Definition:Proportion/Continued

Definition
Four magnitudes $a, b, c, d$ are in continued proportion if $a : b = b : c = c : d$.

Also known as
A sequence of term in continued proportion is more frequently referred to as a geometric progression.

The term continuously proportional can also be found in to mean in continued proportion:

Historical Note
The term continued proportion is rarely seen outside.

In fact, while Euclid used the term continued proportion throughout Book $\text{VIII}$ of, he never formally defined it.