This solution is a geometrical one and the implicilty asked question for the length of the side of the doubled square is not answered by giving a number but by drawing a line. This is not surprising because there is no way to express the length of the diagonal throug the length of the sides. It is an irrational number.
Socrates here gives a constructive proof for the existence of a square-side-length that has double the area of a given square. Is it possible to develop a proof for the incommensurability out of this?

	Arithmetic and Weaving in Antiquity A pebble proof of the incommensurability in the square

	This solution is a geometrical one and the implicilty asked question for the length of the side of the doubled square is not answered by giving a number but by drawing a line. This is not surprising because there is no way to express the length of the diagonal throug the length of the sides. It is an irrational number. Socrates here gives a constructive proof for the existence of a square-side-length that has double the area of a given square. Is it possible to develop a proof for the incommensurability out of this?