p.1612

p.12

13165

Geometrical proofs do not show causes, as when we prove a triangle contains two right angles




Full Idea:
Geometry does not ask 'why?' ..When from the exterior angle equalling two opposite interior angles it is shown that the interior angles make two right angles, this is not a causal demonstration. With no exterior angle they still equal two right angles.




From:
Proclus (Commentary on Euclid's 'Elements' [c.452], p.1612), quoted by Paolo Mancosu  Explanation in Mathematics §5




A reaction:
A very nice example. It is hard to imagine how one might demonstrate the cause of the angles making two right angles. If you walk, turn left x°, then turn left y°, then turn left z°, and x+y+z=180°, you end up going in the original direction.
