Euclid

If four magnitudes be proportional, the rectangle contained by the extremes is equal to the rectangle contained by the means.

Similar triangles are to one another in the duplicate ratio of their corresponding sides.

To construct a regular pentagon in a given circle.

To inscribe a regular hexagon in a given circle.

A number is a multitude composed of units.

A prime number is that which is measured by a unit alone.

If a number be the least that is measured by any prime numbers, it will not be measured by any other prime number except those originally measuring it.

The elements of geometry are derived from a small set of axioms and postulates.

A straight line is that which lies evenly between its extreme points.

The extremities of a line are points.

The extremities of a surface are lines.

A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line.

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.

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

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

A boundary is that which is an extremity of anything.

And the point is called the center of the circle.

A diameter of the circle is any straight line drawn through the center 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. And the center of the semicircle is the same as that of the circle.

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