| Dem.—Since | a : b | :: c : d; | |||||||||
| then | = ; | ||||||||||
| therefore | 1 ÷ | = 1 ÷, | |||||||||
| or | = | ||||||||||
| Hence | b : a | :: d : c. |
Prop. C.—Theorem (Simson).
If the first of four magnitudes be the same multiple of the second which the third is of the fourth, the first is to the second as the third is to the fourth.
Let a = mb, c = md; then a : b :: c : d.
Dem.—Since a = mb, we have
= m.
In like manner,
= m; therefore
