( Sno ) 
fariis mek^nonhve difcrimen reperi^ut moxvidehk^ &jam/anh 
vidfjjesmpmeprolixitas ante hac }^fcr then do deter ruijfet. Nequid 
tamen dtjjimulem^cnm NahiliJJimi Hugenii cof^firuSiomm ad cal" 
culos revocarew^ eandem omnino mecum analyjin fecutum effe de* 
prehendi 5 fed cum ex ilia du^ nafcaniur effeShnes^ utraqne per 
hyperboUm circa afimptoios 5 jlle unam^ego alteram^ utifacilio'- 
Vid. nb.li, rem.felegeram. Evident eB autem^nrhil aliud qufzri 
Tig I1,III;1V. l^Qf^ Problemate fjt tlludad terminos mere Geometru 
cos revocemm) nifi in dato circulo^ {cujm centrum A^radius^P) 
funlium aliquod ut a quo duUis adpunUa data E inaiquali^ 
ter a centro A diJiantia^reBis P E^ PB^ reBa AP produ&a bifecef 
angulumEVB, ^odquidemvarioscajmreciptt* Velenimnotn 
malis ex A in reliam E B^ nimirnm A 0^ cadit inter £ ^ B '^vel 
ultra B. si xxltrik^velreUangulum EOB <equale eji quadrate A 
ml ma]ifs vel minm. De cafu asqualitatis videbimm infrk ; nunc 
vero tres alios cafus eademfere confiruoiione compk&emur. Per 
tria punUa AEB tranjeat cir cuius ^ad cujm circumferentiam pro'^ 
ducaiur AO in Ac Jiquidem punUumO cadatimtxE B 
re&a A 0 verfm Oproducenda erit ; Jin autem ultra i5, pquere* 
Sangulum EoB msijas quadrato AO^producenda erit verfns A^a$ 
Jire£}angHlum quadrato mmmfuerit^circulm in ipfopunSo re* 
Sam AOfecabit. Turn duUa A X parallel^ E fee ante circulum 
datum in fiat utreBangulumD AO adquadratum AN^ ita^ 
A X ad A M^ qu£ fumenda erit versus Xyfi 0 cadat inter EdrB 
aut re&angulum EOB minus fit quadrate OA'j at ex parte con- 
traria^fifitmajm. Ponatur nunc 0^£qualis AH (in direUum 
E^ Bprimo &fecundo caju^ tertio vero^^verfus E:) Turn fiant pro- 
porlionaks XA,N A.HKjummda omni cafu verfus X : feifdque 
A 0 in ut fit eadem ratio Kd ad A quce AD ad A X-^ jum 
gatur K ac producatur donee occurrat re^a^M parallels 0 A 
indefinite produ^s^ in punBo L s erunt omni cafu KL L 
af)mptoti Hyper boU, qu£per puf^£tumO defcripta, propopo J^f 
faciei : Hoc tantum dtjcrimine^ quod primo dr ftcundo Cafu hvper- 
bolaperOjFroblemafohetin fpeculo convtxo^fieiio vero ei op^ 
pofita in cooca vo 5 at 3°. cafu contra ^Hyperbola per 0 ferviet con^^ 
cam, ejm oppofua convexo. At que id quidem^cum punlium Vca^ 
dit inter J 0 ; nam ft ultra 0 cadeiet, umca Hjperbola inter 
tafdem ^L, K L defrripta^ tamfpeculo convexo quam concavo 
faiijfacereL CmerumfiV caderet In ipfum pun Bum Oy Probkma 
tunc 
