On some geometric properties and applications of conformal rational transformations in a plane (1912)
Renich, Mary Emma · leaf 106
where u = x3 - 3 x y3 - x3 + y3 + x + 1 * 0, (11)▼ 5 3 x3 y - y3 - 2 x y + y = 0. (12) (11) is the equation of a cubic which is symmetrical tothe x - axis. The equations of its asymptotes^which are allreal, are found to bex - 1/3, 9ys3V3*-\/3>9y = -3V3x + \/3, These asymptotes are concurrent at… … Pig. XVI. (12) is the equation of a degenerate cubic consistingof a straight line^ the x - axis^and an hyperbola. The centerof this cubic is the same as cubic (11). The asymptotes of thehyperbola form angles of 60° degree with each other and also withthe X - axis, the third asymptote of the cubic.…
