"Let it be granted that a circle may be described with any center and any radius."

"To produce a finite straight line continuously in a straight line."

"The only purpose of the 'Elements' is to demonstrate mathematically certain fundamental propositions."

"In any right-angled triangle, the square on the side subtending the right angle is equal to the squares on the sides containing the right angle."

"A surface is that which has length and breadth only."