describe the arch CD; with the same distance, and one foot in B, cross the former arch in C and D, draw the line CD, and it is done. C A B D PROBLEM III. To raise a perpendicular on a given line, as AB, from the point E. RULE. With any convenient distance in the compasses, and one foot in E, make a point on each side, as at c and e; then open the compasses wider, and with one foot in C, describe an arch, as at F; then with the same extent, and one foot in e, intersect the former arch at F, draw EF, and it is To erect a perpendicular, on the end of a given line, as AG. RULE. With any distance, as from A to C, in the compasses, and one foot in C, describe a circle, so as to touch the end of the given line in A; from where that cuts the given line, and through the centre C, draw a line to cut the circle, as in B; from B, draw the line AB, which will be the perpendicular required. B C G Or, With any convenient distance in the compasses, and one foot in the end of the line, describe an arch as FB, set off the same distance from B to E, with one foot in E, describe an arch at C, and with the same distance, turn one foot over to F, and describe an arch to cut the former in C; from C to A, draw a line, and it is done. From a point, as at C, to let fall a perpendicular on the line AB. RULE. With one foot in C, describe an arch to cut the given line AB; with one foot in each place of intersection, describe arches at D, and from C to D, draw a line, and it From a given point C, to let fall a perpendicular on the end of a given line AB, at B. RULE. From any point in the line, as at F, with the distance FC, describe an arch at E; choose any other point in the line, as at D, and with the distance DC, intersect the former arch in E; join CE, and it is done as required. |