( 670 ) 
6‘c. express pet A, B, C, D, dc, transformantut in 
A A jB a -|— 1 B C A -|— 3 ^ “]"■ 3 ^ ^ 
I’ “T" * 
terminos 
(^e. Unde colligendo fummas terminorum, inveniuntur 
Numeratores /3, y, <f, ^c. nempe 
ct 3H: A 
|8 zrr h -|- I A -|— B 
y ■=: h 1 A h 7. B 
t'=zP fr -\- h-\“ I A 7. h B h C D 
&c. 
Unde fumendo differentias fiunc 
h z=: * h A -}- B 
c =: q h A'\- h B C 
d — q qh A -y q h B -\- hC-\- D 
& fic porro, uc in Propofitione exhibentur. 
Cor. I. Si Numeratomm N, 0, P, &c. differen- 
tia vel prima, vel fecunda, vel alia quaedam detur, 
terminis omnibus poft primes aliquot in Serie A, B, C, 
D, drc. evanefeentibus, Differentiae h, c, d, &c. tandem 
incurrent in Progreffionem Geometricam in ratione 1 
ad q. Exempli gratia, fi detur Numeratorum M, N, 
0, P d’c differentia prima B, erunt c, d, drc. in ra* 
tione conrinui Geometrica i ad ^ ; ut conftat per ip- 
forum valorcs q h A h B, qqhA-^qhB, &c. ex- 
iffentibus C ==: o == D = 
Cor. z. Ordo autem primx differentiarum B, C, D, 
C^c- qu£E hoc mode evanefeunt, idem eft ac ordo 
differentiae vel h, vel c, (^e. unde incipit Progreffio ilia 
Geometrica. Sic B =zo —C =: erunt c, d, 
in Progreffione Geometric^ ; fiC=o=:Dr=:^^-. erunt 
€y d, &c. in Progrefffone <aeometrica. Et (ic porro. 
LemmA 6. 
lifdem pofitis fit r terminus unde incipit Progreffio 
Geometrica in Serie differentiarum h, c, d, &c. & per 
t+i 
