Has anyone proved any of the postulates of Euclid?

Answer 1

Postulates are not proven, but taken for granted as true.

Otherwise, they would be called theorems.

Take for example the postulate that says the shortest distance between two points is a straight line.

You can perhaps attempt to prove it by contradiction.

Suppose there is a function g whose arclength is LESS than that given by the distance formula of

the line connecting the points.

Then

integral ( sqrt( 1 + g'(x)^2 ), x=[a,b] < sqrt( (x2-x1)^2 + (y2-y1)^2 )

solving this integral equation results some non-constant function bounded by zero after taking the

derivative of both sides.

since these measures cannot be negative, there is no such function which supports the postulate.

LIke they say, KNOCK YOURSELF OUT!!!