Definitions

Definition 1.

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

Definition 2.

A number is a multitude composed of units.

Definition 3.

A number is a part of a number, the less of the greater, when it measures the greater;

Definition 4.

But parts when it does not measure it.

Definition 5.

The greater number is a multiple of the less when it is measured by the less.

Definition 6.

An even number is that which is divisible into two equal parts.

Definition 7.

An odd number is that which is not divisible into two equal parts, or that which differs by a unit from an even number.

Definition 8.

An even-times-even number is that which is measured by an even number according to an even number.

Definition 9.

An even-times-odd number is that which is measured by an even number according to an odd number.

Definition 10.

An odd-times-odd number is that which is measured by an odd number according to an odd number.

Definition 11.

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

Definition 12.

Numbers relatively prime are those which are measured by a unit alone as a common measure.

Definition 13.

A composite number is that which is measured by some number.

Definition 14.

Numbers relatively composite are those which are measured by some number as a common measure.

Definition 15.

A number is said to multiply a number when the latter is added as many times as there are units in the former.

Definition 16.

And, when two numbers having multiplied one another make some number, the number so produced be called plane, and its sides are the numbers which have multiplied one another.

Definition 17.

And, when three numbers having multiplied one another make some number, the number so produced be called solid, and its sides are the numbers which have multiplied one another.

Definition 18.

A square number is equal multiplied by equal, or a number which is contained by two equal numbers.

Definition 19.

And a cube is equal multiplied by equal and again by equal, or a number which is contained by three equal numbers.

Definition 20.

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.

Definition 21.

Similar plane and solid numbers are those which have their sides proportional.

Definition 22.

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