Third Fourth and Mean Proportions

In this class, we discuss Third Fourth and Mean Proportions.

The reader should have prior knowledge of ratios. Click Here.

Proportion: The equality of two ratios is called proportion.

a: b = c: d is written as a: b:: c: d

a, b are extremes.

b, c are mean terms.

Product of means = product of extremes

Example:

10: 1 = 20: 2

Product of extremes = 10 * 2 = 20

Product of means = 1 * 20 = 20

Fourth Proportion:

If a: b = c: d, then d is the fourth proportion to a, b, and c.

Third proportion:

If a: b = b: c, then c is the third proportion to a, b.

Mean proportion or geometric mean:

The mean proportion or geometric mean of a,b is √ab

Assume the mean proportion of a, b is x

x satisfies a/x = x/b

a: x = x: b

product of means = product of extremes.

ab = x^2

x = √ab