Fig. 189.
[ CII]
To Draw Semicircles Standing upon a Circle at any Angle
Given the circle ACBH, on diagonal AB draw semicircle AKB, and on the same line AB draw rectangle AEFB, its height being determined by radius OK of semicircle. From centre O draw OF to corner of rectangle. Through f·, where that line intersects the semicircle, draw mn parallel to AB. This will give intersection O· on the vertical OK, through which all such horizontals as m·n·, level with mn, must pass. Now take any other diameter, such as GH, and thereon raise rectangle GghH, the same height as the other. The manner of doing this is to produce diameter GH to the horizon till it finds its vanishing point at V. From V through
K draw hg, and through O· draw n·m·. From O draw the two diagonals og and oh, intersecting m·n· at O, O, and thus we have the five points GOKOH through which to draw the required semicircle.
Fig. 190.