"That which is without parts has no magnitude."

"Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angle…"

"A quantity is said to be a part of a quantity, the less of the greater, when it measures the greater."

"Proof by contradiction is a powerful tool."

"If a straight line be cut into two equal parts and also into two unequal parts, the rectangle contained by the unequal parts together with the square on the line between the points of section is equal…"