Woods, Frederick S. (Frederick Shenstone), 1864-, Bailey, Frederick H. (Frederick Harold), 1865- · Boston, New York [etc.] Ginn and Company · leaf 102
reater than2 a, and that // = 0 is an asymptote. 48. The cissoid. Let 01)A (fig. 81) .be a circle with the diameter OA,and let LK be the tangent to thecircle at A. Through 0 draw anyline intersecting the circle in D andLK in E. On OE lay off a distanceOP, equal to DE. Then the locus ofP is a curve… … Fig. 81 86 CE11TAIN OUJiVES Denoting angle MOP by 0, we haveOJ0=2aaec0,OD=2acos0;DE = OE -0D=2a (sec 0 - cos 0).OP=2a(sec0-cos0).x = OM= OP cos0= 2a(l-cos26>)= 2asin20.MP v whenceThereforeNow But sin 0 = Substituting in (5), we have whence 2 a This equation is satisfied by thecoordinates of any…
Geometry, Analytic · Calculus
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