PROBLEMATrM DIOFHJNTJEGRFM, 177 



Sed quiii hiiius radicem qiiadricem ponimus $ n -\- e 

 -h- '^ V (a}j^ -t- bii-^c), er it liinc etian i ax^ -\-bx 

 -\~c iiequiilis feqiienti quanticati. 



ac^-n- -Y-bi,-n-\-v^^-\-2B^^ 



His dn.ibus formis inter fe aequatis, habebutitur fequen- 



tes aequationes. 



aa--\-a'y"—§^-\-a^'^,iaa&-^aby''-\-boL—2^£-\-b(!,^, 



a^--^acy--\-b^-{- c^z^^-^-c^^, a^ay — sa~< 



2 ^ § y -1- /? Y — 2. e <^. 

 Ex quibus ehcitur dz::.''^--- et £Zz;-=-y^^ — , et valoir 

 jpfius S in prima aequadone fubftitutus dat, a'^ ^"^ -\^ 

 '?y^<^^— ^a- Y' -h^* , quae in duas rcfokiitur <^^ n: 

 a- , et <^-— <rY'- Hanim autcm pofterior, nifi fit <7 

 quadratum , locuni habere nequit. Habebimus ergo ^=ra, 

 et fecunda acquatio fidis fubftitutionibus hisce fimiliter 

 in has rcfoluctur ay^^—a-y et g — — "^^, quarum 

 jterum pofterior tantum locum habet. His inueutis ter- 

 tia tandcm aequatio dabit u—V (ay- -\- i ]: inueniri 

 igitur dcbet valor pro y^ quo ay--\-i fiat quadratum. 



• §. 5. Sit j) ifte numerus, qui loco y fubftitutii^ 

 rcddat ay--\-i quadratum, st huius radix ponatiu- </; 

 ita vt fit cj- V, ap--\- I ), erit a—q,y~p,^ -^-, 

 $ — ap, £~-^ et ^~q- Ex his coUigitur fcquen? 

 Theorcma : 



Si a x^- -\- b X -\- c ejl qmdratum cajit qiio xzizn ^ erit 



quoque quadratum caju , quo x — q n -\- -f^ -\- p 



V ian^^-^-bn-^-c]-^ eiusque quadrati radix erii ap ''^ 



-i-'-^-\-q^':an--\-bn-\-c). 



Tom. VL Z c: 



