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Special cubics and quartics produced by projective pencils of straight lines and conics (1916)

Marshall, Robert Haskell · leaf 40

An illustration from Special cubics and quartics produced by projective pencils of straight lines and conics, 1916, leaf 40 — solution to - 0 ^ Q ?x ~ 3yIt is therefore of deficiency one. The derivative of {4j is dy _ 1 -f- axy — 2xdx 2y - X*- -3y ^ From this equation it is seen that the slopes of the tangents at the^origin and at the points (1.0), (0,1) are respectively <x, , l, and —1. To construct the locus of (4)… … >1 16- are points on the locus of (4). Figure II exhibits the locus of (4).3. Another cubic may be generated by taking the product of apencil of parabolas and a pencil of lines.Let be the pencil of parabolas, and JL- 4-y - 1 the pencil of lines. If ^ is eliminated between these twoequations…

Curves, Cubic · Curves, Quartic · Polynomial operator pencils · Conics, Spherical · Geometry, Projective · Theses

Internet Archive · University of Illinois Urbana-Champaign · Public Domain Mark 1.0. Free to use for anything.

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$An illustration from Opticks, or, A treatise of the reflexions, refractions, inflexions and colours of light ; Also two treatises of the species and magnitude of curvilinear figures (1704)$