

inter fe permufari poflc, cum fit X/ neqiiivnlcns /!£. ITic au- 

 tcm probc meminillc oportct, diipliccm redificationem infuper 

 cffe adiungendam. 



Exemplnm. 



§. 20. Sit propofita progrcfiiO numerorum pentagona- 

 lium 1,5,1-, ^2, • ••• ^-^4^, if^ ^^t ^^ X = i^^. Hinc 

 cum fit fXdx=: \ x^ — \ x x , tum vcro ^ = 3 -v — l et 

 r 3, fequcntia vero differentiaiia rro, hinc obtinetur 

 2: X = ^ -v^ — '^xx,-hl X X — U, -h « ( 3 -V — -0 



— I .V^ "f- l X X. 



Hinc iam formetur noua feries, cuins terminus generalis 



= /x a r = = x' — 4 A- X -i- ^ , 



vnde nafcitur hacc fcries: 



l-hi-\-^4 etc Ix^ — Ix x-hl' 



Eius igitur fumma erit 



XfXdx —fd .V X X -[- C -h D X. 

 lam vero ob ^X — lx^-^l x .v, crit fdx^X=. [ x* -\- [ x\ 

 ideoque fumma quaefita r=,^ jr^ -f- J .v' -f- C -}- D .v , quae vt 

 cuanefcat fumto .v n: o, ficri dcbet Ccizo; at vt pofito x-x 

 prodeat primus tcrminus 5, ^i""f^i dcbct D rr i^ , ita vt ver.i 

 fnmma fit \x' -^l x^ -{-l\ x. Ifa fi fumamus .v = 2, prodit fi , 

 quae eft fumma termini primi ct fecundi. 



Scholion. 



§. 21. Ex his ficile intcliigitur, tam differentiationcm 

 quam intcgrationcm pro Jubitu vltcnus continuaii poflc, id 

 quod brcuiter fcquentibus duobus Thcorcmatibus fum com- 

 plexurus. 



Thco- 



