CONSIDERATIO 



qVAKVAlDAM SHKlKRViM , 



QVAE SINGVLARIBVS PROPRIETATIBVS 

 5VNT PRAEDITAE. 



AVCTOR.F. 



L. EILLRO. 



§. 1. 



Sacpe niimero confidcratio Jerierum ^ qiiae qunfi ca« 

 (ii fc nobis otfcriint , non contcnincnda fiippcdita- 

 rc folct nrtiticia , quibiib dcinccps in vniucrdi fciicrum 

 doftiina fummo cum frudlu vti licct. Cum igitur docflri- 

 na de Jcriebus fit maximi momcnti in Analyfi , liuius- 

 modi fpccuhitioncs omnino dignac funt habcndac , quac 

 omni indnflria euoluantur. llunc in fincm fcqucnrcm fc- 

 ricm ofFcrrc conltitui , quae, tum ob fingularcs, qiiibus prae- 

 dita dcprchcnditur proprictatc , tum Acro proptcr inligncs 

 vfus , quos nobis cxhibct , omni attcntionc dii^na vidctur. 

 Serics autcm ita fc h.ibct : 



,.x , ( .-oO-a-x ) ( ■— xXa — yXa'— y) ■ 0-iVa- 3r V^»-T'(a »-x) 



Lex numcratorum cx fola infpccftionc cfi manifcfta , for- 

 mantur cnim cx multipMcationc tcrminorum huius fcrici : 

 I— .V ; a~x ; a*—x \ a'~x ; a*-x ; a*—x ; a*-x ; ctc 

 Denominatorcs omncs duobus confiaiit tcrminis , qui fiint 

 potcfiatcs ipfius a , quarum cxponcntcs fiint niincri tri- 

 gonalcs. llinc tcrmiiuis ordinc n fcrici propofitac erit : 

 (i-x)ia-x) ia"-x )(a-x) rg"— -.v ) 



