mACINJRIIS CONSTRVENDIS, aos 



quatuw Cafiis: l.v*—pv—q'^o-^ W. v^^-hpv—q—o "^, 

 III. 'v^*—pv-\-qz=zo\ W . v^^+pv^ q—o, 

 In Cafii I. fiat v~y'*--\-mpy~' ; erit 



•y^inij' + 3 i'«/>J' 4- 3 mp^y~'-\- fnp'y—^ j 

 —pv~ — pj'— mp^y^' C r;r o. 



- ^= -^ 3 



lam ponatiir :imp-p~o ; erit 3;;;-i=:o , et w=|, adeoqiie 



3W*p*-?«p'— Ip^-j/)*— o.Exquofitj'**-fjV/)j'-^? 



~q S — ^'^^ 



per y' miiltiplicando , y^ — qy' -\- ~ p' — o , quam 

 aequationem quadraticam ad duas fimplices reducen* 

 do , et ex his radicem cubicam extrahendo , fit j :r: 

 [lqTy{\q-^jf)r'. Vnde, ob i^ ^r^' -{-^?, prod- 



it v^l^q^y^qyf)r-^^^t^- . Eft 



autem \p-\:.q-\--V{{q-l,f)J-'. ['.^±V(-:/-.V)]' ' S 



ip 

 vti adu mukiplicando patet , adeoque rT^ ^/^^.jyyi.:, 



=:[^^^-y(5^*— 5V/>*}]'^^- Ergo , fiue figna inferiora , fiue 

 fuperiora valere debere ponas , erit 'r~[i^+y^:^'-jV/>*)]'* * 

 -^{l^^-^i^^q—hp')]'''' Quae eft ipfa Regula Cardani 

 pro Cafu I : in qua de fignis -}- et — notandum eft , 

 cubum 4^p' affici eodem , quantitatem autem \q contrario 

 figno , refpedu fignorum , qnibus quantitates ^ et ^ in 

 aequationc nihilo aequali I, afficiuntur. 



§• 34-' Qiiodfi porro in aequationibus propofitis 

 I. II. 111. IV , loco p et q , refpediiue ponutur 3 P et 

 2 Q; Re^ulae Cardani concinnius cxprimi poterunt. 



Cc a Fiet 



