May 12, 2014 10:57 AM Subscribe

I'm looking for a textual version of *a*^{2} + *b*^{2} = *c*^{2} that is as old as possible, among all the Greek sources.

I am looking for the earliest statement of the Pythagorean theorem in Greek. I want it to be as text, hopefully something like "the sum of the squares on the sides is equal to the square on the hypotenuse".

- It's probably not stated that way, but that's fine.

- Greek text is a requirement.

- Older is better.

I've gotten some indication that I should look in Euclid's*Elements*, but haven't managed to track that down. I thought there might be some MeFi classicists who had this at their fingertips. Thanks.
posted by benito.strauss to Science & Nature (5 answers total) 2 users marked this as a favorite

I am looking for the earliest statement of the Pythagorean theorem in Greek. I want it to be as text, hopefully something like "the sum of the squares on the sides is equal to the square on the hypotenuse".

- It's probably not stated that way, but that's fine.

- Greek text is a requirement.

- Older is better.

I've gotten some indication that I should look in Euclid's

Here's the direct link to the Pythagorean theorem in *Elements* (Book I Prop 47). If you click 'load' in the top right you can see a parallel English translation.

posted by Maecenas at 11:03 AM on May 12 [9 favorites]

posted by Maecenas at 11:03 AM on May 12 [9 favorites]

You folks are fantastic! For anyone finding this question in the future:

posted by benito.strauss at 11:08 AM on May 12 [1 favorite]

ἐν τοῖς ὀρθογωνίοις τριγώνοις τὸ ἀπὸ τῆς τὴν ὀρθὴν γωνίαν ὑποτεινούσης πλευρᾶς τετράγωνον ἴσον ἐστὶ τοῖς ἀπὸ τῶν τὴν ὀρθὴν γωνίαν περιεχουσῶν πλευρῶν τετραγώνοις."In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle."

posted by benito.strauss at 11:08 AM on May 12 [1 favorite]

This may be just what you want, but as you can tell by the name the Pythagorean theorem was known well before Euclid. I would suspect that there are many written statements but I can't really point you at one. BUT:

In a famous section of Plato's*Meno* (dated about 380BC), Socrates leads a slave through a geometric argument for a special case of the Pythagorean theorem. The theorem is not stated in the form you want but I think the argument in the dialog does prove the general case of the theorem. Link.

posted by grobstein at 11:26 AM on May 12 [3 favorites]

In a famous section of Plato's

posted by grobstein at 11:26 AM on May 12 [3 favorites]

You won't find that algebraic formula in ancient Greek because algebra happened about fifteen hundred years later. (About 1100 AD, give or take.)

posted by Chocolate Pickle at 1:00 PM on May 12 [2 favorites]

posted by Chocolate Pickle at 1:00 PM on May 12 [2 favorites]

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posted by thelonius at 11:00 AM on May 12 [1 favorite]