J4 DE REDVCTIOnE 



CoroII. 5. 



33. Vt autem formula noftra inuenta arcum rea* 



f k 



lem fedionis conicae exprimat , non fufficit, efle 'i^ et -^ 

 qnantitatcs reaks , fed praeterea xequiritur , vt abfcifla 

 fit pofitiua ; vbi duos cafus perpendi conuenit , prout 

 fedio conica fuerit ellipfis, \el hyperbola. 



Coroll. 4. 



34. Sit ergo primo fedlio conica ellipfis, feu y^ _^ -g 

 quantitas pofitiua , atque necefle eft, vt fit i - sV ^>o, 

 feu i>:=^~, vnde fit ^-^->o. At per hypo- 



thefin iG. h-^kzz^o. Qiiare ca(u, quo ^fe £ i >o, ad 



realitatem infuper rcquiritur, vt b fit quantitas pofitiua. 



Coroll. 5. 



t h 



35. Pro hyperboh , feu fi j„^g h fi^erit quanti- 

 tas negatiua, integratio noftra ita debtt repraefentari : 



>v>mS=C + '-^V-4.njii.(,y--:-,)[-7fl] 



/ h 



ita vt ^„-jk iam fit qnantitas pofitiua. Necefle autem 



eftjVt fit s V nr > ijfcU"^*^"^'^©, quareob^-t-^cs>o, 

 arcus hyperbolicua non crit realis , nifi fit h quantitas 

 negatiua. 



Coroll. 6, 



3^. Pro ellipfi ergo , feu fi fit j^^^^ ^o , 

 noftra expreflio arcum continebit realem , fi fuerit 

 i""'./?^©; a^^^.&^o; ac 3"V>o- Pro liyperDola au- 

 tem , feu fi nr^T > o > ^^^^^us erit rcalis , fi fuerit ; 



Scho- 



