/ 



^02 MEDITATIOKES DE Ql^AKTlTATlBVS. 



§. 32. Hos diios cafiis intcr fc confcicnti patcbit etiam 

 i) cfTe fictum calus I — fcmif. aDcarusII — "p'-;/. Etcontra 

 a) eflc rcmirummamDacafusIzzfci(flocafib 11— ;/)'+; '^*- Jitcontra 

 Hinc fequens formuhi geucralis F infcruit ct Dto fcmifum- 

 mae , ct femifummac Dtorum , et fi(fto radicum , et Dto 

 femidifFcrentiac in vtroque ca(u fimul rcpracfcntandis. 

 F - - - - - =:\p2^'J\ Nam 



11 ^ottanir // — o ; fict F— {/)*-4-n — ^' — nt-M <^rr.iri]nim.ic in 



Vtroque cafu. 

 Si ponatur p—O , valeatque fignum inferius, fiet Y—o-\-\d''—-\-\<t 



~ato fcmidifferentiae cafus I. 

 Si ponatur p~o , valeatque lignum fupcriusj fietFzzo-^/— -^i' 



— Dto fcmidiffcrcntiac Cafus II. 

 Vtroque autem mcmbro rctcnto , 

 Si valcat riguum infcrius j fict Y::z.'^''-\-\d*— fcmif aa cafus I.^ 



— fiKfto cafus II.S 

 Si valcat fignum fupcrius \ fiet Yzz:\p^—\d^— i\d.o cafiis 1. ? 



— femifiDDcafusII.S 

 §• 33- Nunc progredior ad aequationcs cubicas. 



Hanim conflrucflio fupponit notitiam Formularum genera- 

 lium pro radicibus cx data accjuationc cubica cxtralicndis. 

 Etfi vero Formulae iilae , fiib tiiulo Kcguiarwn Cardaniy 

 liitis notae fint \ iuuat tamcn casdcm alia mcthodo, ma- 

 gis naturali ct paulo commodiore , in quam antc annos 

 complures incidi , crucrc , ct additamcntis , quac ad reli- 

 quas duas radiccs dcterminandas pcrtincnt , illutharc: prac- 

 fcrtim cum co ip(() Rc^iilac Cardanl , quac multis fufpe- 

 «flac videri lolcut , valdc confunicniur. Nimirum aequa- 

 lioncs cubicae , Iccundo Tciiniuo fublato , rcducuntur ad hos 



