Euclid

The volume of a cone is one-third the volume of a cylinder with the same base and height.

The volume of a pyramid is one-third the volume of a prism with the same base and height.

Spheres are to one another in the triplicate ratio of their diameters.

The elements of a cone are similar to the elements of a pyramid.

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.

Magnitudes are said to be in the ratio which like magnitudes, when one is taken as the first and the other as the second, have when compared in order.

Ratios which are the same with the same ratio are the same with one another.

If there be any number of magnitudes whatever which are in proportion, they will also be in proportion alternately.

Equal triangles upon equal bases in the same parallels are equal.

Triangles upon equal bases and in the same parallels are equal.

If four straight lines be proportional, the rectangle contained by the first and fourth is equal to the rectangle contained by the second and third.

In equal circles equal angles stand on equal arcs, whether they stand at the centres or at the circumferences.

The angle subtended by an arc at the centre is double that subtended at the circumference.

The opposite sides and angles of a parallelogram are equal.

The diagonals of a parallelogram bisect each other.

The square on the hypotenuse is equal to the sum of the squares on the other two sides.

A solid angle is the inclination of more than two plane angles to one another, which are contained by straight lines lying in one plane and meeting one another at one point.

If two triangles have two angles equal and the sides adjacent to the equal angles equal, then they are congruent.

The area of a circle is equal to the area of a right-angled triangle whose legs are equal to the radius and the circumference of the circle.

The volume of a sphere is four-thirds times the volume of a cone with the same base and height.