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.