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Definitions 1 and 2

Def. 1. A magnitude is a part of a magnitude, the less of the greater, when it measures the greater.

Def. 2. The greater is a multiple of the less when it is measured by the less.

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The two magnitudes mentioned in each definition are of the same kind. Following Euclid, they are illustrated here as lines, but they could both be planar figures, or solids, or angles, or any other kind of magnitude so long as they are of the same kind.
The illustration shows two magnitudes, A and B, and A is one third of B since A measures B three times. Thus, A is a part of B, and B is a multiple of A. |

Book V Introduction - Definitions V.3 and V.4.

© 1997
D.E.Joyce
Clark University