Page:First six books of the elements of Euclid 1847 Byrne.djvu/45

ROM a given point (), in a given straight line (), to draw a perpendicular.

Take any point () in the given line, cut off = (pr. 3.), construct (pr. 1.), draw and it shall be perpendicular to the given line.

For = (const.)

= (const.)

and common to the two triangles.

Therefore = (pr. 8.)

∴ $\perp$ (def. 10.).

Q.E.D.