"A semicircle is the figure contained by the diameter and the circumference cut off by it. And the center of the semicircle is the same as that of the circle."

"A diameter of the circle is any straight line drawn through the center and terminated in both directions by the circumference of the circle, and such a straight line also bisects the circle."

"Sire, there is no royal road to geometry."

"The square on the side subtending the right angle in right-angled triangles is equal to the squares on the sides containing the right angle."

"A ratio is a sort of relation in respect of size between two magnitudes of the same kind."