Archimedes

The area of a segment of a parabola is four-thirds of the area of the triangle with the same base and height.

The value of pi lies between 3 10/71 and 3 1/7.

I would rather discover a single proof of a theorem than be King of Persia.

The center of gravity of any plane figure is the point within it such that, if the figure is suspended from that point, it will remain in equilibrium in any position.

The center of gravity of a triangle is the point where its medians intersect.

The center of gravity of a parallelogram is the point where its diagonals intersect.

The center of gravity of any solid figure is the point within it such that, if the figure is suspended from that point, it will remain in equilibrium in any position.

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 spiral of Archimedes is a curve generated by a point moving uniformly along a line that rotates uniformly about a fixed point.

The tangent to a spiral at any point makes an angle with the radius vector to that point equal to the angle between the radius vector and the perpendicular to the tangent at the origin.

The problem of squaring the circle is impossible using only a compass and straightedge.

The problem of trisecting an angle is impossible using only a compass and straightedge.

The problem of duplicating the cube is impossible using only a compass and straightedge.

The method of exhaustion can be used to find the areas and volumes of various geometric figures.

The principle of the lever states that when two weights are suspended from a lever, they will be in equilibrium if the ratio of their weights is inversely proportional to the ratio of their distances from the fulcrum.

The weight of any body is the sum of the weights of its parts.

The center of gravity of a system of bodies is the point at which the entire weight of the system can be considered to act.

The specific gravity of a substance is the ratio of its weight to the weight of an equal volume of water.

The method of mechanical theorems can be used to discover new mathematical results.

The number of grains of sand that could be contained in the universe is finite, but unimaginably large.