=
;
and if a be greater than b,
is greater than unity; therefore
is greater than unity, and c is greater than d.
In like manner, if a be equal to b, c is equal to d, and if less, less.
Prop. B.—Theorem (Simson).
If two ratios are equal their reciprocals are equal (invertendo).
Let a : b :: c : d, then b : a :: d : c.