->g=4^ ) 34 ( l?i<- 



dedi. Noua nutcm mcthodiis, quam hic fum traditurus, 

 huic innitiuir principio, qnod pofito z — a omncs illac 

 fiaiftioncs partiales euadant infinitae, dum reliquae omnes 

 inanent finitac magiiitudinis, idcoque prac illis quafi eua- 

 ncfcant. Hinc fi in fradionc prc^pofita ~ fiatuatur s^a, 

 c^ vtiquc etiam in infinitum cxcrcfcct, ciusque valor dc- 

 bitc cuolutus pracbcbit ipfas illas fr.idioncs fimpliccs ia 

 infinitum abcuntcs, id quod hic accuratius lum perfc- 

 cutuius. 



$. 3. Ne igitur hic confiderntio infiniti moram 

 faceflat, ftatuamus non z—azzo^ fcd z ~ a — oi, dcnotan- 

 te w quantitatcm infiiiitc piruain atquc adco ipfnn cui- 

 ncfccntcm, ac ponamus tam in numcratorc P quai7i in- 

 denominatorc Q'\biquc z — a -^ (a, quo fa(flo numcrator 

 P euoluatur in huinsmodi formam-. 



Pr=A-+-Baj-{-Cwa)-HDa)'-h etc. 



denominator vcro Q, quia per hypothcfin euancfcit pofito 

 z.z:^a, talcm induct formam: 



(2zr2(a)-f-25oju-h(£w'-hX5w*-4- etc. 



vbi fi fa<flor z — a fiicrit folitarius , primus terminus 31 o) 

 ncccffario adcrif. Sin autein dcnominator Q facf^orem ha- 

 beat {z — a)*, erit 31 — O, ac denominator a termino S3(o* 

 incipict, Quodfi vcro dcnominatoris fd(flor fucrit [z--a,\ 

 primus tcrminus in denominatorc crit ffcu', ct ita por- 

 ro, ita vt fi in gcncrc facflor fucrit (s — «)", infima potcs- 

 tas in dcnominatoce fit ?? o)". 



^. 4. Haec quidcm fubfiitutio, ponendo jKra + u , 

 operationcs tantum vulgarcs algcbraicas pofiulat: interim 



tamca 



