Definitions

A unit is that according to which each existing (thing) is said (to be) one.

A number is a multitude composed of units.

A number is part of a(nother) number, the lesser of the greater, when it measures the greater.

But (the lesser is) parts (of the greater) when it does not measure it.

The greater (number is) a multiple of the lesser when it is measured by the lesser.

An even number is one (which can be) divided in half.

An odd number is one (which can)not (be) divided in half, or which differs from an even number by a unit.

An even-times-even number is one (which is) measured by an even number according to an even number.

An even-times-odd number is one (which is) measured by an even number according to an odd number.

And an odd-times-odd number is one (which is) measured by an odd number according to an odd number.

A primek number is one (which is) measured by a unit alone.

Numbers prime to one another are those (which are) measured by a unit alone as a common measure.

A composite number is one (which is) measured by some number.

And numbers composite to one another are those (which are) measured by some number as a common measure.

A number is said to multiply a(nother) number when the (number being) multiplied is added (to itself) as many times as there are units in the former (number), and (thereby) some (other number) is produced.

And when two numbers multiplying one another make some (other number) then the (number so) created is called plane, and its sides (are) the numbers which multiply one another.

When 3 numbers multiplying one another make some (other number) then the (number so) created is (called) solid, and its sides (are) the numbers which multiply one another.

A square number is an equal times an equal, or (a plane number) contained by two equal numbers.

A cube (number) is an equal times an equal times an equal, or (a solid number) contained by 3 equal numbers.

Numbers are proportional when the first is the same multiple, or the same part, or the same parts, of the second that the third (is) of the fourth.

Similar plane and solid numbers are those having proportional sides.

A perfect number is that which is equal to its own parts.