(37)== 



ciiius rei vcritatcm cx conucrfionc aequationis Riccatianac iti 

 fradioncm continuam dcduxcram. Cum autem hacc dcmon- 

 ftratio nimis longe petita videri qucat, eandcm rcduclionem 

 hic ex principiis fimplicioribus fum traditurus. 



§. 2. Primo autcm iftam feriem generalem in formani 

 concinniorem contrahi conucnict ponendo ;«A*~fl ct nx^zb^ 

 vt propofita fit ifta feries infinita: 



\—a-^a (^a-^b') — a (a-hb) (a-k-zb) -»- a (a-^b) (a-^zb) (a-i-^b) — ctc. 

 Practerea vero vt fequcntcs rcfolutioncs commodhis peragi 

 queant, ncque tot claufulis fit opus, ftatuam vt fequitur; 



fl — A, fl-+-Z' — B, fl-f-2^ — C, a-+-3^ — D, ctc. 

 ficquc habcbitur ifta ferics : 



I— A-f-AB— -ABC-hABCD— etc. 



cuius fnmmam quaefitam dcfignemus littera S, ita vt fit 



Si=i— A-l-AB — ABC-HABCD— ctc. 

 hinc porro 



1 — A-t-AB — AflC-(-ABCD — etC. 



§. 3. Cum igirur fit s'>i, poftrcma aequatio rcdu- 

 catiir ad hanc formam : 



I -— j l_ A — AH-t-ABC — ABCP-I- rfc. 

 * ' A-t-AB — ABCH-A B C D etC. 



Nunc autcm ponamus J — i-|-^, critquc 



P t — A-f-«B — ABCH-ABCD ete . 



t — B-t-BC — ECD-+-BCOE etC. ' 



quae exprcfilo cum iterum vnitatcm fupcrct, ob B— A=z^, 

 C — A— 2^, D — A — 3^, ctc. ca dabit 



P ZZ: I — }— JL ~ ^ ^ ^ ~*-^ 6bC' — 4h K c r> -+- et c. 

 I — B-f-BC^BCD-*-»COB «(e7 



Ponatur crgo P — i 4- .^ eritque 



E 3 Q = 



