I iO 



LINEA BREVISSIMA 



y compofitae ctiam homogcneae et nullius di* 

 menfionis. 



27. Vocetur haec fiHKftio F -, erit IrrF. Dif- 



fercntialc vero huius fundionis F habcbit hanc for- 

 mam ^dx-\-^c\y. In qua litterac MetN hanc ha- 

 bebunt inter fe rehitionem , vt fit ALv -f- Nj rr 0. 

 Nam ponatur in funcflionc Yy^qx , mutabitur ca, 

 quia elt homogcnea et nulUus dimenfionis,in aliam , 

 in qua tantum httera// occurrct , ncque .v neque^ 

 ampHus in ea repcrietur. Fropterca eius difFercn- 

 tiale habcbit hanc formam "Ldq. Eft \cro L<y^~ 

 ?:^-i2l£— Mf/.v-hNVr. Erit igitur Mi:z~':> et N 

 — -. Ex quo apparet fore M.r-HNj~o. Habetur 

 ergo N— -^- vel Mir:-N=y. 



zS. Unia cft 1— F ; erit^^^t=L4£— ^F — Mdx 



^^ X ' XX 



-{-'!<idj—-~^^^^-\-'Ndj'. Ex hac prodibit ifta aequa- 

 tio irJ.r-N.\;r^.v — — N.v.v^'-f- .v^/ quae comparata 

 cum generali ?d.x—Qdj'-{-Kdt dabit Prr/-N.vj'-,Q=- 

 N.ra'-, et R— A*. Ex aequationibus vero duabus tdx 

 -'i^lxjd.x^—Nx xdj-{-xdt et M.r-hNj — <?, inuenitur 

 M— xdt- tdx et m—-^=zl2^. Erit igitur P = 



xxdy—xydx 3 '-' 



xxydx — X dy 



txdy^jcydi ej Q— yxdt-tydx ^ ^aais his fubrtitutionibus 



xdy—ydx ^ xdy—ydx 



in acquatione generaUQ^^zi:-f^rt^^^inue- 



dt -f-dx -i-dy 



nietur haec aequatio ^^^'^^^-^^'^f ^^-^ ^'f ^. ^^-^•^^ ^^^'^■^— 



yxdtdx — tydx -i-txdy — xydtdy 

 dxddx-^ dy ddy 



r. /> 2 



29. Ad hanc aequationem reducendam pono 

 ti-h-vx-i-jj—zai j et dt' -^dx - -f- r/;' = — (/.f " ^ e r it 



xdx 



