J. 15. Praeterea vero maxime memorabilis eft haec 

 conversio, qua eft (±) (^f) = (^) (^). Cum enim fit 



/o+j3\ (a + 3)(a+3-l"a + 3 -?)... (3-t- i) ^ 



V a ' 1.2.3... • _a ' > 



/ji_N — n(n — i)re — 2) • . ■ . (n — a — g p f±yQ 

 \x+3' __.2-3.. . a x (x+i (a+2) ..(a+3) ' 



(___.) — nm-vnm-o . ... ' "— ^— f z__ , productum erit 



v a+-3' 1.2.3 • • 3 .(3+D • • ((3r2) (3-f-a) 7 ^ 



/ ■a +- 3 \ / ?t ^ , n(n — 1) (n — 2) (*■ — " — 3 +1) 



^ a J^a-hP- 1 1.2.3 3x1. 2. 3. ...a * 



in quam eandem formam resolvitur formula (~) ("—)• 



J. 16. Per hanc igitur transformationem superiores fe- 

 rics sequenti modo exprimi poterunt: 



p = ' + Q (i) + rp © +- (|) ffi * (!) (|) ■*■ «tc 

 «7 = G) fi) ■* (I) (I) * (1) ® * (li (?) * etc - 



q =(f) (1) + (D Q) * (13 (1) + (!) (I) + etc. 



* = (t) (I) f ® (!) + ® (?)■*-(!) (I) * etc - 



z = (2.) f • ) -. (S*sj (^) (Li*) (^) 4l (*+i) (g_) + etc. 



J. 17. Notari adhuc meretnr alia transformatio , quae 

 ad calculum numericum imprimis est accommodata. Cum. 

 enim ex prima forma fit z = (-£) -+- (~) (££) + &) (^f)-*~ etc. 

 quilibet terminus hujus feriei eft (±) (!j=i ), qui dicatum 17, 

 eritque facta evolutione: 



n _- _L ~I) <^ . . . ,» - ^ + i) , , . . (n-2a - X +_) ^ au()dfi jam ^^ 



loco u fcribamus a+i, ut oriatur terminus fequens • 

 qui ergo erit _: n( "~ l) i"— 2) n ~ - 3a ~ *■ — n 



I.2.3....(a+i)Xi.2.3(A+-a+-D> 

 NovaActaAcad.Imp.Sciettt.Tom.XIF. L hic 



