Definition & Reality in the General Theory of Political Economy

by Thomas Cool

Thus:

· From the big square itself: z² = (a + b)²

· From the tilted square and the triangles: z² = c² + 4 ab/2.

Elimination of z then gives a² + b² = c².

This proof has been taken from DeLong (1971), and he remarks that Pythagoras proved it differently.

How do we explain that one and the same equation can have two interpretations that are so widely different, one with the need for complicated proof and the other with direct acceptance by definition ?

There may be other explanations, but I think the following will do fine. Note that the definition of the circle relies on the notion of ‘distance’. There are two points of view again, so that point 2 above actually splits in two parts:

2A) Basically the (Euclidian) distance between two points can be measured by a straight line section. That is rather simple, and makes for a readily acceptable definition of a circle.