An elementary treatise on coordinate geometry of three dimensions (1912)
Bell, Robert J. T. (Robert John Tainsh), 1877-1963 · London : Macmillan and co., limited · leaf 49
-cosines are cosoc, cos/3,cos y. Take P, (x, y, z) any point on AOA. and let themeasure of OP be r. Draw PN parallel to OZ to meetthe plane XOY in N, and NM parallel to OY to meet OXin M. Then, since the projection of OP is equal to the 26 COORDINATE GEOMETRY [ch. ii. sum of the projections of OM,… … Fig. 20. Therefore, eliminating r, cc, y, 0, we have the relationsatisfied by the direction-cosines of any line 1, cos v, cos ^ cos a =0,cosj/, 1, cosX, cos/3 cos fx, cos X, 1, cos y cosoc, cos/3, cosy, 1 which may be written, X sin2X cos2oc— 22(cos X — cos /x cos y)cos /3 cos y = 1 — cos2 X — cos2…
Geometry, Analytic
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