FROBLEMA ALGEBRAICViVI. ni 



qiio diaidenio per' v-z, prodit acqiiatio (C). Qiiod 

 vem ai aequationem- (B) attiiier ,. cbferuamus iilam 

 fic exprimi polTe : 



^ igitiir Iieic in rociim ipforum ^% /, ^^ lubltituant- 

 xx\r V z y i/ z"^ v" z etc. omnesque termini per z^ 

 diuidantur , emerget 



z''-^r^ — [d-e)[z'"-''^{e-\'V)z'"'-\'(ev-^v)z'"' 



+ .. .. .+^i^''-'-V-iJ.''") 

 vnde. deducftur :. 



(D) 



4-^"-'^' + .. .- +5;'z;''-^ + 'y"'''). Huius autem aequatio- 



nis inueftigatio fequenti quoque ratione inltitui poteft, 



quia nimirum Iioc in cafu ^'"-^ -5;'"-^'::^5;(^'''-'-^'"") 

 .■vel. ^2n-h2_^2;=n_}-,_^^^^27i__^^2n-ij^ fubftituendo igitur 



f^jz pro /, et diuidendo totam aequationem emergentem 

 per z^-^\ fiet, n)^-^' —ez'^zzdnf-'-dez'^~' qoum vero 

 fimili ratione eliciatur 2;"-^' - e nf'— d z^ - de v^'^' , fubtra- 

 hendo hanc a priori , prodibit 'z^""'-'-:^.""^' -((^-^) [v^^-z"^) 

 +de(v'^~' — z''") et diuifa denique hac per iz — <$;, 

 emergct aequatio fupra allata (D), 



5. lam vt aequatio inucnta (C) transformari 

 poftlt, aft^umatur z -}- v ~ u et ponatur prius aequa- 

 tionis lUius membrum , nimirum z^ + z^^^^v-^rz^^^n/ 



+ + z"v''-'+z'u''-' + n)'' — u''-\-Ae"u''-'^Be*u'''* 



+ ctc. , pofterius "vero ^{5;''-" + ;2!'~'i; + s"^^i;' + 



