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A Treatise of Algebra in three Parts : I. the fundamental Rules and Operations : II. the Composition and Resolution of Equations of all Degrees and the different Affections of their Roots : III. the Application of Algebra and Geometry to each other ; The general Properties of Geometrical Lines (1779)

MacLaurin, Colin · printed for Nourse... · leaf 349

An illustration from A Treatise of Algebra in three Parts : I. the fundamental Rules and Operations : II. the Composition and Resolution of Equations of all Degrees and the different Affections of their Roots : III. the Application of Algebra and Geometry to each other ; The general Properties of Geometrical Lines, 1779, leaf 349
Chap . 2 . ALGEBRA . 33 r wants both the terms , xy and it may be always accommodated to a parabola . § 28 . The general equation for the ellipse is deduced from the property of the ordinates of any diameter , in the fame manner ; the con struction of the figure being the fame as in § 26 . Only ,… … let C be the center of the ellipse . Suppose CL — / , and the parameter of that diameter — / > , then GMij ’ : CI y — CGq : : p : 2 t . But , as d , and CG in § 26 , GM — y a a a therefore , y a | p a — . v — e l : whence this equation : a 2 1 > And

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More pictures from A Treatise of Algebra in three Parts : I. the fundamental Rules and Operations : II. the Composition and Resolution of Equations of all Degrees and the different Affections of their Roots : III. the Application of Algebra and Geometry to each other ; The general Properties of Geometrical Lines

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