132 
This herd projectivelgroup yields the complete system 
n Qn n 
= df , » af ~~. hai 
3 yin a ae a. |x ae +- Xiyi zt ===) 
se we ae the ae 
Serif 
ee 
yi’ 
of the first two equations in the last two, and have 
af df df ) 
ea —- — | — 
3 Pi aan =3: }0° 2 : 06; ?j% i Ou; f 0. 
The last of ne new ee is satisfied by 
eee Hs i uf] (k= 6 252. Rp 2 a 
O, OK 5” 
the first now becomes 
3k u — 
3 «du 
The solutions of this equation are the requred invariants: 
el a ee Fk an 
SECTION III. INVARIANTS OF THE PRIMITIVE GROUPS. 
The remaining finite continuous groups of the plane leave no family of .,” 
curves invariant, and may be reduced by a proper choice of variables to some one 
of the canonical forms known as (1) special linear, (2) general linear, (3) general 
projective.* 
25. The special linear group 
| P, 4, Xq,; XP — Yq, yp | « 
The invariant functions of the codrdinates of n points will be the 2n — 5 inde- 
ate solutions of the complete system 
. n n > ° n 
df df { dt i df 
—_—_ = i »—— di . Fase Apes CCE — 
33 iz a Ovi — 7 dyi ae Fae 2 dyi J ri Yt xi Oe 
*Lie: Math. Annalen, Bd. XVI, p. p. 518-522, also Contin. Gruppen, p. 351. 
