# Euclid's Fifth Proposition in the Poincaré Disk

**Euclid's Fifth Proposition in the Poincaré Disk**-http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI5.html

*In isosceles triangles the angles at the base equal one another, and, if the equal straight lines are produced further, then the angles under the base equal one another.*Let ABC be an isosceles triangle having the side AB equal to the side AC, and let the straight lines BD and CE be produced further in a straight line with AB and AC. I say that the angle ABC equals the angle ACB, and the angle CBD equals the angle BCE. Take an arbitrary point F on BD. Cut off AG from AE the greater equal to AF the less, and join the straight lines FC and GB.

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