FORMVLARVM DIFFERENTIALIVM. 227 



31. Confidcrcmus nunc formukm difFereutia- 

 lem homogcncam 



pro qua muUiplicator idoneus eam integrabilem red- 

 dens cxquiri dcbcat , adeo vt fi is ponatur (J), fit 

 formula 



(p {K d X -{- S dy -\-T dz) 

 integrabilis. Ex natura autcm quaenionis intelligi- 

 tur pro afTumi pofle fundionem liomogeneam 

 ipfitrum .v, j', z, tunc \'ero fi ponatur 



(pR — X, (pSrr Y, (p T — Z 

 erunt quoque X, Y, Z fundioncs homogeneae eius- 

 dem dimenfionis ipfarum x, j, z. Per naturam au- 

 tcm fundionum homogencarum iam liabebimus : 



Atqui ob integrabilitatem formulac 

 Xdx ^Y dj-]-Zdz cfTc debet 



Ijy^— ^dlc^J' 'ri''— ^d-T^' '^dT^''— dj>' 



his igitur aequalitat.bus in vlum vocatis acquationes 

 fuperiores in fequcntes transformantur : 



«,X = .v(l-^)+Wf|)-4- = <M) 

 »Y = .v.i|)+.,(ll) + ^(j-|-) 



«Z = A-(i|)+.^(H-)-i-Mrj 



f t 2 cx 



