5<J SOIVTIO VROBLEMATIS BIFFICILLIMI 



Solutio tcrtia. 



§.14.. Ciim ^xx-\-YV~ j\.p* -\- ^q* — 4tJ^rr-Jr- 

 r* cfle dcbcac qiiadratiim , ciiis nidiccm pDiiamiis hic zzz 

 pp -\- 2<7</, vt lit V i^xx -{- yy) — 2.pp -]- ^qt]; atquc 

 proJibit li.iec iCi]u.mo r* — ^qqrr— -h&ppqq; vndc fit 



pp zr -t ^-*^^ et yc\p = ^^V{zrr-Sqq) vcl 



p— {.jV ( %qq — ->'f') Q|>ia "^cro ob yznzqq — rr cfle 



oportet zqq^rr, prior valor crit iiuitilis , lubcbimus- 



que 



p= T-^y{Sqq-^rr)\ x = pp; y=zqq-rr\ 



et l/(4.v.v-i-J7)= -/'/'- -'/'7 

 atquc vt antc z = x-\-^^^-- Erit crgo 

 I cuhctus- '! , II cath. -}; hypot. =^-^^^^^ 

 Nunc crgo huc dcucnimus , vt Sqq~ ^^rr rcddatur qua- 

 dratum : fit cius nidix =^^ {zq -\- r) critquc 4^— 2r 



— d^(2^-f-r) fcu ^ddq -z(iiir=zccq-\-ccr, hmc' 

 quc q = cc -f- zdd ci r=^dd-zcc\, zq-{~r= %dd atqiiC 



y(8^^-2;-r)= 8.V, hincquc p- i^J^^l^ Quarc in 



intcgris multiplicando pcr zdd-\-cc fict 



P = ^cd{zdd-cc) 

 q = {zdd-\-cc) 



x=pp 

 y = zqq — rr 

 r= 2{zdd-cc){2dd-]-cc), V {^xx-\-jj)=zpp — zqq 



Excinplum. i. 



§. 15. Sit f — I j d= I , crit : 



P- 



