Definition:Euclid's Definitions - Book VII

These definitions appear at the start of Book VII of by Euclid.


 * 1) Numbers composite to one another are those which are measured by some number as a common measure
 * 2) A number is said to multiply a number when that which is multiplied is added to itself as many times as there are units in the other, and thus some number is produced.
 * 3) 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.
 * 4) 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.
 * 5) A square number is equal multiplied by equal, or a number which is contained by two equal numbers.
 * 6) And a cube is equal multiplied by equal and again by equal, or a number which is contained by three equal numbers.
 * 7) 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.
 * 8) Similar plane and solid numbers are those which have their sides proportional.
 * 9) A perfect number is that which is equal to the sum its own parts.
 * 1) Numbers composite to one another are those which are measured by some number as a common measure
 * 2) A number is said to multiply a number when that which is multiplied is added to itself as many times as there are units in the other, and thus some number is produced.
 * 3) 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.
 * 4) 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.
 * 5) A square number is equal multiplied by equal, or a number which is contained by two equal numbers.
 * 6) And a cube is equal multiplied by equal and again by equal, or a number which is contained by three equal numbers.
 * 7) 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.
 * 8) Similar plane and solid numbers are those which have their sides proportional.
 * 9) A perfect number is that which is equal to the sum its own parts.
 * 1) And a cube is equal multiplied by equal and again by equal, or a number which is contained by three equal numbers.
 * 2) 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.
 * 3) Similar plane and solid numbers are those which have their sides proportional.
 * 4) A perfect number is that which is equal to the sum its own parts.