Thales, Mathematical Works

LCL 335: 164-165

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Greek Mathematics

V. Thales

The circle is bisected by its diameter

Procl. in Eucl. i., ed. Friedlein 157. 10–13

Τὸ μὲν οὖν διχοτομεῖσθαι τὸν κύκλον ὑπὸ τῆς διαμέτρου πρῶτον Θαλῆν ἐκεῖνον ἀποδεῖξαί φασιν, αἰτία δὲ τῆς διχοτομίας ἡ τῆς εὐθείας ἀπαρέγκλιτος διὰ τοῦ κέντρου χώρησις.

The angles at the base of an isosceles triangle are equal

Ibid. 250. 22–251. 2

Λέγεται γὰρ δὴ πρῶτος ἐκεῖνος ἐπιστῆσαι καὶ εἰπεῖν, ὡς ἄρα παντὸς ἰσοσκελοῦς αἱ πρὸς τῇ βάσει γωνίαι ἴσαι εἰσίν, ἀρχαϊκώτερον δὲ τὰς ἴσας ὁμοίας προσειρηκέναι.

164

Thales

V. Thales

The circle is bisected by its diameter

Proclus, on Euclid i., ed. Friedlein 157. 10–13

They say that Thales was the first to demonstratea that the circle is bisected by the diameter, the cause of the bisection being the unimpeded passage of the straight line through the centre.

The angles at the base of an isosceles triangle are equal Ibid. 250. 22–251. 2

[Thales] is said to have been the first to have known and to have enunciated [the theorem] that the angles at the base of any isosceles triangle are equal, though in the more archaic manner he described the equal angles as similar.b

165
DOI: 10.4159/DLCL.thales-mathematical_works.1939