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angle arbitrary auxiliary axes axis centre chord coefficients common comp condition cone confocal conjugate const constant corresponding curve in space cusp-edge cyclic cylinder deduced denote derived determined developable surface differential equation direction ellipse ellipsoid expression formula generatrix geodetic geometrical given curve given point given surface helix hodograph hyperbola hyperboloid index surface intersection linear lines of curvature locus normal plane oomp osculating circle osculating plane osculating sphere parallel perpendicular principal curvatures quadric quadric cone quaternions radius radius of curvature real or imaginary reciprocal rectangular rectifying line represents right cylinder right line rotation satisfied scalar equations scalar variable second curvature second order self-conjugate semiaxes spherical sub-articles supposed tangent plane theorem transformation twisted cubic values vector equation vector function velocity vertex VIII whence whereof whioh write XVII XVIII XXIII XXVII