quae feries fi comparetur cum aflumta, fiet 



grzo, ^=:-;C, v)zzo, etc. 



His igitur litteris A , B , C , D , etc. inirodudis fumma 

 generalis erit: 



Si:-/X^.v + ^X-^Af^ + ^BJ-f^-iC£^ + etc. 



Si porro faciamus A — 2 9(, B = 2 ^, C — 2 Q;, etc re- 

 lationes inter has litteras ita fe habcbunt: 



$5 = ^^ S- 



(j- — 73J55 (;ft 2 Jilg-|-^.^g-t-^gO 



V ^ , v^ _ . - , 



© = ^^, etc. 



tum vero erit 



Sr:-/X^^-f--X-5(j-f-^23y|-€^-hetc. 



Ex his formulis iam intelhgitur, iftos numeros affines eflTc 

 illis , qui in poteftates reciprocas pares ingrediuntur; erit 

 enim 



Of — II «*— >i «*— !_'_ (?>,— 1 i Cr_> I. 



<* — 2«(S» SJ— ;^'9r,J ^ — 2' • S + S » "^ — 2' • P4S0 5 ^ — iS^gfsil» 



quos numeros vltra trigefimam poteftatem olim iam euolu- 

 tos dedi. 



§. 31. Hinc igitur pro noftro inftituto fequens 

 theorema vniuerfale proponamus. 



Theorema. 



Si propofita fuerit feries in infinitum excurrens: 



S = X 4- X' 4- X" -4- X'" -h etc. , 



tum 



