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 40
ree points a, B, c on a given pla/ne a/re a, b, c.then AABc = cosf). abc, where 6 is the a/ngle between theplanes abc, abc. Consider first the areas ABC, ABC without regard tosign. (i) If the planes ABC, ABC are parallel, the equationA ABC = cos 0 A ABC is obviously true. (ii) If one side of the… … Fig. 15. A2D and AA2, and therefore BC is normal to the plane AA0D,and therefore at right angles to AD. Hence the angle A.,DAis equal to 0, or its supplement. But A ABC = A A2BC, and A A2BC : A ABC = A2D : AD = COS L A2DA : therefore A ABC = cos 6 a ABC. (iii) If none of the sides of the triangle…
Geometry, Analytic
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