Elements of geometry : containing the first six books of Euclid, with a supplement on the quadrature of the circle, and the geometry of solids : to which are added, Elements of plane and spherical geometry (1826)
Playfair, John, 1748-1819, Euclid · Philadelphia : Marot & Walter · leaf 233
CG : IK, and it has been shown that EI=cos. BC, and IK=|(BF-f DH); therefore R : cos. BC :: sin. AC: 5 (sin. AB-f-sin. AD).Q.E. D. CoR. Hence, if the point B coincide with A,R : COS. BC : : sin. BC : 5 sin. BD, that is the radius is to (be cosineof any arch, as Ihe sine of the arch is to half the… … A F PLANE TRIGONOMETRY. 233 Again, 1, 2, 3 being three such arches that the tiifferenee betweenthe first and second is the same as between the second and third,R : cos. l:: sin. 2 : k (sin. l-|-sin.3),or sin.l4-sin.S=2cos. Ixsin. 2, and taking sin. Ifrom both,sin.3=2 cos. Ixsin. 2 —sin. 1. In like…
Euclid's Elements · Geometry · Trigonometry
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