Beman, Wooster Woodruff, 1850-1922, Smith, David Eugene, 1860-1944 · Boston, Ginn & company · leaf 369
a smallcircle, their circumferences are said to be perpendicular to eachother. Proposition XXIII. 487. Theorem. If from a point on a sphere arcs of greatcircles both perpendicular and oblique, are drawn to anycircumference, then, 1. The shorter perpendicular is less than any oblique; 2. Two… … Given S, any circle of a sphere; P any point on thespherical surface; minor arcs, PC J_ circumferenceS, PA, PB, PD obliques ; PC = CD, and AC > CDor its equal BC. To prove that (1) PC < PB; (2) PB = PD; (3) Rk > PD or its equal PB. Prop. XXIII.] THE SPHERE. 353 Proof. 1. Suppose N the pole…
Geometry
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