81 DEMOnSTRATlO THEOREMATIS 



cuius differentiale per '— diuifum, dabit j»h'um valorern 

 pro z, nempe 



1 X-f- ;X^ - 5 1« - 7X^->- I I x"- H isJ:'^ i; x» -etc. 



* I _x _ 3c»-f- x« _f_ x'- x'» - x'5 _t_ *«» -4-efc. 



qui valor fi aequalis ponatur affiimco , et vtrinque per 

 denominatorem i — A' — A"* -i- x' -h x^ — a" etc. mul- 

 tiplicetur , reperietur terminis fecundum poi:e[lates ipfiu» 

 X dilponendis, omnibusque ad eandem partem collocandis: 



O — */i -♦- x*/2-+-x Vi-»--^*/* -f-*'/s-Hx«/«-f-x V7-Hx'/«-4- -'j9-(--'«"'j''<"?'c- 

 • - /.- Ji- St- /♦- /s- /6 - /7 - /3 - j» 



•- /.- Sz~ h- U- Ss - S6 - S? - /. 

 -H /. -4- /= -f /: -f A + /5 



. . . . . . . + A 4- /, + / , 



— I — 2 * ^ —1— ^ *-i-7 * * ^ 



Tnde fingularum poteft.itum ipfius x coefficientibus ni- 

 hilo acquatis, fequitur fore 



fi=x j6-JS-hU~fi 



/2-/i-Ha /7->4-/5-A- 7 



/3 -f2 -h/i / 8 -/7 4-/5 -/3 -/i 



/4 -/3 -f-/2 / 9 ==/S -t-./'7 - /4 -/2 



/5 =/4.-1-/3-5 /iorr/9-4-/8-/5-/3 



atquc indolem illius aeqiiatiauis vel leuiter atteivdenti 

 patebit, eflc generatim : 



/«z/(«-i)H-/«-2)-/(«-5)-/(«-7)+/(n-ia)4-/(«-i5)etc. 

 hac progrcllione quouis cafu eousque continuata, donec 

 perueniatar ad fumma* numerorum negatiuorum. Dein- 

 dc per fe eft perfpicuum, nuraeros ^bfolutos 1, 2, 5, 7^ 



etc. 



