Proposition 12.
To a given infinite straight line, from a given point which is not on it, to draw a perpendicular straight line.
Let AB be the given infinite straight line, and C the given point which is not on it;
thus it is required to draw to the given infinite straight line AB, from the given point C which is not on it, a perpendicular straight line. For let a point D be taken
at random on the other side of the straight line AB, and with centre C and distance CD let the circle EFG be described; [Post. 3]
For, since GH is equal to HE, and HC is common,
called a perpendicular to that on which it stands. [Def. 10] Therefore CH has been drawn perpendicular to the given infinite straight line AB from the given point C which is not on it.
Q. E. F. 1 2