AEQVATIOWM D1FFERENT1ALIJ>M. 33 



vbi per hypothefin v eft functio cognita ipfius x , ideo- 

 que etiam Szzr-W*** *** 



Coroll. 1. 



57. Multiplicator ergo, qui primum ie obtuEt , eft 



XyZ^v )i ? tum vcro etiam multiplicator erit s{y-vu(y-v) i jo_sdx 

 qui etfi continet formulam integralem /QS.4x, faepe nu* 

 jmero ilJo fimplicior euadere poteft. 



Coroll. 2. 



58. Si enlm S eft quantitas exponentialis , 

 iieri poteft, vt JQS dx huiusmodi formam S T itiduat, 

 exiftente T fiin&ione algebraica , quo cafu multiplicator 

 exit 



y—v-~[y-v)*T (y—vli-ry-t-Tv) 



jdeoque algebraicus , quod in priori forma fieri nequit» 



Coroll. 3. 



59. Cum his duobus cafibus multiplicator fit fra- 

 dio , in cuius folum denominatorem variabilis y ingre» 

 ditur , ibique vltra quadratum non afcendat , innume- 

 rabiles aiii huiusmodi multiplicatores exhiberi poflfunt: 

 Sit enim /QSdxzzV, et fra&ionis (yZ&p denominato- 

 rem multiplicare licebit per A + B(3^~V)+CC^.--V) S , 

 ficque erit generalior multiplicatoris forma: 



s 



A{y — v) 3 ^-SS(y — ■v) — BV(j — t>)*-+-CSS — zCSV{y-v)-j-CVV[y-v)* 



fiue ; 



s 



{A— BV-f-CVV^MzA-u— BS-2BVi;-H2CSV+aCVV'Uiy+.AVu— BSV~ BVwt-CaS-t-aCSVzH-CW», 



Nou. Comm. Tom. VIII. E Coroll. 4. 



