sdx — dx — !i.xdx-i-:ixxdx—4Jc^dx-^$x*dx^6x^dx-h ctCt 



vnde 



fsdxzzz x--xx-\-x* — Jif*-t-j:* — x* -{- x' — ctc. 



Eft autem 



X — jf a: -f- jf' — jr* H- JK"* — x* ~i- etc. =z _£— , 



Hinc sd xzn , ^* ,^ et x zz: ' , , ac polito x z=z i prodit 



(1-+-«)* u -♦-*)* * * 



s zzzii fcilicet 



I — 2-1-3 — 4-t-5 — ^-1-7 — 8H- etc. = ^ 



Cafus. II. Ponatur « — 2 , et habebitur feries fum- 

 manda 



1 — 2' 4- 3* — 4-* -I- 5' — <5* -I- 7* — ctc. 



Sit vt fupra 



s^^ — i — 2*x-*-^*xx—4^x^-h5*x^—6^x^-+-^*x^— etc. 



multiplicetur vtrinque in dx^ et fumto integrali obtinebitur: 



//'' D jr — jr — 2 jf -t- 3 .v' — 4 jc* -+- 5 jf^ — <J jc* -t- 7 ^c'^ — etc. 

 fiue 



fs^^dx:=x(i—zx-i-^xx—4.x^-*-Sx*—6x^-h^x'— etc.) 



Eft vero ex cafu praecedente 



1 — 2 X -h ^ X X — A.x'^ -^- 5 X*— 6 x^ -*- ^ x^ — etc. ±=' — - — , . 



Hinc //''3jr=^^^^, atque /^ — -1^:^^, quamobrem pofito 

 X zzzi prodibit 



1 — 2« -I- 3* _ ^* _l_ 5» — 6« -H 7* — etc. = o. 



Cafus III. Statuatur porro « 11:: 3, et feries fummen- 

 da erit 



I — a' + 3' — 4' -h 5' — 6' -t- 73 — etc. 

 fiat vt fupra 



s^'''' =: i — ^^x-hii^xx—^^x^-i-S^x^^—^^^x^-i-^j^x^— etc. 



P 2 vnde 



