A treatise on special or elementary geometry (1877)
Olney, Edward, 1827-1887, Olney, Edward, 1827-1887. Elements of trigonometry, plane and spherical · New York : Sheldon · leaf 239
564z, A Tanffcnt I^lane to a curved surface at a given pointis the plane of two lines respectively tangent to two plane sectionsthrough the point. III.—Let P be a point in the cui*vedsurfiice at which we wish a tangentplane. Pass any two planes throughthe surface and the point P, and let OPQand MPN… … Fig. 326. PROPOSITION X. 565. TIieorein.—A tangent plane to a sphere is perpendicularto the radius at the point of tanrjency. Dem.—Let P be any point in the surfaceof a sphere; pass two great circles, as PaA,etc., and PwAR, through P, and draw STtangent to the arc 7nP, and UV tangent to thearc aP;…
Geometry · Trigonometry
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