Editing Thales's theorem (section)

==History==
[[File:Dante-thales-theorem.jpg|thumb|right|upright=1.2|
<p>{{lang|la|Non si est dare primum motum esse}}<br>
{{lang|it|o se del mezzo cerchio far si puote<br>
triangol sì c'un recto nonauesse.}}<br>
– Dante's ''Paradiso'', Canto 13, lines 100–102</p>
<p>{{lang|la|Non si est dare primum motum esse,}}<br>
Or if in semicircle can be made<br>
Triangle so that it have no right angle.<br>
– English translation by [[Henry Wadsworth Longfellow|Longfellow]]</p>]]

[[Babylonian mathematics|Babylonian mathematician]]s knew this for special cases before Greek mathematicians proved it.<ref>de Laet, Siegfried J. (1996). ''History of Humanity: Scientific and Cultural Development''. [[UNESCO]], Volume 3, p. 14. {{isbn|92-3-102812-X}}</ref>

[[Thales of Miletus]] (early 6th century BC) is traditionally credited with proving the theorem; however, even by the 5th century BC there was nothing extant of Thales' writing, and inventions and ideas were attributed to men of wisdom such as Thales and Pythagoras by later [[doxography|doxographers]] based on hearsay and speculation.<ref name=dicks>{{cite journal |last=Dicks |first=D. R. |title=Thales |journal=The Classical Quarterly |year=1959 |volume=9 |number=2 |pages=294–309 |doi=10.1017/S0009838800041586 }}</ref><ref>{{cite web |first=G. Donald |last=Allen |title=Thales of Miletus |url=http://www.math.tamu.edu/~dallen/masters/Greek/thales.pdf |date=2000 |access-date=2012-02-12}}</ref> Reference to Thales was made by [[Proclus]] (5th century AD), and by [[Diogenes Laërtius]] (3rd century AD) documenting [[Pamphila of Epidaurus|Pamphila]]'s (1st century AD) statement that Thales "was the first to inscribe in a circle a right-angle triangle".<ref>{{cite journal |last1=Patronis |first1=Tasos |last2=Patsopoulos |first2=Dimitris |date=January 2006 |title=The Theorem of Thales: A Study of the Naming of Theorems in School Geometry Textbooks |journal=The International Journal for the History of Mathematics Education |issn=1932-8826 |archive-url=https://web.archive.org/web/20131105213425/http://journals.tc-library.org/index.php/hist_math_ed/article/viewFile/189/184 |url=http://journals.tc-library.org/index.php/hist_math_ed/article/viewFile/189/184 |url-status=usurped |archive-date=2013-11-05 |pages=57–68}}</ref>

Thales was claimed to have traveled to [[Egypt]] and [[Babylonia]], where he is supposed to have learned about geometry and astronomy and thence brought their knowledge to the Greeks, along the way inventing the concept of geometric proof and proving various geometric theorems. However, there is no direct evidence for any of these claims, and they were most likely invented speculative rationalizations. Modern scholars believe that Greek deductive geometry as found in [[Euclid's Elements|Euclid's ''Elements'']] was not developed until the 4th century BC, and any geometric knowledge Thales may have had would have been observational.{{r|dicks}}<ref>{{cite book |last=Sidoli |first=Nathan |year=2018 |chapter=Greek mathematics |editor1-last=Jones |editor1-first=A. |editor2-last=Taub |editor2-first=L. |title=The Cambridge History of Science: Vol. 1, Ancient Science |publisher=Cambridge University Press |pages=345–373 |chapter-url=http://individual.utoronto.ca/acephalous/Sidoli_2018c.pdf }}</ref>

The theorem appears in Book III of Euclid's ''Elements'' ({{c.|300 BC}}) as proposition 31: "In a circle the angle in the semicircle is right, that in a greater segment less than a right angle, and that in a less segment greater than a right angle; further the angle of the greater segment is greater than a right angle, and the angle of the less segment is less than a right angle."

[[Dante Alighieri]]'s ''[[Paradiso (Dante)|Paradiso]]'' (canto 13, lines 101–102) refers to Thales's theorem in the course of a speech.