Definition:Compound Ratio

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Definition

Let $R_1 = a : b$ and $R_2 = c : d$ be ratios.


The compound ratio of $R_1$ and $R_2$ is defined as:

$R_1 R_2 = a c : b d$

That is, it is the product of the two ratios.


Historical Note

Euclid never formally defined a compound ratio, but instead referred to a ratio compounded of two ratios.

In the words of Euclid:

Equiangular parallelograms have to one another the ratio compounded of the ratios of their sides.

(The Elements: Book $\text{VI}$: Proposition $23$)