68 G. FLEURI. 
but Pr R= P17? ~-Peee y=a—b+1 
and Po- R= Pi) PAYS oa B=a—b—l 
Ifa <b 
POP OE Eat 
AMG as le ee therefore 
Rp Pt] 7 pio 
and as Je via ol ~ thus 
qT Pr—a-1 — P-1 TP Plb—a—1)—-1 — P—k J Pb—a—1-k 
and thus obviously 
T P—a-1 — P—(b-0-1) J — Po-b41 7 
eyoel ely Jel Je, 
Po-b+17'— Par R 
If a>o and be—o as RPO=T 
then =?¢ uP? = Pegyepy st 
anol eas) of Pala therefore 
Pet Pot1= Patly Pbti+l— Porky Pb+k+1 
wherefore 
Pel Prerti= Prt(—b)-17 Ppb+(—>) = Pat-17 
eines ah el wie 
Po—>-1f= Poa f 
And soon. These examples are sufficient to show how easily 
calculations of this kind can be made. In short the general 
formule are the following ones : 
P*kR P = PR = Poel] = PooriwqT 
Pel P> = Par>T = Pr-rt+1R = Pobvi2z27 
PtT PP? = PrwtT7 =] Pat PR ]— Pa 
a and b being whole numbers positive or negative. 
From the formule we have established we can draw as conclusion 
the following theorem : 
Any succession of operations as above defined performed on a 
curve C can be put under the three forms - 
Ph, P? dandseeag | 
a, a’, a” being positive or negative whole numbers. 
that is to say : 
