Woods, Frederick S. (Frederick Shenstone), 1864-, Bailey, Frederick H. (Frederick Harold), 1865- · Boston, New York [etc.] Ginn and Company · leaf 331
gin, as in fig. 199, it isevident that the same straight line makes the angles a, /3, 7 or17 — a, ir — /3, 17 — 7 with the coordinateaxes, according to the direction in whichthe line is drawn. Hence its directioncosines are either cos a, cos/3, cos 7 or— cosa;, — cos/3, —cos 7. Hence thestraight… … PQ or cos 7 = a Va2 + &2 + c2 cVa2 + 62 + 62 1]E cos/3 = PS -^-1 COS/3 = — , C0S7 = ——, CI) P,P2 P,P2 7 JJJJ W b Va2 + b% + c* (2) Squaring and adding equations (2), we have cos2a-f cos2/3 + cos27=l; (3) that is, the sum of the squares of the direction cosines of anystraight line is always…
Geometry, Analytic · Calculus
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