DE SFMMIS DIFISORFM, 77 



D E M O N S T R A T I O. 



Ciim enim feriei primus terminiis fit (i-}-a) et 

 feciindus — (3 ( I -f- a ) , erit fumma primi et fecundi 

 — (i-4-a) ( i-h^) : fi mr\ addatur tcrtuis terminus 

 y (iH-a) (i-4-(3), prodibit (i-t-a) (i-f-(3) (i_|-y) : 

 addatur infuper terminus quartus, qui eft ^(i-i-a)(i -+-(3) 

 (i-l-V), crit fumma=:(iH-a;(i-+-j3)(i-|-y)(i_|-a^). 

 Atque fic in infinitnm procedendo, lummn totius feriei, 

 feu omnium eius terminorum, perducetur ad hoc pro- 



dudum: (i-f-a)(i-i-pj(i-f-Y)(i-i-^)(i-|-£)(i-i-^) etc. 

 Vnde manifefturn eft, fi fuerit 



fbre viciiTim: 



fi::^('-+-a)-*-P(i-t-a)-»-r(.-+-a)(.-f-P)-H5'(.-f-a)(.-t-S)(.-4-^)-4. efe, 



PROPOSITIO II. 



Si fuerit s =: (i-x)(i-.xu-)(r-/)(i-.v*)(r-v')(i-A'*jetc. 

 produftum hoc, cx infinitis fadoribus conftaas , re- 

 ducetur ad hanc feriem : 

 s — i-x-xr(x-x")-x*(r-.x')(i-v'}-.v*(r-A:)(i-.v*)(i-.r^) etc. 



DEMONSTRATIO. 



Si haec forma j — (i-a")(r-A'A')(r-.r';(i-.v*)(r-v*)etc. 

 cum forma praecedente j zz (i -ha)(i-i-p)(i -+-y) 

 (i-f-^^^^r-he) etc. comparetur , manifeftum eft fore: 

 a :=z —X-, (3 — — x' j y — — x'; ^z=-.v*; e:=z-x^ , etc. 

 His igiiur valoribus in ferie ibi data, quae produdo s 

 aequalis eft inuenta, rite fubftitutis , patebit propofitionii 

 veritas, fcilicet efle; 



j— i-a:-.vx(i -x)-x\i-x){i -x')-x\i-x){i -x^)[i~x')- etc. 

 K s PROPO- 



