t!i6 REDVCTIO AEQFATIONFM 



rcntiali alterutra indcterminata caret : facile cfleam 

 ftd rimplicitcr dilfcrcntialem rediicere rubftitucndo 

 loco differentialis quantitatis deiicientis faclum cx 

 nouaquadam indeterminata in altcrum difFerentia- 

 lc. Hac enim ratione, fi conftans quoddam diffe- 

 rentiale fucrit pofitum , differentio-difFercntialiae- 

 quale inuenitur fimpliciter differentiale ; quo fub- 

 ftituto acquatio habetur differcntialis primi gradus. 

 Vt in hac aequatione ?iif—Qdron_^^,yn-2 ^^,.j ^ ^.^1 

 P et Q_ fignificant funcfliones quascunque ipfius/>', at- 

 que dy conitans ponitur. Qiiia ipfa v non ingrcdi- 

 tur aequationem , fiat dv~z(hy crit dclv—dzdy. His 

 fubftitutis ifta oritur acquatio P<^}'"— Qsy^^H-^^-^ 

 ^''-' dz , diuifaquc hac per r/)"""' ifta Ydy — Qi'^ 

 dj-\-z''-- dz \ quac cfl flmplicitcr difFerentialis. 



4. Alias acquationesdiffercntiodiffcrentiales, 

 nifi huiuimodi , ncmo adhuc , quantum fcio, ad 

 differentialcs primi gradus vnquam rcduxit , nifi 

 forte in promtu fucrit cas prorfus integrare. Hic 

 autcm methodum cxponam , qua non quidem om- 

 nes, fed tamen innumerabiles aequationes differentio- 

 diffcrcntialcs vtut ab vtraquc indcterminata affeclae 

 ad fimplicitcrdifferentialcs rcducipotcrunt.lta vcro 

 in iis reduccndis verfor , vt eas certa quadam fubfli- 

 tutione in alias transformem, in quibus altcrutra in- 

 determinata deefl.Quo fado ope fubflitutionis §. prae- 

 ccd. expofitae cae aequationes penitus ad differen- 

 tiales primi gradus rcducentur. 



5. Cum obferuaffem cam effe quantitatum cx- 

 ponentialium, fcu potius earum dignitatum , qua- 



rum 



