Euclid of Alexandria

Mathematics Greek -325 – -265 267 quotes

Often referred to as the 'Father of Geometry,' his work 'Elements' is one of the most influential mathematical treatises in history.

Quotes by Euclid of Alexandria

To construct a cube on a given straight line.

Euclid's Elements, Book XI, Proposition 28 (Implied, part of solid geometry)

To construct a pyramid on a given triangular base.

Euclid's Elements, Book XII (Implied, part of solid geometry)

If two straight lines cut one another, the vertically opposite angles are equal.

Euclid's Elements, Book I, Proposition 15

The sum of the angles of any triangle is equal to two right angles.

Euclid's Elements, Book I, Proposition 32

If a straight line fall on parallel straight lines, it makes the alternate angles equal to one another, the exterior angle equal to the interior and opposite angle on the same side, and the interior angles on the same side equal to two right angles.

Euclid's Elements, Book I, Proposition 29

The square on the diameter of a circle is double the square on the radius.

Euclid's Elements, Book X, Proposition 28 (Implied in context of incommensurability)

The diagonal of a square is incommensurable with its side.

Euclid's Elements, Book X, Proposition 117 (often attributed to earlier Pythagoreans, but proved by Euclid)