Jump to navigation Jump to search
Let $a, b, c, d$ be magnitudes such that:
- $a : b = b : c = c : d$
Then $a$ has the triplicate ratio to $d$ of the ratio it has to $b$.
- $a : d$ is the triplicate ratio of $a : b$.
In the words of Euclid:
- When four magnitudes are $<$ continuously $>$ proportional, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on continually, whatever be the proportion.