■(- 



notc^ri mcreeur, quod ternae quantttates xXj yy^ aa pcr- 

 fedc inter fe fint pcrmutabiles. Si enim membrum irra- 

 tionale ad akeram partem transferatur, vt fit 



xx-{~Yf--aa~naax xjy — — 2 $( jvj/ , 



ct quadrata fumantur, rtftituendo pro 51' valorem fuum 

 I -h m a a ~{- n a*^ , prodibit ifta aequatio : 



4-j»;' — 2X xjj — ^m a a X xjjf — i}i a* X xj y -{- n fj a* x*y] 

 -{-y—naaxx —anaax^yy 



'\-a''~ zaayy —i.naaxxy* 



vbi permutabilitas litterarum a, jr, j manifefto in oculos 

 incurrit. In ipfis quidem formulis fuperioribus, vbi ipfa 

 quantitas a ingreditnr, permutabilicas non adeo efl: mani- 

 fefta , fed prorfus elucebit, fi loco a fcribamus -- b, item- 

 que ^ loco 5(,* tum enim , quemadmodum crat 



V — — *^ -^3E gf „ — _ y9& - 63> 

 ^ i—nbbxx t~nbbyy ' 



ita erit b zi Tz ^f' /^^') fimilique modo pro formulis ra- 

 dicalibus feu littcris maiufculis erit 



<y\ — (mbx ■+- ^S) (t-i- nbbxx) ->- 2nbx (bb -+. x x) 

 ^ — (i - n b b X X)* ~ > 



JC (viby -f- gig); ft-+- nhbyy) -t- inby '.bb -t- yy) 



•^ — (i - n b b y y)- ' 



ga ( mxy -4- 3Eg)j (' -4- n x; 



•^ — (i — n 



n xxyy) -f- inxy (xx -i- yy) 



K X y yr 



i 



ficque perfeda permutabilitas perfpicitur. 



Operatio II. 



§. II. DifFerentiemus nunc noftram aequationcm^ 

 algebraicam aflTumtam, quae eft 



xx-\-y y ~- aa-^ 2%xy - n a a x xyy :=zO, 



A^a Acad. Imp, Sc, Tom, F. P. IL B ct 



