I — I -I -^-1 , +1 — I — M I , 'l-i —I -I -l-i , etc. = o 



^cL -^ct-^a. —a , — a+a+a-a, — a+a-|-a-a, ctc. r: O 



— a*4-a'+a'-a', — a'4-a'4-a'-a"', — aM-a'-fa'-a% ctc. := o 



+ a'-a'-a'+a', ■^a'-a'-a'-\-a.% -{■a'~a'-a'+a\ ctc :: o 



§. 20. Qiiamqiinm liinc noflra conclufio pro ra- 

 dicibiis altioribiis iam fdtis c(l confirmata, tanicn ncccfTc 

 eil infiiper carum, qiio a' rz. i , cuoliierc , qiiandoquidcm 

 hic non oiiincs potcrtates qninta inferiores occurrcnr. 

 Sit igitur a' — 1 et hacc lcries pcriodica prodibit; 



I — a +1 — a'-fa'-i-fa — I -fa'— a'+i|— a +1 



— - ctc. 



-a'-l-a'-— I -\-a — i-fa' -a'-f-i -a JH-i-a^-fa' 



\bi potellatcs a' ct a* pcnitus excliuluntur. Qii.irc cum 

 quaclibet peiiodus 20 conrtet terminis, rcliquae potcftatcs 

 facpius occurrant ncccfle c(l, fingulis aufcm (eorlim fum- 

 tis tres fequcntes ferics periodicae occnrrunt : 



i4-i_i_i_i— i+i-fi, i-fi -i-i -i_ifi_|_i^ etc.ro 



— a-fa-fa — a, — a -i a -fa— a, — a -fa -fa -a, ctc. = 



— a'+a'— a'-f a'-fa'- a' + a'-a% - a' -f a' - a' 4-a', cic. z: o 



Hinc iam veritas fcrici i[ firiim a cx piacccdcntibus cft 

 mnnife(Ui binae reliqnac autcm , quarum pcriodi oiflo tcr- 

 minis con(\dnt, fi feciindum principia h ic^enus (tabilita 

 cxaniincntiir, ctiam nihilo acquales deprchcndv.ntur, quo- 

 niam non foUim tcrmini fohus pcriodi (c niiituo dc!lru- 

 unt, (cd ctiam termini feiici (nmnjatricis indc formatac. 

 ka cx (cric vnitatum oritnr h.icc fcrics fummatrix: 

 I , 2, 1,0, — I, - 2, - I, o: 



ciiius fumma itidcm cuancfcit, quod idcm "vfu vcnit in 

 feric quadratorum. 



