Euclid's Proposition #11 in the Poincaré Disk
Euclid's Proposition #11 in the Poincaré Disk - http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI11.html
To draw a straight line at right angles to a given straight line from a given point on it.
Let AB be the given straight line, and C the given point on it.
It is required to draw a straight line at right angles to the straight line AB from the point C.
Take an arbitrary point D on AC. Make CE equal to CD. Construct the equilateral triangle FDE on DE, and join CF.
I say that the straight line CF has been drawn at right angles to the given straight line AB from C the given point on it.