Proposition: 6.04: Equiangular Triangles are Similar

(Proposition 4 from Book 6 of Euclid's “Elements”)

In equiangular triangles the sides about the equal angles are proportional, and those (sides) subtending equal angles correspond. * Let $ABC$ and $DCE$ be equiangular triangles, having angle $ABC$ equal to $DCE$, and (angle) $BAC$ to $CDE$, and, further, (angle) $ACB$ to $CED$. * I say that in triangles $ABC$ and $DCE$ the sides about the equal angles are proportional, and those (sides) subtending equal angles correspond.

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