Abstract
American Journal of Mathematics, vol. xx. No. 2.—On the focal surfaces of the congruences of tangents to a given surface, by A. Pell. This paper is based upon two theorems given by Darboux (“Théorie générale des Surfaces,” vol. iii. p. 121) and Koenigs (“Sur les propriétés infinitésimal de l'espace régié”), viz.: the locus of the centres of geodesic curvature of lines of curvature of any surface is the edge of regression of the developable surface, generated by the tangent planes of the surface at all points of the lines of curvature, and the edges of regression of the developable surfaces of a congruence form two families of curves on the focal surfaces (say SA and SB corresponding to the focal surfaces A and B), the osculating planes of which are tangent to the surfaces B and A respectively, and the points of contact describe on these surfaces two families of conjugate lines SA and SB.
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Scientific Serials. Nature 58, 22 (1898). https://doi.org/10.1038/058022b0
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DOI: https://doi.org/10.1038/058022b0