Archimedes

The properties of the lever are such that a small force can lift a large weight if the lever is long enough.

The principle of buoyancy states that an object immersed in a fluid experiences an upward force equal to the weight of the fluid displaced by the object.

The center of gravity of a body is the point at which the entire weight of the body may be considered to act.

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

The surface area of a paraboloid of revolution is equal to the area of a circle whose radius is the length of the arc of the generating parabola from the vertex to the base.

The volume of a spheroid is 2/3 the volume of the circumscribing cylinder.

The surface area of a spheroid is equal to the area of a circle whose radius is the length of the arc of the generating ellipse from the vertex to the base.

The method of mechanical theorems is a method of discovering mathematical theorems by means of mechanical analogies.

The area of a circular segment is equal to the area of a triangle whose base is the chord of the segment and whose height is the sagitta of the segment.

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

The surface area of a spherical segment is equal to the area of a zone whose height is the height of the segment and whose radii are the radii of the bases of the segment.

The volume of a spherical sector is equal to the volume of a cone whose base is the spherical surface of the sector and whose height is the radius of the sphere.

The surface area of a spherical sector is equal to the area of the spherical surface of the sector plus the area of the conical surface of the sector.

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

The volume of an ellipsoid is 4/3 * pi * a * b * c, where a, b, and c are the semi-axes of the ellipsoid.

The surface area of an ellipsoid is more complex to calculate and was not fully solved by Archimedes.

The value of pi can be approximated by inscribing and circumscribing polygons around a circle.

The properties of the screw are such that a small force can lift a large weight if the screw is long enough.

The burning mirror can focus sunlight to ignite objects at a distance.

The claw of Archimedes was a weapon designed to lift and overturn enemy ships.