I'm attempting to prove that Proclus' axiom:
"If a straight line intersects one of two parallel lines, it will intersect the other also."
is equivalent to Playfair's axiom:
"In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point."
However, before coming to this problem, we've proved Euclid's first $28$ postulates where lines intersected by "magic." Does anyone have an idea/solution to then do this:
You should show that your axiom is equivalent to Playfair's Axiom (so if one holds, so does the other, and vice-versa).