..PROBLEMA ALGEBRAICVM. 1x5 



quaeruntur , ope notiflimi probkmatis , de inuenien- 

 dib duabus quantitatibus , quarum datur fumma et 

 produdum. Erit nimirum u — zrziJ et uz—z^zze*^ 

 ex quo fit zzzlu^^V [lu -e"), Tbi funul obferuan- 

 dum , quod li fuerit zzzlu -i- V {l u — e ) , forc 

 V =z 'i u — V (l u — e* ) et viciflim. Hinc quoniam 

 z — d-x'^ erit ^"^ zzd—lu T ^^ ( i «* - ^') «ec 

 non. y'^~d'-vzz:d'-~u± V {iu — e^), Inuentis 

 autem primo vel vkimo progreflionis termino , re- 

 liqui facile innotefcunt , nam x"" : x^^^^yy.xiy ::e ', z 



\ Z X"^ Z. (d-^Z) .;.-...,--;•; rfV 



ideoque A'^""ji=: zz , quomodo autem 



ex primo et fecundo termino, reliqui determinentur 

 ftt ft patet. *\ [l- -biiir::.; H) 



8.. 5r iam aeqiiationem (D) examinl fubiicia- 

 mus , inuenimus ftatui pofle : 



n-Ae\. {z + *i?r.-H B e^iz-^v^^^-^+CA^z^-^vf-' Hf^etc 



^^\ {^^e){z''-^ +z''-'v-\^i^''-^-v:"^^j,i-,:^z-r^^^^^^^ 

 ^i^-e) [{z -I- vy-' ^ae\{z-^- 'vf-'-^ ^/. {z-\- vf-' 



--f- Yf*.(5;-4-V)"'~''+ etc.) et 

 3'". ^e (2"—=^ +z''-''v-^z''-'v*-^ . . . . -^ -s -z;"-'-^ W"~=^5 

 ^^e{{z-i'V}''-^-]r?e\{z-^vf-^--^(le'^.(z:-i^^^^ 



4-R^^^(^-f^<i?)^-^ + ete.).^ 

 vnde pofito vt antea z -^ v — u ^ prodit 



-4-a/«^^'4^p.^««-^^_y^<'^^;^ etc), faaec vero 



P 2 . aequatio 



1 — is» 



