Ratios of Equal Magnitudes/Porism

Porism to Ratios of Equal Magnitudes

In the words of Euclid:

From this it is manifest that, if any magnitudes are proportional, they will also be inversely proportional.

(The Elements: Book $\text{V}$: Proposition $7$ : Porism)


Proof

Apparent from the construction.

$\blacksquare$


Historical Note

This proof is Proposition $7$ of Book $\text{V}$ of Euclid's The Elements.


Sources

  • 1926: Sir Thomas L. Heath: Euclid: The Thirteen Books of The Elements: Volume 2 (2nd ed.) ... (previous) ... (next): Book $\text{V}$. Propositions
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