Page:Euclid's Elements 1714 Barrow translation.djvu/155

XIX. A Cube is that number which is equally equal equally, or,which is contained under three equal numbers. Let A be the ſide of a Cube; the Cube is thus noted, AAA, or Ac. or A'.

In this definition, and the three foregoing, unity is a number.

XX. Numbers are proportional, when the firſt is as multiple of the ſecond, as the third is of the fourth; or, the ſame part; or, when a part of the firſt number measures the ſecond, and the ſame part of the third meaſures the fourth, equally: and on the contrary. So A. B :: C. D, that is, 3. 9 :: 5. 15.

XXJ. Like plane, and ſolid numbers are they, which have their ſides proportional : Namely not all the ſides, but ſome.

XXII. A perfect number is that which is equal to all its aliquot parts.

As 6 and 28. But a number that is leſs than its aliquot-parts is called an Abounding number; and a greater a Diminutive; ſo 12 is an Abounding, 15 a Diminutive number.

XXIII. One number is ſaid to measure another, by that number, which, when it multiplies, or is multiplied by it, it produces.

In Diviſion, a unit is to the quotient as the diviſor is to the dividend. Note, that a number placed under another with a line betwixt them,ſigniſies Divisſion: So ⁠A/B⁠ = A divided by B, and ⁠CA/B⁠ = C x A divided by B.

Two numbers are called Terms or Roots of Proportion, leſſer than which cannot be found in the ſame proportion.

1.THat numbers equal or manifold to any number may be taken at pleaſure.

2. That a greater number may be taken than any number whatſoever.