ioS THE0REMA7A 



alios non admittunt diuuores , nifi qui ipfi fint eiusdcm 

 formae , ponamus : 



nn-\- 3 kkzz (aa-\-$bb)(cc-\-$dd) 

 vt fit : 



pzz.aa-\-$bb et qzzcc-\-$dd 

 critque 



vel nzzac-\-$bd\ kzzbc-ad\ mzz^bc- $ad 



veS n zz a c — zbd; kzzbc \-ad\ mzz^bc \- %ad 

 Hanc pluralitatem \alorum per ambiguitatcm fignorum 

 ita exhibere poterimus, vt fit 



mzz-j- $(bc+ad) : nzz ■+- (ac^r $bd) 

 ideoque diuerfi valores pro m et », fumtis pro a t b, c t d f 

 numcris quibu^cunque, erunt 



I. m-\-nzz 3 ( bc~\-a<d) -+- (ac-$bd) ; m—nzz^ (bc-\-ad) 



—(ac—$bd) 



II. m-\-nzz$ (bc-\-ad) — (ac+$bd) t m-nzz$(bc-\-ad) 



-\(ac—%bd) 

 III m-\-nzz^(bc-ad)-\-(ac-\-%bd)\ m-nzz^bc-ad) 



-(ac-\-%bd) 

 IV. m-\-nzz^(bc-ad) — (ac-\^bd)\ m—nzz%(bc-ad) 



-\(ac-\-$bd) 

 Hinc autem fequuntur fblutiones , quas iam dudum fii- 

 fiis expofui , quare ad propofitum reuertor, fequentes 

 propofitionei» d.monftraturus. 



Propofitio I. 



i. Si numeri a et b non fint numeri inter fe 

 primi , tttm nume:us aa-\- $bb non erit primus , fed 

 diuifibilis cnt per quadratum maximi communis diuifo* 

 m numerorum a et h 



Demon- 



