A NOTE ON THE CONSTRUCTION OF THE EQUILATERAL TRIANGLE WITH SCALENE ELEMENTARY TRIANGLES IN PLATO'S TIMAEUS: PL. TI. 54A-B

Abstract

In the Timaeus Plato says that, among the infinite number of right-angled scalene elementary triangles, the best (τὸ κάλλιστον) is that ἐξ οὗ τὸ ἰσόπλευρον ἐκ τρίτου συνέστηκε. Apart from few exceptions to be mentioned shortly, the translations of the Timaeus, which I am aware of spanning the period from the second half of the nineteenth century up to recent times, have usually rendered this passage as meaning that such an elementary triangle is that which, when two are combined, the equilateral triangle forms as a third figure. For instance, Bury and Zeyl respectively translate: out of which, when two are conjoined, the equilateral triangle is constructed as a third. and from [a pair of] which the equilateral triangle is constructed as a third figure. I shall refer to this sort of translation as the Prevailing Translation (hereafter PT).