Elements of analytical geometry and the differential and integral calculus (1856)
Robinson, Horatio N. (Horatio Nelson), 1806-1867 · Cincinnati : J. Ernst · leaf 140
ar to theplane; this line will be at right angles toevery line drawn in the plane from thepoint p. Whence Oi? §=90°, OpB=90°,Ojt?P=90°. Let Op=p. Designate the angle p OP by X, pOQby Y,andpOEhj Z. By the preceding scholium we learn that 0P=--. 0Q=-^, and 0B=-:^,A B C Af B, C, and D, being the… … The right angled triangle OpR gives •^ : I ::p : cos.Z, (3) 132 ANALYTICAL GEOMETRY. Proportion (1) gives us i>2 (2) gives COS.* Y=^^B^,and (3) gives cos.* Z= ^ (7*. (4)(5)(6) Adding these three equations, and observing that the sum ofthe first members is unity, (Prop. VII, Chap. I, Sec. II,J…
Geometry, Analytic · Calculus
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