qivie aeqiiatio ab ea quam fiipra §. 4. pro CaufHca Parabolae 

 iniienimus, tantum in eo differt, quod liic loco p habeamus 

 l a. Praeter hanc igitur curuam nulla alia conditioni Pro- 

 bleraatis fatibfacit. 



Problema 2. 



§. 15. Itmenire ciiruam ATM, ad qua.m fi in ptm&o y^^^^i^. 

 guouis T duLatur normnlis TN^ axi AB occurrcns in Ny difercntia Fig. 3, * 

 arcus et reCiae A N ftt conjlans. 



Solutio. 



Sit abfcifia AXrr jr, apph'cata XY~j', pofitoqiie 

 dy — qdx., erit arcus AYzr^fdxY {1 -{- q q) et reda AN 

 :zz. X ~\- qy. Fieri ergo debet 



X-^qy —fdxy^ (^i-\-qq)~C, 

 Hinc differcntiando erit 



d X -\- qdy + y d q — d X Y {l -\- q q)z=ZO'^ 

 fiuc ponendo ^ loco dx prodibit 



tZ _r: — ? 3? ^ 



Ponatur / (i -+■ q q) — ti^ erit 1 -^ q q -rzuu et qd qznudu, 

 quibus rubftitutis habebimus ^ — — -i^, hincque iutegrando 

 lyzizla— l(jt—i) et ad numeros furgendo 



y= ' 



u — 1 y H -t- q q) — i 



Hinc porro fit -/('i -4- ^ ^) — IzhJ-^ ideoque q q nz tl±±Ly ^ 

 vnde porro concluditur 



3 .V zz: ?-? ~ — y^y , 



q V {a a-i- 1 a y)* 



Ad banc formulam comraodius integrandam ponatur 

 Y (a a -\- 2. ay) ~ 2;, fietque 



Noua Aaa Acad. Imp. Se. T, VUL B b y zzz 



