Definition:Continued Proportion/Historical Note

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Historical Note on Continued Proportion

The term continued proportion is rarely seen outside Euclid's The Elements.

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

In the words of Euclid:

If there be as many numbers as we please in continued proportion, and the extremes of them be prime to one another, the numbers are the least of those which have the same ratio with them.

(The Elements: Book $\text{VIII}$: Proposition $1$)