# Definition:Reciprocal Proportion

## Definition

Let $P$ and $Q$ be geometric figures of the same type (that is, having the same number and configuration of sides).

Let $A$ and $B$ be sides of $P$, and let $C$ and $D$ be sides of $Q$, such that $A$ and $C$ are corresponding sides, and $B$ and $D$ also be corresponding sides.

Then $P$ and $Q$ have sides which are **in reciprocal proportion**, or are **reciprocally proportional**, if:

- $A : D = B : C$

where $A : D$ is the ratio of the lengths of $A$ and $D$.

## Also see

The definition of Reciprocally Related Figures:

*Two figures are***reciprocally related**when there are in each of the two figures antecedent and consequent ratios.

(*The Elements*: Book $\text{VI}$: Definition $2$)

There is no explicit definition for reciprocal proportion in Euclid's *The Elements*. It can be supposed that this definition (or something similar) may be the one which was intended for that.