(18)== 



eos t:intiim cafiis ciioluiflc, qiiibus fradiones pro n aflrumtae 

 inrra limitcs o et r confirtuntj haeque fradliones commodc in 

 varias claflcs dirtribuuntur, prouti denominatorcs harum fra- 

 (Tuonum fucrint vel :i, vcl 3, vcl 4, vcl 5, ctc. 



§. 5. Cum nupcr feries, quae ex vnciis poteflatum 

 Binomii formantur , effcm contemplatus , oftendi , fi pona- 

 tur (i -\~zj^ — i-f-A;3-f-Bs--i-Cs% etc. tum vero 

 etiam (i -\~ zy r=z i -\- a. z -\- ^ z" -{- y z^ ^ etc. tum fummam 

 huius feriei i-f-Aa -|-Bp-HCy-|- etc. — .r, ita exprimi 



, quae crgo fumma pcr valores 



fii^dx.fii^dx 



formnlae integralis propofitae definiturj dcinde vero etiam mon- 



ftruui, eandem fummam quoque hoc modo cxprimi pofle: 



111 -\- n ■ 



^ ~ mn fx"^-' dx (^i -xf'-' ' 



vnde ergo fequitur femper fore 



VL±Jhfirdx . f u'' d X ~ f ir^"" d x . f x"^-' 'dx{i — xy-'\ 



fiquidcm fingula hacc intcgralia a termino x =: o vsque ad 

 terminum .v zz: i extcndantur. 



§. 6. Quoniam autcm praefcns noftrum infiitutum cir- 

 ca fradioncs, casquc vnitatc minorcs, verfatur , ponamus in gc- 

 iicrc m — ^- et « — f, ira vt fit 



K K 



H V ;x + v |U.— X V — X 



hlt±l}f j^x" d X .fu^ d X zzzfu"^ d X fx^^'^ d x (i — .v)'^"'. 



p. V 



Nunc vero vt pofircmam formulam intcgralcm ab cxponenti- 

 bus fratftis libcrcnius, fiatuamus jr r s\ et ob dx-^hz^^—^dz^ 

 crit 



//x ^x(^i-xy^ —Xfz>''-'dzCi-z'^)>^', 



quac 



