= 9 l -=— 



§, 44. Charactere autem hoc differentiali A in ui'um 

 vocato, cum fit 29— :Ap, erit 2^7:= AAp ideoque 



ir — AAp — 2 p , hincque 2 A r — A 3 p — 2 A p , ex quo 

 porro fit 2<y — A 3 p — 3 Ap ideoque 



2 A £ — n 4 p — 3 AA p, ergo 2 1 — A 4 p — 4 A A p -+■ 2 p, ideoque 



2 A t — A 5 p — 4 A 3 p -+• 2 A p. Hinc porro fit 



2U — A 5 p — 5 A 3 p -+- 5 Ap, ideoque 



iLu ~ k 6 p — 5 A 4 p -+■ 5 AAp, unde deducitur 



iv ~ A 6 p — <>A 4 p -+- 9 AAp -+- 2jo, et ita porro. 



J. 4<r. Quod fi hos coefficientes numericos attentius 

 confideremus, lex progressionis convenire deprehenditur cum 

 ferie Geometris fatis nota , unde pro valore z , cui ordi- 

 nis index pofitus eft A, obtinebimus fequentem formam : 



2 z = A x p — A A x ~ 2 p •+- ^-rL' A x_4 p ■— X(X ~ 41(X 3 - ^ A x_6 p 



-+- X(X— ?)'/X— 6 ) <X— 7) ^X— 8 jq _ X(X— 6)(>>— 7) (X— 8) 'X— 9; A X-JOp + e | Ca 

 1.^.3. 4 " i.li.3.4. 5 ^ r 



quam feriem eo usque tantum continuari oportet , quamdiu 

 indices ipfius A non evadunt negativi. Ita fi fumamus 

 X — 6, quo casu fit zrzv, ex hac lege generali utique prodit 



22; — A 6 p — 6A 4 p -+- 9 A 2 p — 2.p. 



$. 46. Quo indoles hujusferiei clarius perfpiciatur, me- 



. . , r (x-+- y^xx — 4;" -+- (x— i/xx — 4; 71 



minisse oportet, hanc formam i — 



2* 



in fequentem feriem refolvi ; 



X n - 71 X n - 2 -^ VZfU X n ~ 4 ~ ,"("-4Hn-i) n- 6 + etc> 



1.2 1.2.3 



Hoc igitur modo noftro scopo jam eft fatisfactum , cum om- 

 nes litteras q,r,j,t, etc. per folam primam p fuasque de- 

 livatas p ', p", p" \, etc. expressas elicuerimus. 



M 2 De- 



