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(c) The Irrational

Schol. lxii. in Eucl. Elem. x., Eucl. ed. Heiberg v. 450. 16–18

Τὸ θεώρημα τοῦτο Θεαιτήτειόν ἐστιν εὕρημα, καὶ μέμνηται αὐτοῦ ὁ Πλάτων ἐν Θεαιτήτῳ, ἀλλ᾿ ἐκεῖ μὲν μερικώτερον ἔγκειται, ἐνταῦθα δὲ καθόλου.

Plat. Theaet. 147 d–148 b

ΘΕΑΙΤΗΤΟΣ. Περὶ δυνάμεών τι ἡμῖν Θεόδωρος ὅδε ἔγραφε, τῆς τε τρίποδος πέρι καὶ πεντέποδος [ἀποφαίνων]1 ὅτι μήκει οὐ σύμμετροι τῇ ποδιαίᾳ, καὶ οὕτω κατὰ μίαν ἑκάστην προαιρούμενος μέχρι τῆς ἑπτακαιδεκάποδος· ἐν δὲ ταύτῃ πως ἐνέσχετο. ἡμῖν οὖν εἰσῆλθέ τι τοιοῦτον, ἐπειδὴ ἄπειροι τὸ πλῆθος αἱ δυνάμεις ἐφαίνοντο, πειραθῆναι συλλαβεῖν εἰς ἕν, ὅτῳ πάσας ταύτας προσαγορεύσομεν τὰς δυνάμεις.

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Theaetetus

(c)The Irrational

Euclid, Elements x., Scholium lxii., ed. Heiberg v. 450. 16–18

This theorem [Eucl. Elem. x. 9]a is the discovery of Theaetetus, and Plato recalls it in the Theaetetus, but there it arises in a particular case, here it is treated generally.

Plato, Theaetetus 147 d–148 b

Theaetetus. Theodorusb was proving to us a certain thing about square roots, I mean the square roots of three square feet and five square feet, namely, that these roots are not commensurable in length with the foot-length, and he proceeded in this way, taking each case in turn up to the root of seventeen square feet; at this point for some reason he stopped.c Now it occurred to us, since the number of square roots appeared to be unlimited, to try to gather them into one class, by which we could henceforth describe all the roots.

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DOI: 10.4159/DLCL.theaetetus-mathematical_works.1939