On some geometric properties and applications of conformal rational transformations in a plane (1912)
Renich, Mary Emma · leaf 46
es may be distin-quished. Case 1^ - By choosing the co-ordinates of our pointsas shown in Pig, VIII, the transformation. z» ■ <* z becomesz* ■ l/z, which consists of a reciprocation and a reflection onthe axis of reals. The co-ordinates of z1 are x* - x/(x8 + y8) , y - - y/(x8 + y8J, and Pig,… … \f-.o Pig. VIII 19. u ^ x8 - y2 - 1 = 0^ and v m 2 xy = 0, The problem is to find the equation of those cubicswhich pass through Ax(l,0), Aa(-1,0), Aa(0,i), A4(0,-i), B3(0,0),I (y/x ■ +i, x =oo ) and I (y/x = -i, x - ) . and are trans- 1 8 formed into themselves by the transformation z% ■ l/z.…
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