I (
i[ I I
si
ON THE INVERSION OF A QUADRIC SURFACE.
For x, y, z write x—^^w, y— 2 and put for shortness
lx + my + nz = u, l 2 + m 2 + n 2 = ol,
al 4- hm + gn = a, (a, b, c, f, g, fitfl, m, n) 2 = A,
hi + bm +fn = b,
gl + fm + cn = c,
becomes r 2 — ^ + \ ~ w 2 ,
lx + my 4- nz ,,
(a, ...\x, y, z) 2
Hence the equation is
7 [ . ~ „ uw „ (7 a „ u 2 \ . auw 2 , a 2
d r~ 2r, Y +m
[498
U — h -} w,
“ cl
(a, ...l[x, y, z) 2 - (ax + hy + cz)™ + ±A ™
( „ UW 2
i a
( i OL \
\ wr - 1T +
*<P W J
(a, ...Jx, y, z) 2 - (ax + by + cz) ~ + lA ^[ = 0 ;
( , a u 2
+ w ]~^n r,2 --r + (a, ...Jx, y, z) 2