Ex. 3.—To draw a perpendicular to a straight line, from a given point in that line, [Fig. 100]. With any radius from any given point A in the line B C, cut the line at B and C. Next, with a longer radius, describe arcs from B and C, cutting each other at D, and draw the perpendicular D A.
Second Method, [Fig. 101]. From any center F above B C, describe a circle passing through the given point A, and cutting the given line at D; draw D F, and produce it to cut the circle at E; and draw the perpendicular A E.
Fig. 102.
Third Method, [Fig. 102]. From A describe an arc E C, and from E, with the same radius, the arc A C cutting the other at C; through C draw a line E C D and set off C D equal to C E, and through D draw the perpendicular A D.
Fig. 103.
Fig. 104.
Ex. 4.—To draw a perpendicular to a straight line from any point without it, [Fig. 103]. From the point A with a sufficient radius cut the given line at F and G; and from these points describe arcs cutting at E. Draw the perpendicular A E.