Euclid

The study of the infinite through the finite.

Geometry is the assurance of the mind.

Propositions build upon one another like stones in a wall.

The harmony of numbers and shapes reveals cosmic order.

Euclid laid the foundation for all future mathematics.

In the circle, perfection is found.

The triangle is the simplest and most fundamental figure.

Ratios govern the proportions of the world.

The method of exhaustion approximates the infinite.

Solids are to one another as the cubes of their like linear parts.

If a solid angle be contained by three plane angles which together are less than two right angles, the solid angle is less than a right angle.

To describe a sphere with any centre and distance.

The surface of any plane figure is the sum of the surfaces of the triangles into which it is divided.

The volume of any solid is the sum of the volumes of the pyramids into which it is divided.

Cones and cylinders are to one another in the ratio of their bases and heights.

The area of similar figures is to one another as the squares of their homologous sides.

The volumes of similar solids are to one another as the cubes of their homologous sides.

In a right-angled triangle, the altitude to the hypotenuse creates two smaller triangles similar to each other and to the original triangle.

The geometric mean of two numbers is the side of the square equal in area to the rectangle formed by those numbers.

To divide a given straight line into two segments so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment.