 | Michel Chasles - Cone - 1837 - 564 pages
...when a line cutting the hyperbola is parallel to a diameter, the rectangle of the parts of this secant between a point of the curve and the asymptotes is equal to the square of the semi-diameter. 208. From any point P (fig. 63) of the hyperbola, draw parallels PG, PF to the asymptotes,... | |
 | John Hymers - Conic sections - 1837 - 486 pages
...when a line cutting the hyperbola is parallel to a diameter, the rectangle of the parts of this secant between a point of the curve and the asymptotes is equal to the square of the semi-diameter. 208. From any point P (fig. 63) of the hyperbola, draw parallels PG, PF to the asymptotes,... | |
 | Henry Barnard - Education - 1856 - 768 pages
...on any two conjugate diameters. — The portions of a secant comprised between the hyperbola and ita asymptotes are equal. — Application to the tangent...curve and the asymptotes, is equal to the square of halt of the diameter to which the secant is parallel. Form of the equation of the hyperbola referred... | |
 | Education - 1862 - 752 pages
...of these points and of these lines, analogous to those which they possess in the ellipse. Asvmptotes of the hyperbola. — The asymptotes coincide with...which the secant is parallel. Form of the equation of tho hyperbola referred to its asymptotes. Of the parabola. Axis of the parabola. — Ratio of the squares... | |
 | Henry Barnard - Military education - 1862 - 410 pages
...comprised between the hyperbola and its asymptotes are equal.—Application to the tangent and to ita construction. The rectangle of the parts of a secant,...equation of the hyperbola referred to its asymptotes. Axis of the parabola.—Ratio of the squares of the ordinates perpendicular to the axis. Of (he parabola.... | |
 | Henry Barnard - Military education - 1862 - 412 pages
...chords.—Properties of these points and of these lines, analogous to those which they possess in the ellipse. The rectangle of the parts of a secant, comprised...equation of the hyperbola referred to its asymptotes. Axis of the parabola.—Batio of the squares of the ordinatea perpendicular to the axis. Of the parabola.... | |
 | Charles Briot, Bouguet (M., Jean Claude) - Geometry, Analytic - 1896 - 598 pages
...diameter meets the curve, and one will arrive at an analogous result. Thus, the product of the spgments of a secant, comprised between a point of the curve and the asymptotes, is equal to the nqitare of the semi-diameter parallel to the secant. 194. Being given the asymptotes RR', SS', and... | |
| |
Asvmptotes of the hyperbola. — The asymptotes coincide with the diagonals of the parallelogram formed on any two conjugate diameters. — The portions of a secant comprised between the hyperbola and its asymptotes are equal. — Application to the tangent... 