# Continuous ratio

Consider the following ratio: .

Note that your means are equal, so it is called continuous ratio. Like this:

Continuous proportion is any proportion of equal means.

Generally speaking, a continuous proportion can be represented by:

## Proportional Third

Dice two natural numbers The and B, non-null, is called third proportional of these numbers the number x such that:

Example:

• Determine the third proportional of numbers 20 and 10.
Solution:
We indicate by x the third proportional and we set the proportion:
(applying the fundamental property)
20 x = 10. 10
20x = 100

x = 5
So the third proportional is 5.

## Geometric mean or proportional mean

Given a continuous ratio , the number B is called geometric mean or proportional average in between The and ç. Example:

• Determine the positive geometric mean between 5 and 20.
Solution:

5 20 = b. B
100 = b2
B2 = 100
b =

b = 10
Therefore, the positive geometric mean is 10.
Next: Proportion Properties