io6 METUODVS CVRVAKm 



peret ; ad hoc ponatur kVznx et AQ^'— j/, fitquc 

 yzzixVii-^-hk^-kVii-^-xx)'^ et cum fit Atc.pq^ 

 zzU x-Ti.y , erit: 



Arc.p q' zz Arc. Ak-\- kxy 

 Vtraque igitur folutio ita coniungetur , vt pofita abfcifla 

 data A P —p \ capiendum fit : 



AQiip V ( I \kk)\kV{^ I \pp\ et AQt/jV ( i-\kkYky{i. -^pp) 

 quo 6do erit : 



Xxc.pq zz Arc. Ak-{-kp.A(^ 

 Arc.p q' — Arc.Ak-{~ kp. A Q" 

 ficqae duplici modo problemati ert fatisfadum. 



Coroll. I. 



61, Fieri autem nequit , vt exceffas kxy^ qiio 

 arcus pq arcum A^ fuperat , euanefcat, deberet enim 

 effe vel xzz.o , vel yzzo. At cafu xzzo fieret 

 yzzz-kj arcusque in ipfo Ycrtice A inciperet in altero 

 ramo ipfi arcui A^ fimilis capiendus ; aitero autem 

 cafu, quoj'— o, fieret x~k^ et arcus pq in arcum 

 Ak abiret : vnde arcui A^ geometrice in parabola 

 abfcindi nequit alius arcus ipfi aequalis , qui ipfi noa 

 fimul futurus fit fimilis. 



CorolJ. 2. 



63. VicilTim ergo dato arcu quocunque /)^ in 

 parabola , femper a vertice arcus abfcindi poterit Ak^ 

 qui ab illo deficiat quantitate geometrica. Cum enim 

 nunc datae fint abfciffae AP— j' et AQ=:^.v. erit 

 A K ~ ^ — x V( I -\-yy) -7/(14-^ x) , qua inuenta , erit 

 Aic.pq-Aic.Akzzkxy* 



Coroll. 



