23 If an infinite right line be cut of a periphery of an externall center, in a point assigned and contingent, and the diameter be drawne from the contingent point, a right line from the point assigned knitting it with the diameter, shall be perpendicular unto the infinite line given.
Let the infinite right line be ae, from whose point a, a perpendicular is to be raised.
The right line ae, let it be cut by the periphery aei, (whose center o, is out of the assigned ae,) and that in the point a, and a contingent point, as in e: And from e, let the
diamiter be eoi: The right line ai, from a, the point given, knitting it with the diameter ioe, shall be perpendicular upon the infinite line ae; Because with the said infinite, it maketh an angle in a semicircle.
And
24 If a right line from a point given, making an acute angle with an infinite line, be made the diameter of a periphery cutting the infinite, a right line from the point assigned knitting the segment, shall be perpendicular upon the infinite line.
As in the same example, having an externall point given, let a perpendicular unto the infinite right line ae be sought: Let the right line ioe, be made the diameter of the peripherie; and withall let it make with the infinite right line given an acute angle in e, from whose bisection for the center, let a periphery cut the infinite, &c.
And
