D E L L' ACCADEMIA. 1+9 



X , & quantitate M^^ fublata fiat dZ = 'ì^ldy -+- j^ , cum prò 

 maximi, aat minimi valoris cafu efTe debeat N^;f— ^P=o, fiet 

 ctiamN^/>=^, ^dL——j^ , atque inde eraetur Z.-t-U 



= -7 . Qnodlì etiamr/ydehceret in ditfcrentiali aequatione > atque 



c{ret^Z=:^',pofito-^. =o,iieretP = C6iZ,=S^ = 



V^,-+-D . Pariter ^\ in difFerentiali squatione edèt M=o: N 



~"o, & </Z= T^-t- - ^ -^ j prò cafu valoris maximi» aut mi- 



nimi prodìrer -J^-<-^ = o, & C-P-^^=o: quos ca- 



fns diftincVe expofuit Eulerus in Corollariis Prop. III. & IV 

 Gap. 11. Operis jam memorati. 



COROLLARIUM III. 



Si fit rfZ = N^-H-^, & quantitas ^Zdx effe debeat 



maxima vel minima , ac juxta priorem illam quantitarum ma- 

 ximarum , & minimarum regulam elementum etiam ILdx efl'e 

 debcat maximum) vel minimum, fumptis differentialibiis, lìec 



-«/Z=:N^-»--^ = o, ac fiet propterea N -+-;j^ = N— ^-=0 , 



& Vddy — -d^.ày. Eulerus in Scholio III. Prop. Ili- Gap. II. 

 dixi: defiderari adhuc methodum a rcfolutione Geometrica» & 

 Imcari liberam, qua pateat in cafu qnantitatis alicujus maxi- 

 vcvxi vel minimi- loco '?ddy allumi pcde — dV . dy . Mctbodnm 

 hujufmodi tradidit Clarifs la Grange To.ll. Atadcmia: Tauri- 

 ncnfis, inventoque variationum calculo maxime ffnerales q':an- 

 titatum ifoperimetricarum formulas cxhibuit. Ncvim v;.ria- 

 tionum calculum ad eadni difllrcntialis calculi iin.brla brevi- 

 ter revocabimus, puflq i.im aliquot cxcmplis formularum prajce- 

 dentium ulus innotefcet . 



Pro- 



