Euclid

To draw a straight line perpendicular to a given straight line from a given point on it.

If a straight line fall on two 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.

If two straight lines cut one another, they make the vertically opposite angles equal to one another.

Any two sides of a triangle are together greater than the remaining one.

The greater angle is subtended by the greater side.

The greater side subtends the greater angle.

If a straight line be drawn through the centre of a circle bisecting a straight line not through the centre, it will also cut it at right angles; and if it cut it at right angles, it will also bisect it.

In equal circles equal circumferences subtend equal angles at the centres and at the circumferences.

In equal circles equal chords cut off equal circumferences, the greater equal to the greater and the less to the less.

In equal circles equal circumferences are subtended by equal chords.

What is proved without a diagram is not proved.

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

A diameter of the circle is any straight line drawn through the centre and terminated in both directions by the circumference of the circle, and such a straight line also bisects the circle.

A semicircle is the figure contained by the diameter and the circumference cut off by it.

Rectilinear figures are those which are contained by straight lines, trilateral figures those contained by three, quadrilateral those contained by four, and multilateral those contained by more than four straight lines.

Let it be granted that a circle may be described with any centre and radius.

Let it be granted that, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

The knowledge of which geometry aims is the knowledge of the eternal.

Mathematics is the language in which God has written the universe.

What is asserted without proof can be denied without proof.