An elementary treatise on analytical geometry : embracing plane co-ordinate geometry, and an introduction to geometry of three dimensions (1869)
Johnson, William Woolsey, 1841-1927 · Philadelphia : J.B. Lippincott · leaf 201
ing topolar co-ordinates, we have (A cos2 0 -f C sin2 0) r2 -f (D cos 0 -f E sin 0) r -f F = 0, 196 THE HYPERBOLA. in which the initial line is parallel to one or other of the principalaxes of the curve. This equation gives in general two values of rcorresponding to any value of 6. Now the product… … A cos 6 -f C sin2 6> where 6 is the inclination of the chord to the axis of X. Since, bythe last Article, A and C are unchanged by transformation to a neworigin, the products of the segments of parallel chords passingthrough different points are proportional to the values of F forthose points ;…
Geometry, Analytic
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