An Elementary Treatise On Cubic And Quartic Curves
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In our eReader you can find the full English version of the book. Read An Elementary Treatise On Cubic And Quartic Curves Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book An Elementary Treatise On Cubic And Quartic Curves
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Since /is a constant, (1) may be written in the form (vi + v„) (?•' + w, + lu,) + F = 0, CIRCULAR CUBICS. 75 where V is the general equation of a conic in Cartesian coordinates and Vn, Wn are binary quantics in x and y. This equation is equivalent to Vir2 + w, + Mi + i«„ = .; (2), where Un is also a binary quantic in x and y. Equation (2) is the general equation of a circular cubic in Cartesian coordinates.
123. To find the equation of a circular cubic which has a pair of imaginary points of in...flexion at the circular points.
If u, V, w be any three straight lines, the equation u (i)' + v?) + /•* = represents a cubic having one real and two imaginary points of inflexion on the line at infinity, and the tangents at the two latter points are i; + tw = 0. Let the origin of a system of Cartesian coordinates be the point of intersection of these two tangents, then, if the two imaginary points are the circular points, v = x, w = y, and the equation of the curve becomes u (a;2 + y-) + /■' = 0, or {x- + y") (px + qy + r) + c' = 0, where p, q, r and c are constants.
What to read after An Elementary Treatise On Cubic And Quartic Curves?
You can find similar books in the "Read Also" column, or choose other free books by Alfred Barnard Basset to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Since /is a constant, (1) may be written in the form (vi + v„) (?•' + w, + lu,) + F = 0, CIRCULAR CUBICS. 75 where V is the general equation of a conic in Cartesian coordinates and Vn, Wn are binary quantics in x and y. This equation is equivalent to Vir2 + w, + Mi + i«„ = .; (2), where Un is also a binary quantic in x and y. Equation (2) is the general equation of a circular cubic in Cartesian coordinates.
123. To find the equation of a circular cubic which has a pair of imaginary points of in...flexion at the circular points.
If u, V, w be any three straight lines, the equation u (i)' + v?) + /•* = represents a cubic having one real and two imaginary points of inflexion on the line at infinity, and the tangents at the two latter points are i; + tw = 0. Let the origin of a system of Cartesian coordinates be the point of intersection of these two tangents, then, if the two imaginary points are the circular points, v = x, w = y, and the equation of the curve becomes u (a;2 + y-) + /■' = 0, or {x- + y") (px + qy + r) + c' = 0, where p, q, r and c are constants.
What to read after An Elementary Treatise On Cubic And Quartic Curves?
You can find similar books in the "Read Also" column, or choose other free books by Alfred Barnard Basset to read onlineMoreLess
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