Opuscula # i6i 
citas fit ea, quam acquireret corpus follicitatum a potentia 
b 
per Ipatium L = • 
Si diligenter inlpicias formulam cafus alterius, facile co- 
gnofces , eam vei efle c/cloidem , vel cycloidis analogam . De- 
fcribatur cycioisEAV QFig.ii^, cujus circulus genitor EIG 
habeat diametrum EG=: — — . Huic ordinetur DLj tum 
ubique fiat Qjjl : l/ ^ -— Z : : L D : L d , pun(flum d erit 
in curva quicfita . Ea autem fit Eav; ordinetur a f — ^ ; a/o 
corpus A projec^um ex ^ mm expofitis conditionibus hanc 
curvam defcribere . Si foret Q}/ Z= V a b — f'' L y five 
Z -4- P'' L — a L — a by five L^h , curva E a v coincide- 
ret cum cycloide EAV, & diameter circuli genitoris ita in- 
a 1}" a h a h 
veniretur E G = 
In tertio cafu curvae conllrudio pendet ab hyperboJae 
quadratura . Quod ut manifeftum fiat , pofito facilitatis caulfa 
<^^h'' ., .' r y ^yJl ^ J~y 
=: c, mihi propono formuJam ■ . rac *^ — 
¥ L^a b vy-\-e v/jy+o 
z . . . ez o j zdz 
^= — , ex qua sequatione mvenies y = — — ^ oz ay ^ ^ : 
ergo - ^^ = zzizzz^z- ^I^'^ autem formuJa in has quatuoK 
partiales refolvitur — — - — ■ ~ h ^ — - — ; — - Prima ^ 
* a c — z — ; — - e -f- z ' 
c ^ z c -f- z 
& tertia ex hifce formulis algebraice integrabilis ell , fecunda,' 
& quarta integratur pofita defciiptiorie logarithraicae . Hifce 
animadverJis defcriptio curvx , quam mobiJe in itinere percur^ 
reret , per logarithmicam abfolvitur . Si autem defcribatur , 
apparebit habere progreflum fimilem iJJij qui a fg. lo expri-. 
T. IV. ^ irutur 
