F2(X2 + Y2) = y12 + y22 + y32 − G2,
(21)
| F(X + Yi) = | Fy3 − Gx3 + i √ X3 | εψi. |
| √ (F2 − x32) |
(22)
Suppose x3 − F is a repeated factor of X3, then y3 = G, and
| X3 = (x3 − F)2 [ | p′ − p | (x3 + F)2 + 2 | q′ − q | G (x3 + F) − G2 ], |
| r | r |
(23)
and putting x3 − F = y,
| ( | dy | ) | 2 | = r2y2 [ 4 | p′ − p | F2 + 4 | q′ − q | FG − G2 + 2 ( 2 | p′ − p | F + | q′ − q | G ) y + | p′ − p | y2 ], |
| dt | r | r | r | r | r |
(24)