35 SOLVTIO PROBLEMATIS 



p:=::2mm'-zmn'^nn; q-izmm-' 2.mnzzm{m-'2n) 

 s zzrzzmm-^-mn — nn i vnde fit 

 p-^- s zz ^mm —mnzz m^^^m—n) 

 p-^szzmm—%mn-^znnzz{m — n)(m—^n) 

 q^r-zz ^mm — mn—nniz[m'-n)[2.7n^n) 

 q — rcZ'-^mn-\-nn-z=.-'n[:^m'-n), 



Hic fignum negationis in valore q—r^ nihil planc 



turbat , tantum enim opus eft litteras ^ et r inter 



fe permutari , ita vt fit 



pzz^mm — ^mn-^-nn; qzzmm-^mn—nn 

 szzmm -\- m n —nn-^ rzzmm — ^mnzz.mim^zn) 



vnde fit 

 p-^-szz:^ mm^mnzzm{^ m^n) 

 p — szr m m — ^^mn-^- innzzim — n^^m-^^n) 

 q-^-rzzimm-^mn — nnzi {2m + n){m^n) 

 q^rzz^mn — nn zzn{:^m — n) 



quibus valoribus in fequenti calculo vtemur. 



13. His conftiiutis valoribus, pro numeratore 

 noftme fradionis habebimus : 



pp -\- s s zz s m* -^ 6 m^ n -{- ^7 m m nn " 6 m n' -{- 2. n^ (eu 

 pp^s sz^{mm-\-nn)( smm— 6mn-\-2nn) et 

 qq-\-rr—2m^ — 27n n-\-:^mmnn—2mn-{n\ fiue 

 qq -\-rrzr{mm-\-nn]){2mm — zmn^nn) 

 ■ynde fradio ncftra aJ quadratum reducenda erit: 



^ M (s »71 -^ — 6 -n n -i- ■! n n). [mm -i- n n)- 



N N 2 71(2 m-H?i,. rn'.{m — nf (wi — z n}'^ {i m — (iy-[mm -t- nm -^ nn)^ 



h nc- 



