On some geometric properties and applications of conformal rational transformations in a plane (1912)
Renich, Mary Emma · leaf 90
x = - 1/3, y = 0. One asymptote coincides with thex - axis, the slopes of the other two are + V$. The asymptotesare concurrent at x = - 1/3, y = 0, and make equal angles with eachother. Therefore, (10) is also an equiangular curve of the 3rd*Ft Lucas, loc. cit. in historical sketch. Rhizic curves… … Branch points. For any value of z1 we may write 21 = \\*fs in the f°m A z8 + B z + C = 0, (8) where A = z* r , B = $ z1 - a, C - 4 z1 -/£ . To find the particular values of z1 for which (8) has two equalroots we place B2 - 4 A C = 0. This gives the equation[6 z1 - a)2 - 4 (zir)(-€ zi -<3) = 0.…
