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

Rh 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.