§. 7. FiinJamentum aiircm omniiim harum ml« 

 rabiliiim proprictatiim in cuolutione huiiis produifti infiniti: 



conrinctur: deiDonllraui enim , fi finguli hi fa(ftorcs a(flii 

 in fe inuicem multipliccntur, tum dcnique refultare illam 

 fericm : 



S — i — X' - x' + x' + x' - x" - x' + X" -\- .v" — ctc. 

 \bi cxponcntcs ipfius x conHituunt noftiam fcricm nnmc- 

 rorum pentagonaHum , rationc fit;norum autem -\- et — 

 ambo alrern.itim gcminautiir, it^ vi qui exponentcs ex 

 rumcris paribus pro « aHumtis oriunrur, e ic potcllaics h.i- 

 bcant fignum -f-, rchqui vcro cx iinp.iribiis orcis fignuni 

 — . Hacc igitur non niinus admirationcin noflram mcre- 

 tur quam proprieras anrc commcmorata, cum nulla ccrte 

 appaicat ratio, vndc vllus ncxus intclligi polfit inter cuo- 

 luiioncm illius produdi ct nollros numcros pcntagonalcs. 



§. 8. Cum igitur (crics irta potenatiim ipfius x 

 acqualis fit prodti(flo illi infinito, fi cam nihilo ac(iualcm 

 flatuanuis, vt habcamus hanc acquatioiicni •. 



o— i — x' - x" + x' + a' — .X-'* - x 4- .v" -f- Jf'* — ctc. 



ca omncs cabdem inuohiet radicc^, quas protJu^rtum iJlud 

 nihilo aequatum inchidit. Ex primo fcilicct ftc^lorc i-x 

 crit X — 1 ., cx fccundo faclore 1 — x x crit vcl jr — -f i 

 vcl j: ~— i; cx tcrtio fa^-^^orc i — x' na.icuntur hac trcs 

 radiccs: 



1°) .V — I, 2°) X-- '-dtJlLiU, 3») .V - - L=^-zj. 



cx quarro autcm faclorc 1 — x" ~ o oriuntur hae qua- 

 tuor radiccs : 



