On some geometric properties and applications of conformal rational transformations in a plane (1912)
Renich, Mary Emma · leaf 102
v = 2 x y, s=2xy. Rationalizing the denominator, ur + 78 = (x2 + y8)8 - 1 = 0f (4) vr - us = 4 x y = 0> (5) r2 + s2 = (x2 + y2)2 + 2 x2 - 2 y8 + 1 = 0. (6) ^Loria, loc. cit. p. Il8. 46. (4-) and (6) are the equations of degenerate bicircular quartics,while (5) is that of a degenerate hyperbola… … Pig. XV. For the invariant points, described in Art. VI, we havethe roots of the equation. « = **L±£-*+l. . (7) J22 + 4 Z + O) (7) is the equation of the cubic $ z3 + ( •€ - a) z2 + (a) -(*) z - r = o. (8) Substituting in (8) the values of the complex numbers, it becomes (aa + i b3)(x + iy)3 + (a4…
