A N A L Y T I C A E. 137 



vbi ciim trinomii propofiti fingiilae poteftates oc- 

 currant , a cxplicatis orictiLr ; 



y^[a -\-zabx^zacx^ ~\-^bcx* -{-ccx*) 

 -^ b b 

 V*{a-\- ^abx-^-^a^cx^^-^^abcx^-^-Zbbcx^-^-^ibccx^-^c^x*) 

 -\- 3 ab'' -\~ b^ -4-3 acc 

 ctc. 



hinc fi primo termini medii , tiim vero tcrmini a 

 mediis vtrinqiie aequidiftantes capiantur , nafcentur 

 fequcntes fcries : 



1 -\-bxy-'t-{'i.ac-\-bh)xxjj-\-{6abc-\-b')x'y-\- etc. 



^[a-^-cxx)^! -\-^bxj-\-[:iac-\- :^bb)xxjj -^-ttc.) 

 j' [a H- c* x*)[i-\-:ib xj ~\- ctc.) 

 j\a -\-c'x*){x -\-^bxj -\- etc.) 

 y (fl* -\^c*x")[i-\-sbxj -\- etc.) 

 etc. 



Omiffis ergo his multiplicatoribus , quia in feriebus 

 ipfis adfunt poteftates produdi aj, ponamus xjzzz 

 et indicemus iftas feries hoc modo : 



i-\-bz-\-[iac-\- bb)zz-\-[6abc-\-b')z' — ? 

 i-\--2.bz-\-(5ac-\- ;ibb)zz -\- ctc. — Q, 



x-^-^bz-^- etc. — R 



i-^-^bz-^- etc. =^S 



etc. 

 Tom.XI.Nou.Comm. S ita 



