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:
Dice two natural numbers The and B, non-null, is called third proportional of these numbers the number x such that:
- Determine the third proportional of numbers 20 and 10.
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.
5 20 = b. B
100 = b2
B2 = 100
b = 10
Therefore, the positive geometric mean is 10.