Davies, Charles, 1798-1876 · New York, Cincinnati [etc.] American book company · leaf 325
proceed to describe the method of locatingcurves, first giving the mathematical principles applicable tothe subject. Let AD and DB, Fig. 168, be two tangents to the arc of acircle, AB. Draw the radii AC, BC, and the secant CD. The following relations are easily deduced. The tangentsAD and DB are… … (1) plements of each other. The angle TDB, therefore, must be equal to the angle ACB. The right-angled triangles ADC and BDC are equal (Leg., Bk. I, Prop. 17); hence, the angle DC A is equal to DCB, and each equal to ^TDB. Let the radius AC hQ rep-resented by r, the distance ADby d, and the angle…
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