Principles of modern geometry, with numerious applications to plane and spherical figures; and an appendix, containing questions for exercise. Intended chiefly for the use of junior students (1862)
Mulcahy, John, 1810?-1853 · Dublin Hodges, Smith · leaf 213
gn), for the hyperbola (see fig.), CP2.sin0.sm0=CQ2.sin0.sin0, and therefore the triangle CPS isequal to the triangle CQT. If CA be the major semi-axis, the equation will become CP8 • sin 9 - cos 0 = + CQ/S • sin Q> • cos 0,or CP2 - sin 20 ± CQ2 • sin 20 = 0. The upper sign being taken in the… … sin- + sm3 In the case of the hyperbola, this becomes (changing the signof CQ) OS8-- CT2 = CA8. Again, the equation CP/2+CQ2 = constant, becomes, of course,CP/2—CQ/2 = constant = the difference of the squares of the semi- axes. 3°. It was proved in Proposition 4° of the last Article thatthe locus…
Geometry -- Problems, exercises, etc · Geometry
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