1(54 DE CALCFLO IKTEGRALl 



^3/7' x^^yydy—Caax^^jdy^^^ax^^^dy — 6aax'^j:)'dx 



^izax^^^ydx — 6dx 



=12 A.v~ V^-+-Ba:~ ' dy-^-^Ax^^jydx-^-^Bx^^jdx 



J^-^Cdx-^-^^^dx-^-xdN 



Comparatio terminorum homologorum praebet , 



Arr— 3^^, Brr3^,Crr:— I, & remanebit squatio fequens 



'^a^x^^^yjdj^iz^li^dx-^-xdN. 

 Ducatur hacc «quatio in x^ , provenietque '^a\yydy 

 zn^^^x^ dx-\-x^ dN.XJtraqnt parshuiusasquationis eft in- 

 tegrabilis , invenietur enim integralis eius 

 c^j^— N/f^ . Habemus ergo '^zza^x^^y^ , adeoquc 

 M(=i:AAr~fj-f-B.r~^j-f-CH-N)zi: -^^tfA;"'^;:)^-^^^"- 

 y—i-ha'^ x~^y^ 1 adeoque 

 ulznMK^^iUx^^^^-^^aaxxyy-^^^ax^y-x^-^-a^y^ 

 ziza^y^ —'^aaxxyy-\~'^ax'^y—x'^ zz^[ay-xxY . 

 Hoc idem integrale inyenilTemus ponendo dlizizjayydf 

 —^aaxxydy-^-^^ax^dy—^aaxyydx-^- 1 zax^^ydx—Cx^ dx. 

 Dein R:z:;vvelz:=)', fedX— 0, adeoqueX-hi—t. 

 Exemplum ip. 



Sit dt^-yyydy-^-^-^aifhty-' dy)y{a'^ b-2cy^ -\-yhhtY 



cxiftente t—Vaccyy. Hoc loco eft dK=z-^cyydy 



-^-j-^ahhty- ' ^,Rz:r<2^ ^— srK^ ■'\''^ahht^'K~~-^y adeoque 



X-Hizr^. & sequatio canonica ^Kzn 4:M(^-t-R^M. Nunc 



I 

 vero, quia 4fdR.zzdK , crit M=::«, adeoque «(— MR''') 



:zzy{a^ h-zcy^ -^-'^abht). 



Exemplum 1 1 . 

 Si duzz{2axyydx-^cxyydy-{y'^ dx—Qccyydy--/i^axxydx 

 ^-4^x^ dy-\-Sccyydx-2axxydy) : {y^-^xy"^ -\- 1 6xxyy). 

 Quoniam y^-^^xy^^^^i^xxyy eft quadratuin, cuius radix 



eft 



