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 260
e tangent of half theside adjacent to them, to the tangent of half the sum ofthe sides opposite. Let C+B=2S, C-B=2D, the base BC=2B, and the differenceof the spa:men(s of the base, or BD —CD=2X. Then, because (30.)sin. (C+B) :sin. (C-B) II tan. | BC; tan. ^ (BD-CF)),sin.2S: sin.SD :: tan. B : tan.… … sin U :: sin AB+sia AC : sm AB—siu AC. But (3. PI. Tr.) sin AB-|-siuAC:siaAB-sin AC :: tan | (AB + AC): tan i (AB—AC) *.: tan S : tan A, S being equal to | (AB+AC) and A to ^ (AB-AC). Therefore sin Sxeos D : cos Sxsin D ll tan X : tan A- Since then tanX sinDxcusD , tanA cosSxsinD, ,.- , . 7 rj— ■…
Euclid's Elements · Geometry · Trigonometry
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