On some geometric properties and applications of conformal rational transformations in a plane (1912)
Renich, Mary Emma · leaf 44
e designated by A and A and their associates, A and A • 4 The co-ordinates of B^, the center of the hyperbolas,which are found by the method given in Art. IV, are, x = - /a a - aa8+ b2b3 - b0b2^ 2 3 Q . / 2T a- + b*) — > (aabs - aabo - bgaa + aoba)7 ~ 2 (a| + bf) — Prom Art. IV (b), we know… … M2i Pig. VII The slope of the line z2z3 is - i while that of Zx^is + i.. The equation of line Z2Z3 is (y - ha) s - i (x - as), (6) that of line z1z3is (y - b1) s i ( x - ax)# (7) Solving (6) and (7) simultaneously we have for the co-ordinatesof A3 =: z3, x, = (a, +».)♦!(»,- t.) , y3 ■ !(».-*,) +…
