Ratio of Areas of Similar Triangles/Porism

Porism to Ratio of Areas of Similar Triangles

In the words of Euclid:

From this it is manifest that, if three straight lines be proportional, then, as the first is to the third, so is the figure described on the first to that which is similar and similarly described in the second.

(The Elements: Book $\text{VI}$: Proposition $19$ : Porism)

Proof

Follows immediately from Ratio of Areas of Similar Triangles.

$\blacksquare$

Historical Note

This proof is Proposition $19$ of Book $\text{VI}$ 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 $\text{VI}$. Propositions