Euclid's Twelfth Proposition in the Poincaré Disk
Euclid's Twelfth Proposition in the Poincaré Disk - http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI12.html
TO draw a straight line perpendicular to a given infinite straight line from a given point not on it.
Let AB be the given infinite straight line, and C the given point which is not on it.
It is required to draw a straight line perpendicular to the given infinite straight line AB from the given point C which is not on it.
Take an arbitrary point D on the other side of the straight line AB, and describe the circle EFG with center C and radius CD. Bisect the straight line EG at H, and join the straight lines CG, CH, and CE.
I say that CH has been drawn perpendicular to the given infinite straight line AB from the given point C which is not on it.