Definition:Reciprocal Proportion

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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.