145 JDE PARTITIONE 



fit w = I , quia quilibct numenis vnico tnodo ex me- 

 ris vnitatibus pcr additioncm elici potclt , crit 7/''~ i , 



quod idem prima formula 5( — TZii ■, ^^u fcrics indc 

 formata : '^ — i -]- x ~{- .v* -H .v' -+- x* H- .v' -i- ctc. 

 manifefto indicat. 



§. 29. Qiioniam (crics 23 = (,_ xxV- ^^ '"'^icat , qnot 

 modis quisquc niimcrus cx nunicns 1 ct 2 per additio- 

 ncm formari polfit , in hac fcric potclbtis .v" coefiiciens 

 crit zn ri^^ , haec enim exprclVio affiimta ell ad figuitican- 

 dum , c|uot modis numems n ex numeris i et 2 per ad- 

 ditioncm oriri potfit. Hinc igitur crit : 

 S5iri + i(=lv+2('lv*4-3<=lv'+4.'^>A-*-f-5^'^.v'4-5f'lv*-f etc. 

 atque ad fimilitudinem huius cxprcfllonis erit : 

 5(-i + i(''ji"-f2<').v'4-3^'V--h4.<'lv*-|-5^'^A-*-|-6('lv*+ etc. 



Deinde vcro cum fit 5i — r^ et 25 — (,_x)(T=l5) erit 

 5{ =: 25 ( I - .V ' 3 , vnde lequcns intcr h;is fcrics icla- 

 tio oritar : 



51 =1 + i('\v+2('lvM-3^'V4V'lv*-|-5('lv*+6('^A'-f ctc. 

 +23 l-i + i'=lv+2( V+3'^'A'+4('lv*-f 5''lv'+6('lv*-+ctc. 

 -23c'S - .v'-i(=y-2f^>.v*-3f'U- -4<V- ctc. 



Qiiodfi hinc coaeqiiatio tcrminorum homogcncorum in 

 fticuatur , crit : 



,(0 — 1(0 



2(0— 2^.) 



3(0-3(.)_4_i( 



7(.)-^(0_^5(.) 

 g;.)— g(.)_4_6(o 



^(0— ^(.)_|_2(0 



,(:)-5(.)_^3(.) 



,5(:)— (5f.)_4_^(.)^ p(.)— p(.)_l_7(0 



§. 30. Gcncr.ditcr crgo crit «''' ~ w^*^ -|- («- 2)^''. 

 Cum igit u- fit «"'— I , eiit ;/'' — i -}-(;;- 2 )'■' ; 

 ficquc cwcificicntcs Ibrici 23 i^^ dctcrminabuntur, vt quis- 



(lllC 



