Elements of plane and spherical trigonometry (1833)
Young, J. R. (John Radford), 1799-1885 · Philadelphia, Carey, Lea & Blanchard · leaf 52
RMULAS, AND RULES FOR THE SOLUTION OPSPHERICAL TRIANGLES. (44.) Let ABC be a triangle tracedon the surface of a sphere of whichthe centre is O, and the radius equalto the linear unit. The angles of thistriangle we shall represent by theletters at their vertices, A, B, C,and the sides opposite to… … OD = sec. c = , OE = sec. b = ^ COS. y (1). COS. b Draw DE, then m the two triangles ODE, ADE, we have (17^DE2 = 0E2 -}- 0D2 — 2 OE-OD cos. aDE2 = AE2-f AD2 - 2 AEAD cos. A ;recollecting that (p. 43-44) the plane angle DAE measures the spheri-cal angle A. Substituting in these equations the values…
