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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 372

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 372
A Treatise of Part IIL 354 this may be done , though the parameter of the parabola { viz . b ) be given : that is 1 , if you have a parabola already made or given , by it alone you may resolve all biquadratic equations , and you will only need to vary the center of your circle and its radius . § 44… … last term of the biquadratic ( c 1 + d ' ~ — sll ) Wl ^ vanish ; therefore , dividing the rest by y , there arises the cubic , jy 5 * ± ibc + b * X y — 2db * ~ o . Let the cubic equation proposed to be resolved be y * ± py ± r — o . Compare the terms of these

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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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