€z TROBLEMA ANALVTICVM 



xt+>dy . xt~*"y 



x^'dy x*-*-*ddy ex*+ '-dy 



e J ( ~" jH-i f-+-i •?-+-- • <* * ) "~~ f -»-;•;-+-*-• <'* 



x^-ddy x '-*"d\y _ _ f x^ddy 



jj ( f_ + - 1 .fZ+- i .t(x"~i - ?■+-,.;•-+-- .]>+-.. dx z / £-+- i.fH- s-iH-.- <*■"• 



Culligendo terminos analogos , nafcetur aequatio fe- 



.. . {i-e).xt-*-'dy (f-e) x*+*ddv 

 quens , f(yx?dx-\- ----, -h - ^—p+TTx h 



fx^d\y x*+'y ___x___- z dy { j x^ddy 



±A. Nota , quod A fit conilans arbitraria , quaepoft 



integrationes pcractas addi vel iiibtrahi folet. 



Porro vt meinbrum prius identificetnr cum differen- 



tiali propofito feu cum eius aequiualente yx*dx-\-ax*-*- 1 



bx^ddy cx*-*-'dy 

 dy-\- j^ \- — d X * — , oportet coaequarc cocf- 



ficientes tcrminorum homogeneorum , nempe a~zz. =-, 

 b=^rf^c -f3-£:^i , vnde lucrabimur e=(p-f-i. 

 p-\-2.p-\-^)c-(p-\-i .p-f-ft)£,et/= (p-\-i .pH-2. 

 p-\-$)c-> ipfms vcro /; valor eft radix huius aequationis 

 x-(p-\--)a-\-(p-\--.p-\-^b-(p-\-i.p-\-2.p-\-z)c—o, 

 quac erit trium dimenfionum. 



His igitur valoribus liibilitutis in altero membro , 

 orictur quaclita aequatio diffcrentialis redufta vno gr.idu 

 fimplicior quam propofita , quae (cilicet haec erit : 

 x t-h>y x*+-*dy cx?'*-ddr 



-j+r-+-[b-(p-+-V']—: ir— -+- — ^— ±A=o. 



Rcicfta arbitraria A, et tum diuidendo per i '" + "', 

 prodibit acquatio minus quidem vniuerfalis fed multo fim- 



plkior , jfc +[*- (f-H3)f ] -g -+- -^HP = o. 



Cac- 



