n angle different from o). In order to prove this weshall investigate an expression for ^, the angle made withthe plane of the umbilics by the osculating plane at any pointof that geodesic. It is convenient to prefix the following lemma: In aspherical triangle let one side and the ad-jacent angle… … trigonometry cos ^[A-\- B) = sm^C cos ^ {a-\- b) gives us in the cos-^c limit dd = COBoidxlr. But evidently smad\fr = sm0d<}). Hencedd _ d(f>sin 6 tana Now we know (Art. 405) that the tangent line at any pointof a geodesic passing through an umbihc, if produced, goes tomeet the plane of the…
Geometry, Analytic · Surfaces
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