Page:Euclid's Elements 1714 Barrow translation.djvu/153

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Nity is that, by which every thing that is, is called One.

II. Number is a multitude compoed of units.

III. One number is a part of another, the leer of the greater, when the leer meaures the greater.

Every part is denominated from that number by which it meaures the number whereof it is a part; as 4 is called the third part of 12, becaue it meaures 12 by 3.

IV. But the leer number is termed Parts, when it meaures not the greater.

All parts whatoever are denominated from thoe two numbers, by which the greatet common meaure of the two numbers meaures each of them; as 10 is aid to be ⅔ of the number 15; becaue the greatet common meaure, which is 5, meaures 10 by 2, and 15 by 3.

V. A number is Multiple (or Manifold) a greater in comparion of a leer, when the leer meaures the greater.

VI. An even number is that which may be divided into two equal parts.

VII. But an odd number is that which cannot be divided into two equal parts; or, that which differs from an even number by an unit.

VIII. A number evenly even is that which an even number meaures by an even number.

IX. But a number evenly odd is that which an even number meaures by an odd number.

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