€ DE PRODFCriS EX INFINITIS 



mini intcrmedii pendeant. Qiianquam enim fi n fit nu- 

 merus fladiis , non ita facile conftat , qualem quadratu- 

 ram Jdx{—lxf contineat , tamen eodem loco oftendi 

 pofito t loco n formulam Jdx{^lx)^ congruere cum 



f (1.2.3 P).(^H~i)(^^^+^)(*-^+i) (^-^0 



Jdxix^xx^tJdxtx^-x^Jdxix^'-'^^^^^ Jdx{x^-^x^)^ 



cuius redudionis ope valor ipfius Jdx{—lx)2 per quadratu- 

 ras curuarum algebraicarum exprimi poteft. 



§ 5. Si nunc in fcrie aflfumta terminus, cujus index 

 eft z:z.\ , ponatur z , ex lege feriei termini , quorum indices 

 funt § , 1 , 5 , etc. fequenti modo fe habebunt : 



l-\-z{J-\-lg)-\-z{J-^m-\-H'-^^J-^l^^^^ 

 Quoniam autem progreftio affumta tandem cum Geome- 

 trica confunnditur , hi termini interpolati euadent tandem 

 medii proportionales inter contiguos feriei terminos. Qua- 

 re fi finguli termini interpolati iam ab initio tanquam 

 medii proportionales fpedentur , fequentes prodibunt appro- 

 ximationes ad terminum z , cuius index eft s. 

 I. zz=zV{J-\-g) 



u. z^y — ^_^3^^(^-_^3^.) 



TTT —V tfj-^^ ^/-^^^^^+ '"^^y^ ^t^J-^^g) 



AAA- ^-'^ i(/+l^)(/+§^0(J-f-l^jf/-hl^) 



etc. 



ex qua progreftionis lege intelligitur terminum indicis \ 

 yere efle :=. {f-\-g)W ^f~^g) ij-^ ^g) (f-^^^) (/ +3^) 



(/H-i^) (/-H^; /-^^) (/-^^) 



(;+3^ 



