THE SEVENTH BOOK
OF
EUCLIDE's ELEMENTS.
Definitions.
I. UNity is that, by which every thing that is, is called One.
II. Number is a multitude compoſed of units.
III. One number is a part of another, the leſſer of the greater, when the leſſer meaſures the greater.
Every part is denominated from that number by which it meaſures the number whereof it is a part; as 4 is called the third part of 12, becauſe it meaſures 12 by 3.
IV. But the leſſer number is termed Parts, when it meaſures not the greater.
All parts whatſoever are denominated from thoſe two numbers, by which the greateſt common meaſure of the two numbers meaſures each of them; as 10 is ſaid to be ⅔ of the number 15; becauſe the greateſt common meaſure, which is 5, meaſures 10 by 2, and 15 by 3.
V. A number is Multiple (or Manifold) a greater in compariſon of a leſſer, when the leſſer meaſures 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 meaſures by an even number.
IX. But a number evenly odd is that which an even number meaſures by an odd number.
X. A
