Mean Proportion

The mean proportion, also called the geometric mean, of a and b is the solution to this equation: $$\frac{a}{x} = \frac{x}{b}$$, in other words $$x = \sqrt{a b}$$.

Given two lengths, the mean proportion of the two can be constructed.

1. Begin with a line with points A, B and C on it.

2. Construct a line perpendicular to AC on point B.

3. Construct the midpoint of A and C.

4. Construct a semicircle centered on M from A to C. It intersects the perpendicular line at point D.

5. The distance AD is the mean proportion of AB and AC. The distance BD is the mean proportion of AB and BC. The distance CD is the mean proportion of BC and AC.