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

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.