Bailey, Frederick H. (Frederick Harold), 1865- · Boston, London, Ginn & Co. · leaf 298
having as directioncosines cos ai, cos ^i, cos yi, and cos ag, cos /?2, cos yo, re-spectively. Let angle MON be denoted by 6. Take P (xi, yi, z^)any point of OM, distant ri from 0. By 1, § 6, the projection of OP on ON is ri cos 6, and theprojection of the broken line OLMP on ON is OL cos a., + LM… … Fig. 10. or cos 9 = cos ai cos ao + cos Pi cos Pa + cos 7i cos y^, [4]since by § 5, — = cos aj, etc. As the angle between any two lines is the angle betweentheir respective parallels drawn from a common point, [4] isobviously true in all cases. If ^ = 90°, cos ^ =; 0. Therefore, if two lines are…
Geometry, Analytic
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