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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