524 Peiri Callegari 



[lC1)^...Ul(^-3)]J— ^)(— ^)^— ^). 



'- ^ 1.2.3 



Itemqne formula (b) , subslilulo ni — 2 in locum in , suppe- 

 ditabit 



[„.,^...'^,<-.]=<^e)|;=5, 



Pariter e formula (ft) , si loco m subsiituaiur m — 3, prodibit 



[l(1)_H..!_Hl(m-3)]==,„_3. 



Exinde post substilutiones, ac reduciiones elicielur 



r ^ ., ,1 w(w— IVw— 2)(w— 3) 



Non pluribus opus esi , ut e formulis ((?) , (b) , (c) , (<^) 



generatim slabiliatur 



1(1 )_t_ l_1 ('■+' J=-^ ■ ^——^ . 



Ideo si eritr<??z — r sen r-f-i <»i — r-HljScribi poteril hoc 

 modo 



fM(/H— 1 ) . . . (/--t-l )_wt ';« — 1 ) . . . (?«— r-Hl ) {m — r) . . . (r-4-2 ) (/'-t-l ) 



1.2.3 ~ ~" 1.2 .3...r(/--+-1) (m— r) 



7«(Hi — 1 ) (f« — r-f.1 ) 



~ 1 .2.3 7- ■ 



Si e conlra fuerit m — r-t-i <r-i-1 , sciibi poteiit 



m{m—^ ). . .(/--hI ) to(7?z— 1 ) . . .(r-(-1 )/■... (m— /--hI ) 



1.2.3..(/H— r) ~1 .2.3....(m— r)(w— r-|-1)...r' 



Ex his generaliter colligemus 



r "'""'' "1 'n(m — ^)...(7?^ — r-t-1) 



(A) [l(i)-H...-Hl C'--^)]= \),2,3....... • 



Hinc in primis hoc theorema inferlur . « Si polynomium in- 

 " ter parentheses rectangulas interclusum evolvitur, uti ».° 2." 

 <i §.' I." docuimus, (quod /--t-l terminos habet, sive ad nu- 

 « merum m conficiendum in eo termini m — (''-+-'') desi- 

 « nuiu) idem terminorum numerus proveniet, qui ex rerum 



