Euclid

Similar polygons inscribed in circles are to one another in the ratio of the squares of their corresponding sides.

In a circle, the angle in the same segment is equal to the angle in the same segment.

The product of the segments of two chords intersecting inside a circle are equal.

The angle between a tangent and a chord is equal to the angle in the alternate segment.

The sum of the interior angles of a polygon with n sides is (n-2) times 180 degrees.

Things which are double of the same things are double of one another.

The base angles of an isosceles triangle are equal.

A number is that which is capable of being measured by some unit.

An unit is that by virtue of which each of the things that exist is called one.

A number is a multitude composed of units.

A part of a number is a number which measures the whole.

The less number measures the greater when the greater is seen how many times it contains the less exactly.

A number is said to measure a number when the less is contained in the greater a number of times exactly.

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

A composite number is that which is measured by some number different from itself.

Numbers are proportional when the first is the same multiple of the second that the third is of the fourth.

To find the greatest common measure of two given numbers.

Given two numbers not prime to one another, to find their greatest common measure.

Given three numbers not prime to one another, to find their greatest common measure.

If two numbers by multiplying the same number make two numbers which are prime to one another, the original numbers will also be prime to one another.