Page:First six books of the elements of Euclid 1847 Byrne.djvu/46

12 O draw a straight line perpendicular to a given indefinite straight line from a given (point ) without.



With the given point as centre, at one side of the line, and any distance  capable of extending to the other side, describe , Make =  (pr. 10.)

draw, and.

then  $$\perp$$.

For (pr. 8). since =  (const.)

common to both, and

= (def. 15.)

∴ =, and

∴ $$\perp$$  (def. 10.).

Q.E.D.