489
414] ON POLYZOMAL CURVES.
The meaning is, that, taking the trizomal curve fl-JJ + fm 1 V+fn 1 W = 0, this regarded as a
tetrazomal curve, U+ Vm x V + fn x W + V0T = 0, satisfies the condition -^ + -^ + -^ + ^ = 0;
and the like as to the trizomal curve f LU + f m. 2 V + fn 2 W = 0.
45. The equation by which the decomposition was effected is, it is clear, one of
twelve equivalent equations; four of these are
№
Vm ,
fn ,0 j
[fu, Vv, \fw, VtJ =
(°
hi
v m -1 ,
a wm
fn , fp ^
( . )•■
-1- -(cfpW-dfnTX,
cda m\ )
(Vi
0
Vre + bV,r ^ )
( - )■
(w
fm ,
o , vp+4.)
c yp/
( - T =
and the others may be deduced from these by a cyclical permutation of (U, V, W),
(a, b, c), (l, m, n), leaving T, d, p unaltered.
Article Nos. 46 to 51. Application to the Trizomal; the Theorem of the Variable Zomal.
46. I take the last equation written under the form
(a fmU - b fl V)'- = (fjpU+ f^pV+ (p + ^ Vf J,
which, putting therein p = 0, is
(afmU-bflVy=~nT,
which is in fact the trizomal curve,
a fmU- b flV + nT = 0,
C. VI.
62