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

There is no royal road to geometry.

Proclus, Commentary on Euclid's Elements

The whole is greater than the part.

Elements, Common Notion 5

Things which are equal to the same thing are also equal to one another.

Elements, Common Notion 1

If equals be added to equals, the wholes are equal.

Elements, Common Notion 2

If equals be subtracted from equals, the remainders are equal.

Elements, Common Notion 3

Things which coincide with one another are equal to one another.

Elements, Common Notion 4

A point is that which has no part.

Elements, Definition 1

A line is breadthless length.

Elements, Definition 2

The extremities of a line are points.

Elements, Definition 3

A straight line is a line which lies evenly with the points on itself.

Elements, Definition 4

A surface is that which has length and breadth only.

Elements, Definition 5

The extremities of a surface are lines.

Elements, Definition 6

A plane surface is a surface which lies evenly with the straight lines on itself.

Elements, Definition 7

A plane angle is the inclination of two lines to one another, which meet one another, but are not in the same straight line.

Elements, Definition 8

When the lines containing the angle are straight, the angle is called rectilinear.

Elements, Definition 9

When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.

Elements, Definition 10

An obtuse angle is an angle greater than a right angle.

Elements, Definition 11

An acute angle is an angle less than a right angle.

Elements, Definition 12

A boundary is that which is an extremity of anything.

Elements, Definition 13

A figure is that which is contained by any boundary or boundaries.

Elements, Definition 14