An elementary course of infinitesimal calculus . Fig. 73. transforms into an ellipse where a = aa, V = fia;. .(3),(4), 326 INFINITESIMAL CALCULUS. [CH. VIII and it is evident that by a proper choice of the ratios a, ^ acircle can be transformed into an ellipse of any given dimen-sions, and vice versd. Also since a system of parallel chords,and the diameter bisecting them, transform into a system ofparallel chords, and the diameter bisecting them, it is evidentthat perpendicular diameters of the circle transform intoconjugate diameters of the ellipse. Further, areas are altered by transformatio
An elementary course of infinitesimal calculus . Fig. 73. transforms into an ellipse where a = aa, V = fia;. .(3),(4), 326 INFINITESIMAL CALCULUS. [CH. VIII and it is evident that by a proper choice of the ratios a, ^ acircle can be transformed into an ellipse of any given dimen-sions, and vice versd. Also since a system of parallel chords,and the diameter bisecting them, transform into a system ofparallel chords, and the diameter bisecting them, it is evidentthat perpendicular diameters of the circle transform intoconjugate diameters of the ellipse. Further, areas are altered by transformation in theconstant ratio a/8. For this is evidently true of any rect-angle having its sides parallel to the principal directionsof the straia; and any area whatever can be approximatedto as closely as we please by the sum of a system of rectanglesof this type. JEx. 1. Thus, the area of the ellipse (3) is o^ times that of thecircle (2); and so = a)8. ira = ir. aa. /8a = nab. Again, a chord cutting off a segment of constant area from acircle touche
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