quac nunc conferri dcbct , cum noftra acquationc propofita, 

 quac erat 



ddx-\- m ddy-\- (a-\- ma!) dx-\-{$-\-m (3 ; ) </./ + (y+»v') * 



-\-(6-\-m'6)y — o, 

 vnde fequentcs prodeunt quatuor aequalitates : 

 A+» = a+ff/a'; B-\-mn~ $-\-m$'\ nA — y-\-my' \ 



« B = 5 -+- m 5' j 

 ex prifna et fecunda fiunt 



« A — n a -\- n m al — n 2 ; nB — nfi-^-mnfi — mn 7 , 

 vnde confequimur 



y-\-my' — na-\-nma!—tf ; $ -\- m S' — n fi -\ m n @' — m n* j 

 ideoquc 



„. •y-f-n» — n g ' ? — n 3 



na'—r nfr — ni — 5' > 



ex quo denuo conficitur haec aequatio quarti gradus : 

 rt-(a-\$')n-\-(y-\-6'-\-aft-a'$)n-(a6'-a'6-\-p'y-$y')n 



-+-(y6' — y'6)—o. 

 Intelligitur itaque hinc, n quadrnplicem habere poffe valorem ; 

 ideoque pro <£> quatuor diuerfos multiplicatores formae pro- 

 pofitae adhibcri pofTe , nifi forfan fi aequatio illa biquadratica, 

 binas vel plures radices habuerit aequalcs. 



§. 22. Inuentis autem quatuor aequationibus differentia- 

 iibus primi gradus huius formae : 



e*" (dx-\-mdy-\-Ax-\-By) — C, 

 feu potius fi placet iftius : 



d x -+- m d y -f- A x -\- B y — C e 1 u 

 fcribendo loco n, — n, inde facillimum erit valores quantitatum 

 x et y eruere , eliminanda fcilicct dx, dj , tumquc vel x , 

 vel y. 



Sint nimirum hae quatuor aequationes : 



dx-\-m dy-\-A x-\-B y — C <f tt 



dx-\-m l dy-\-A' x-\-B' y — C e n '* 



d x-^-m" dy <-+-A" x-\-B''y — 0' e*" u 



dx-\- m"'dy -\- A'"x -+- B'"y — C" e n '" " 



fietque 



