Definition:Triplicate Ratio

Definition

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 $b$.

That is:

$a : d$ is the triplicate ratio of $a : b$.

As Euclid defined it:

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.

(The Elements: Book V: Definition $10$)