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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 354

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 354
^ Treatise c / Part III . 336 § 33 . These may all be demonstrated more directly from the consideration of the general equation of the lines of the second order in § 21 . For it is obvious that , by § 25 . Part II . … OE F the second term of that general equation may be exterminated by assuming z — y - f — > and it will be transformed into + ± c . ~ . t x x 1 , , 1 ab + « — — X v > - o . 2 + e - ~ 4 J which , by transposing the last term , is , _ x a , , ab , » = - - c X * H - d X x 4 4 2 e 1 Let

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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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