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 352
334 A T ' R e at i se of Part IIJ . § zi . The equation of the hyperbola when its ordinates PM are parallel to an asymptote does not come under the general equation of the last article . Let CF and CL be tl e asymptotes of the hyperbola , and let PM be parallel to CL . … Then CG x GM will be equal to a given rectan gle ( which suppose ga ) . Then , CO — DG — LC — — a ’ — e , GM — v — — x — d , and con - a J a a sequently _ y x — d X — x — e — g X a : whence this equation , ea eda ' — — y + — X c Where only one of the terms y * , x z , can be found with xy , and…
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