of curvature meet the curve again in P,P, the locus of the intersection of the transverse geodesies0P\ OP will be a line of curvature of the same species. 418. Mr. Eobertss expression for the element of an arcperpendicular to an d4>j umbilical geodesic hasbeen extended as fol-lows by Dr.… … * This theorem, as well as those on which its proof depends (Art. 414, <fec.), isdue to Mr. M. Roberts, to whom this department of Geometry owes so much(JAouville, vols. xiii. p. 1, and xv. p. 276). CURVES TRACED ON SURFACES. 377 geodesic touclies ^ in a point P (Art. 405); and if TT be…
Geometry, Analytic · Surfaces
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