Archimedes

The volume of a spherical segment is equal to the volume of a cone whose base is the base of the segment and whose height is the height of the segment, plus the volume of a cylinder whose base is the base of the segment and whose height is one-half the height of the segment.

The area of an ellipse is equal to the area of a circle whose radius is the geometric mean of the semi-axes of the ellipse.

The surface area of a sphere is four times the area of its greatest circle.

The volume of a paraboloid of revolution is one-half the volume of the circumscribing cylinder.

The volume of a hyperboloid of revolution is equal to the volume of a cone whose base is the base of the hyperboloid and whose height is the height of the hyperboloid, plus the volume of a cylinder whose base is the base of the hyperboloid and whose height is one-half the height of the hyperboloid.

The center of gravity of a segment of a parabola is on the axis of the parabola, and its distance from the vertex is three-fifths of the height of the segment.

The area of a segment of a spiral is one-third of the area of the circle whose radius is the final radius of the spiral.

The problem of finding the area of a circle is equivalent to finding a square with the same area.

The problem of finding the volume of a sphere is equivalent to finding a cube with the same volume.

Do not disturb my circles.

Magnitudes have the same ratio which equimultiples have.

The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference, of the circle.

The volume of a sphere is four-thirds times pi times the cube of its radius.

The surface area of any sphere is equal to four times the area of its greatest circle.

A body immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced.

The center of gravity of any parallelogram lies on the straight line joining the middle points of opposite sides.

Two magnitudes whether commensurable or incommensurable, balance at distances reciprocally proportional to the magnitudes.

Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.

The perimeter of the circle is greater than that of any inscribed polygon, and less than that of any circumscribed polygon.

There are things which seem incredible to most men who have not studied Mathematics.