The geometry in Plato's Meno

Abstract

In this paper, we analyze the two geometrical passages in Plato's Meno, (81c -- 85c) and (86e4 -- 87b2), from the points of view of a geometer in Plato's time and today. We give, in our opinion, a complete explanation of the difficult second geometrical passage. Our explanation solves an ingenious geometry puzzle that has baffled readers of Plato's Meno for over 2,400 years.

The solution of Plato's triangle inscription problem in the Meno that we describe in Section 9 of this paper is not new. It was already obtained in the 19th century. We shall have more to say about the history of this problem in the future