ond elementof the geodesic production of mn. Ifnow 6 be the angle of contact tnp^and 6^ be tnq the angle of contactof the normal section, we have tp = Ods,tq = 6ds. Now the angle qtp (= (j>)is the angle between the osculating plane of the curve andthe plane of normal section, and since tq = tp… … 6=^6cos<f> and -^ = —-—, which is Meuniers theorem; B CURVES TRACED ON SURFACES. 361 contactj we have pq — u as and pq = tp sm 9, or - = •. The geodesic* radius of curvature is therefore p cosecc^. It iseasy to see that this geodesic radius is the absolute radius ofcurvature of the plane…
Geometry, Analytic · Surfaces
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