Davies, Charles, 1798-1876 · New York, Cincinnati [etc.] American book company · leaf 338
xedtangent points A and B, the angle DAB = A, and the angleABG =z B, to find the common radius EG=GF=:R of areversed curve to unite the tangents HA and BL. From the triangleABK, Fig. 176, wehave (Art. 32), AE . EK :: sin AKE: sin EAK, but since EAK= 90°-^ sin EAK = cos ^; hence, denoting angle AKE… … Fig. 176. 332 ELEMEITTS OF SURVEYING. . [BOOK IX. . •. sin ^ = 1^ (cos A + COS B). (4) But cos ^4-cos ^ = 2 cos J (A-{-B) cos J (A—B),(see Legendre, Trig. Art 67); hence, sin X= cosi{A-\-B) cos ^ (A—B). (5) Having found K, we have the angleAEK= E — 180°-(^+^^^) = 180°-(^+90°-^) :=90°-f^-^. (6) In…
Surveying
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