Euclid

Mathematics Greek -325 – -265 439 quotes

Father of geometry, wrote Elements

Quotes by Euclid

If a straight line falling on two straight lines make the alternate angles equal to one another, the straight lines will be parallel to one another.

Elements, Proposition 27

If a straight line falling on two straight lines make the exterior angle equal to the interior and opposite angle on the same side, or the interior angles on the same side equal to two right angles, the straight lines will be parallel to one another.

Elements, Proposition 28

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

Elements, Proposition 29

Straight lines which are parallel to the same straight line are also parallel to one another.

Elements, Proposition 30

Through a given point to draw a straight line parallel to a given straight line.

Elements, Proposition 31

In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of the triangle are equal to two right angles.

Elements, Proposition 32

Straight lines joining equal and parallel straight lines towards the same parts are themselves equal and parallel.

Elements, Proposition 33

In parallelogrammic areas the opposite sides and angles are equal to one another, and the diameter bisects them.

Elements, Proposition 34

Parallelograms which are on the same base and in the same parallels are equal to one another.

Elements, Proposition 35

Parallelograms which are on equal bases and in the same parallels are equal to one another.

Elements, Proposition 36

Triangles which are on the same base and in the same parallels are equal to one another.

Elements, Proposition 37

Triangles which are on equal bases and in the same parallels are equal to one another.

Elements, Proposition 38

Equal triangles which are on the same base and on the same side of it are also in the same parallels.

Elements, Proposition 39

Equal triangles which are on equal bases and on the same side of them are also in the same parallels.

Elements, Proposition 40

If a parallelogram have the same base with a triangle and be in the same parallels, the parallelogram is double of the triangle.

Elements, Proposition 41

To construct a parallelogram equal to a given triangle in a given rectilineal angle.

Elements, Proposition 42

In any parallelogram the complements of the parallelograms about the diameter are equal to one another.

Elements, Proposition 43

To a given straight line to apply, in a given rectilineal angle, a parallelogram equal to a given triangle.

Elements, Proposition 44

To construct a parallelogram equal to a given rectilineal figure in a given rectilineal angle.

Elements, Proposition 45

On a given straight line to describe a square.

Elements, Proposition 46