50 SOUTIO VROBLEMJTIS DIFFICILUMI 



tationibns fiiis ad Diophantuni Bachcti rcqiicns problcmi 

 tani]ii;im Ibliitu difhcillimiim 



Iniunire triangulum rcclangiilum in mimeris rationalibus 

 exprej)um , cuiiis iterque cathctus area ipjius trianguli 

 viiniUus producat numcrum quadratum. 

 Hiiius crgo problcmatis (cqucntcs , quas mihi quidcm cli- 

 ccrc contigit , folutioncs in mcdium afTcrrc vifum elt , 

 Pracparatio ad iblutioncm. 

 §. 3. Notum cil triangulum rciflanguhim in numc- 

 ris wtionahbus cxprimi , fi ponatur cathctorum altcr ~ 

 2tfZ', et altcr -^ aa — bb ^ tum cnim prodibit hypotcnu- 

 fa z^aa-\- bb. Gcncrahus cathcti ambo poni pofllint -\ 

 et °-^^ ^ prodcuntc hypotcnuia =r ^^- . Ponam au- 

 tem , quoniam naturam trianguli rc(flanguli \Uin-.o loco ia 

 computum vocarc cxpedit , 



vnnm cathctum — ^ 



altcrum cathctum zr -^ 



eiitque arca ~ f^ 



Ac primo per conditioncm problcmatis hac quantitaics 



I~ — — - icU 2. V ^ — V \ J 



... y *y r i" qnadrata cfhci dcbcnt. 



II- i- xi fcujc-Av^ ' 



Tum \cro , quia hypotcnula fit — tLil.=^±2il ^ hj^cc quan- 

 titas 



III. ^.x.x-\-yy rcddi dcbct quadratum. 



§. jf. Qunniam hac ambac quantitas zxz — xy et 

 y z — xy cifc dcbent cjuadrata , earum prodiidum paritcr 

 crit quadratum. Ordior crgo u piodudo, 



^xy 



