right triangle inscribed in a circle ====
{{Main|Thales's theorem}}
[[File:Thales' Theorem Simple.svg|thumb|upright=0.8|Thales's theorem: if {{mvar|{{overline|AC}}}} is a diameter and {{mvar|B}} is a point on the diameter's circle, the angle {{math|1=∠ ''ABC''}} is a right angle.]]
[[Pamphile of Epidaurus|Pamphila]] says that, having learnt geometry from the Egyptians, Thales was the first to inscribe in a circle a right-angled triangle, whereupon he [[Animal sacrifice|sacrificed an ox]].<ref name="gazette"/> This is sometimes cited as history's first mathematical discovery.{{sfn|Boyer|1989|p="Ionia and the Pythagoreans" p. 43}} Due to the variations among testimonies, such as the story of the ox sacrifice being accredited to Pythagoras upon discovery of the [[Pythagorean theorem]] rather than Thales, some historians (such as D. R. Dicks) question whether such anecdotes have any historical worth whatsoever.<ref name="Dicks">{{cite journal |last=Dicks |first=D. R. |title=Thales |pages=294–309 |journal=The Classical Quarterly |volume=9 |date=November 1959 |issue=2 |doi=10.1017/S0009838800041586|s2cid=246881067 }}</ref>

It is believed the Babylonians knew the theorem for special cases.<ref>de Laet, Siegfried J. (1996). ''History of Humanity: Scientific and Cultural Development''. [[UNESCO]], Volume 3, p. 14. {{isbn|92-3-102812-X}}</ref><ref>Boyer, Carl B. and [[Uta Merzbach|Merzbach, Uta C.]] (2010). ''A History of Mathematics''. John Wiley and Sons, Chapter IV. {{isbn|0-470-63056-6}}</ref>
The theorem is mentioned and proved as part of the 31st proposition in the third book of [[Euclid]]'s ''[[Euclid's Elements|Elements]]''.<ref>{{cite book |last=Heath |first=Thomas L. |date=1956 |title=The Thirteen Books of Euclid's Elements |volume=2 (Books 3–9) |edition=2nd |publisher=Dover |isbn=0486600890 |page=61 |url=https://archive.org/details/thirteenbooksofe00eucl/page/61}} Originally published by Cambridge University Press. 1st edition 1908, 2nd edition 1926.</ref>  Dante's ''[[Paradiso (Dante)|Paradiso]]'' refers to Thales's theorem in the course of a speech.<ref>canto 13, lines 101–102</ref>