QVIBFSDAM IKTEGRABILIBFS 191 



quatio data fit ax 3 ^x-^hyx dx^cy dxzzdy. 



I 



cnt j/:=i I — b-f-2 " _2&-4-r' 



'Exmpl. 3 . 

 Siyzri hoc eft , fi aequatio data fit ax^^^-^dx 



t -t-2 -I 



►f-^j'^" ' dX'\-cfdx=J}', erit y=:(- tf : cfx -fai^ ;c * 



atque (lc in fimilibus exemplis determinari poterit valor 

 y per .T & conftantcs ; fmgularis autem cafus eft ubi m 

 non determinatur per coefficientes datas, fcilicet fi fuerit 

 fix-^^^dx-^-byx'^ dx-ir-cy^^dxTiz^y ^ ubi fit 



^—( -(5^-12:+- •i&-f-. ) ""-^ac X r-' . Gabriel Manfredius 



2c 



in trad. de conftrudione asquationum differ. primi gra- 

 dus p. 167. art. 105. cum incidiffet in aequationem 

 nx^^dx-ny^^dx-^-x^dy^izxydiX. hac, inquit, aquatio nonap- 

 paret quomodo confiruibilis Jitj neque enim videmus quomo- 

 io illam integremus^nec quomodo indeterminatas ab invicem 

 feparemus. Sed integrari poteft per formulam noftram 

 hoc modordividatur aequatio per x'^ , fiet ndx-x~^ydx 

 '-nx~'^y^dx—dy , pofitoque x—z"^ ^rit— nz^^^dz-^-z"^ 

 yd»-\-ny^dz=:4y. Ergo yzz{ _, ^Vi^.J z- ' . 



n 



Si asquatio A . . . ax^^^dx-^-byx^dx-^-cy^dx^dy in- 

 tegraripoteft, erit eriam aequatio 



B .. . '^^^iff^x'^H-^^^xhdx-\-cu^dx=z4u 

 ktegrabilis. 



Demonjf' 



