20 INQVISITIO 



guorum. Nimimm y-^-^-^-^-j^--^- ~77 

 - .4_ — *m — _etc - — -J- — -J- - 



a ' s.6. i 2.5-7.9.11 w *" 2. i l 4.1.3 ~ 3. 1.: 



+ .5 1.3.5.7.9 S.O-i 3.5.7.9-n 2. i l 4.1.3 ' 3. 1.3. S 



^7-hetc. = — ■+■ 



3 4-1.3.5.7 ' 4.5.I.3S7.9 5.6.I.3-S.7.9.I 



. 1 ■ 6 78 . 5_r_£ _I , 



" * 6- 1.3- 5 " ' 4.1.3-5-7 4-5-I 3.5-7-9 ~ ' 5 -6- 1 -3 .5 .7-9-1 1 etC. _,:_'"'"" 



-i— H- — h — - — -t---^ 1 — --4-etC. 



4.1.3 ' 6-1.3.5 ' 8.1.3.J.7 ' 5. ; ,t-3. 5. 7-9 5-6-1-3.5. 7.9. n^^ 



-i— -1 L_ _L_ ^ 1 £ 1 _*___-- , ___. . 



" 2.1 ' 4.1.3 ' 6. 1.3-5 ' 8- 1.35-7 * 10. 1.3. 5. 7. 9 ' 6- J. 3. 5 -7. 9. II 



— etc ita vt tandem in terminis mere affirmatiuis habea- 



^ 1 . _i . ■ . 2 , 1 ^___3 | 1 .2.3 . 4 . 



CUl 7 2 . _ — 1 4.1. j~t 6.1.3.5 I 8.1. 3.5.7 ' 10. 1..3.5. 7. o. i 



12. 1.5.5 



7-9- 



^-77-f-etc, cuius feriei progreffio manifefta eft, 



fi enim T fignificet terminum quemuis ordine «, et T 



terminum fequentem , cuius ordo fit n -\- i , erit generali- 



1 



ter /nz T = ( /z -f- i ) ( 2 /_ -f- i ) T. Cum vero relatio ho- 

 rum terminorum componatur ex quantitatibus , in quibus 

 indetermuiata n aicendit ad duas dimenfiones, hoc indicio 

 eft, fimmam didae feriei definiri poffe per aequationem 

 differentiafem fecundi gradus. Proponatur enim inuenienda 

 fumma fequentis feriei generalis j = A x -f- B x z -f-C x z -f- 



Dx* -\ h Tx n -\-Tx n + 1 -f- etc. in qua fit gene- 



raliter (a. n. (n — i)-\-bn-\-c. )T~(e.(n-\- i.)n-\-f 



(n-\-ij-\-g)T y ideft, (^-f-f) A =(^+ 2 /+^) B ,. 

 (2a-\-2.b-\-e)B — (be-\-^f-\-g)C,(6a-\-^b-\-c) 

 Qzn(i2. e -\- \.f-\-g)Y)^(i2. a-\- 4_>-r-f)D = (20_'-r- 

 5f-\-g) E etc. Sivmma eius definietur per fequentem ae- 

 quationem, fumta dx conitante* gydx z -\-fxdydx-\-ex 2 f 

 ddjzzgkxdx 2 ~\-fkxdx z -\-cxjdx 2 -\-bx 2 djdx-\-ax z ddy. Nam 



haec 



