The First Six Books of the Elements of Euclid

by Euclid; John Casey

=

.

Hence

a : b :: c : d.

Prop. D.—Theorem (Simson).

If the first be to the second as to the third is to the fourth, and if the first be a multiple or submultiple of the second, the third is the same multiple or submultiple of the fourth.

1. Let a : b :: c : d, and let a be a multiple of b, then c is the same multiple of d.

Dem.—Let a = mb, then

= m;
but