== (5o) = 



fu/idio qiiaecunifuc dala algcbraka ipfius i', inuenirc pro binii coor» 

 dina::.> x & y ei:omodi funcliones olgebraicas ipfius 'v , c7 inde 

 tuadat }/ ( ^ A-* -\- df' ) — V c) c. Tiini cnim intcgralc fVdv 

 vtii]iie cxprimcrcr Jongitndincm curuac cuiusdam algcbroicac. 

 Hic ftiliccr rcs co rcdircr, vt ollendcrctur, quibusnam cafibus lioc 

 Troblcivia vcl nullam planc (blutioncm admittcrct, qucmadmo- 

 dum cucnirc Ibtuo cal\i Vdv — --; vcl vnicam tantum folu- 



V 



tioncm, vcluti cafu V d v* ~ i^H , fuic etiam VBvr— i^: 



vel dcnique , quibusnam cafibns hoc problcma innnmerabilcs 

 fohuioncs rccipcre poflict , qucmadmodum ollcnrurus lum pro 

 cafu V () V zz: d V 'Z (i -f-vc;), quandoquidcm ciiis inrct^ralc 

 fdi-y^i-i-vv) cxprimit arcum Parabolicum , cuius quippe 

 coordinatac funt v ct i v v, 



§. 3. Antc flutcm quam hoc proMcma particularc fu- 

 fcipiam, dnpliccm mcthodum apcriam , qua problcnia t^cncrale 

 trac^tari Cfiiiucniat. Ac primo qnidcm propofita acquationc 



}/(dx' -hi^f)~Vdv 

 dJfpiciatur, num fortc eiusmodi funcftioncm ipfius c, quac fit U, 

 cxplorarc liccar, vt hac duac formulac : d x — ^ '^ '"'*'' *-*- !.' ct 



r) y — LiJLllilrziL* , fiant intcerabilcs ; ouoniam cnim inde fit 



B .V* -f- df' =z V dv^ , quacflioni forct fatisfadum. Vcl 

 etiam qnacrarur cinsmodi anqnhis (|), qui rationem aJgcbraicam 

 tcncat ad variabilcm r, ita vt ambac iftac formulac V <)rfiu.(|) 

 ct V^ccof.Cj) cuadant intcgrabilcs, qnoniam hinc ficrct 

 x=fVdv fin. Cp ct j z^f V d v cof. (J). 



§. 4. Qiiando autcm hoc rcntamcn nullo modo fuccc- 

 dir, difpiciatur , vtrum foriTiuIa propf^fita V f) v ad huiusmodi 

 forir.am rcduci qucar: f) f )/ ^ P* ■»- Q* ); t'"" cn''^» flatim hnbc- 

 rctur (uluiio x—fVdv ctjzfi^Ov, fi n.odo hac formulac 



cHcut 



