Elements of analytical geometry and the differential and integral calculus (1856)
Robinson, Horatio N. (Horatio Nelson), 1806-1867 · Cincinnati : J. Ernst · leaf 66
which refer to the rectangular axes. But as a general thing itwill not do to draw summary conclusions. PROPOSITION X. As the square of any diameter is to the square of its conjugaietso is the rectangle of any two segments of the diameter to the squareof the corresponding ordinate; that, is, the… … m ANALYTICAL GEOMETRY. Whence A^ : B^ : : (A^—x^) : y*. Or (2Ay : (2By : : (A+x)(A—x) : y\ Now 2^ and 2-5 represent tlie conjugate diameters DJ), EE^and since CH represents x, A-\-x=Dir, and A—x=BJ),Also y= 6^-5^ Hence the above proportions correspond to {DDy : (EUy : : DEy^HD : (6^^)2. Q. E. D.…
Geometry, Analytic · Calculus
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