On some geometric properties and applications of conformal rational transformations in a plane (1912)
Renich, Mary Emma · leaf 26
( aQ a, + bQ bj y +a0 t>2 «2 b0 - 0. (13) (13) can be written /x + aoai + *o*i \I 2 (a2 + b2) J (7 + aobi ai*o) - (aoai + V^^i aiV 2 <a§ + 4 (a2 + b2) 2 + *£&LZ^ a2*0_ = o which is of the form 2f n - C2 = 0 , (14)2 (a2 + b2) S> I (14) is the equation of a hyperbola, having the same… … Pig. III.The co-ordinates of B3 are - aQa1 + bQb12(aJ + b») y — - a b - b^a These co-ordinates can be found analytically from theoriginal equation &a z* +*z +«xs 0. 2 <x CX ftOC 2 (X = - QC ! = -fa, + ib^* 2 oC o 2(a0 +~Ib^T Separating the real and imaginary parts, we have as the…
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