Elements of analytical geometry and the differential and integral calculus . e of the axis of X. Finally, let x equal any value whatever less than A, theny=.dt^(A^^x^)i. THE ELLIPSE. 46 An equation showing two values of y, numerically equal, indi-cating that the curve is symmetrical in respect to the axis of we give to y any value less than B, the general equationgives Showing that the curve is symmetrical in respect to the axisof T, Scholium. The ordinate which passes through one of the foci,corresponds to a;=c. But ^^—B^=c^. Hence -4^—c^ or A*—x^=£^. Or (A^—x^)^=B, and this value substi
Elements of analytical geometry and the differential and integral calculus . e of the axis of X. Finally, let x equal any value whatever less than A, theny=.dt^(A^^x^)i. THE ELLIPSE. 46 An equation showing two values of y, numerically equal, indi-cating that the curve is symmetrical in respect to the axis of we give to y any value less than B, the general equationgives Showing that the curve is symmetrical in respect to the axisof T, Scholium. The ordinate which passes through one of the foci,corresponds to a;=c. But ^^—B^=c^. Hence -4^—c^ or A*—x^=£^. Or (A^—x^)^=B, and this value substituted B^ 2^2 in the last equation, gives y=dz Whence is the A A measure of the parameter of any ellipse, by Def. 10. PROPOSITION II. Every diameter is bisected in the center. Let X, and y, be the co-ordinates of the point D, and x\ y\the co-ordinates of the point by the equation of the curve And ^2y2+^2^2=^2^3. The equation of a line passingthrough the center, must be of theform y=ax. This equation combined with the equations of the curve, gives AB aAB 5^=. Ja^A^+B^ Ja^A^+B- AB , aAB Ja^A-+B^ Ja^A^+B^ These equations show that the co-ordinates of the point Dyare the same as those of the point D\ except opposite in UB is bisected at the
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