Consider the following ratio: .

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

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 = b^{2}

B^{2}= 100

b =*b = 10*

Therefore, the positive geometric mean is 10.