= (50) 



Niinc aiitcm v jiequabitur ifti feriei: 



at-h^tt-{-y't^-h^t* -h etc. 

 cuius coefficientcs quaerimus. 



§. 8. Acquationi inuentae tribuamus hanc formam: 

 tv V — I — |-% ex qua facile intelligitur, cum primus termi- 

 nus feriei pro c? inueftigandae dcbeat efle a /•, fequentes termi- 

 nos tantum per potcltates impares ipfius i efle afccnfuros, quam 

 ob rem pro v" conftituamus fcqucntem feriem: 



c; := A ; H- B /' -i- C ^M- D ;• 4- E ;' -I- etc. 

 critque hinc 



^-A-4-3 B/f-(- 5 C;^-+- 7D;'-4-9E^^-+- 1 1 F/'°-f- 13 Gf"-+- etc. 



a t 



pro partc vero aequationis nofl:rae finiftra erit 

 a' c -|r-|-f- AA//-(-ii\B/^-f-2 AC/'-^-2AD/'-+-2AE/'°-f-2A F r-h etc. 



-f-BB H-2BC -+-2BD -+-2BE -4-etc. 

 -f-CC -t-sCD-f- etc. 



cx qnarum fericrum aequalitate ftatim concluditur forc: A~ 

 -— 4 — a, lum vero rcliqui termini pracbebuiit has reb.rioncs: 



5 B = A A , 



5 C ~j 2 A B , 



•7D — 2 ACH-BB, 



9E = 2AD-h2BC, 



11 F=2 AE-i-2BD-hCC, 



13 G zn 2 A F -f- 2 B E -f- 2 C D , 

 etc, 

 vnde patet, cum valor ipfuis A fit negatiuus — — ^, i-eliqua- 

 rum valorcs altcrnatim fore pofitiuos et negatiuos. 



§• 9' 



