X74- SOLVTIO PROBLEMATIS 



habebimus : 

 /—i^2p-q+pp-iqfi-^zpq-:ippq ^^ h-c-\-f=2(i-\-g){i-{-p-iq) 

 g=Zl+2 q-p+qq- zpp^ 2pq- 3pqq a~C-\-g—2{ I +/ ) ( I + ?- 2p). 



8. luiuibit hinc eti.im fequentes valores eli- 

 cuifTe : 



a^h-C=l-2pp-iqq-ipq^2ppq\-ipqq—z{i-p){i-q){i-\-p\q) 

 b-i-C-aZ=2p+2pp-2pq-^pqq+2pfq =: 2p(i + ^)(l-fp-2^J 

 a-\-C-b—2q-{- iqq- 2pq-^ppq-\-2pqq = 2 ^ ( i +/))( I -\-q—2p) 



\bi cauendum efl , nc harum vlia enanefcat , quia 

 alioquin triangulum periret , cxcluduntur trgo fe- 

 quentes valorcs : 

 p = 0,q = o,p=±i,q = ±^,p-\-q--i,q=:^^,p=:f=tl. 



Praeterea vcro etiani excludi oportet i+-p+-^— sp^ 

 ne fumma laterum cuanelbat. Tum vero etiam no- 

 tetur effe : 



a-b-=iq-\-p^qq-pp-\- ^pqq-^i ppq — iq-p^d+p-^-q+^Pq) 



g-J-sq-sp-^m-m-^pqq+^pp^-^iq-pXi+p-^^i-p^) 



tandem vero eft 



aa-\-bb^cc=2{ i -p-q+p-q^-pp-pq+qq) ( i+ 2('/>+^)+f/'+?)'+ ^ppqq) 



feu tftf+M+rf=i((2-p-^/+3(p-^)')(i+-p+?)'+3PW). 



9. Supereft igitur vt tertia conditio implea- 

 tur , quae in hac formula continetur : 



hh-(a-hbf-\-{a-by--ac={a-b)\(a-\-b-\'c){a-\b-c) 



vbi fi valores modo indicati fubflituantur , coIJi- 

 gitur : 



hh={q-py{i~^p^q-\-5pqf^j^i-p){i^q){i^q){i+p+q-Spq) 



quas 



