56 VAMAE DEMONSTRAT. GEOMETR. 



qiie multiplicando S\OP'r=:S.AR.BP.CQ^, hiiicque 

 radicem quadratam extrahendo habebitur : 



S .OP — yS.AR .BP.CQ^ 

 ideoque area trianguli ABC — VS.AR.BP.CQ^. 

 led ex §. 7 patet efle : 



AR — S-BC; BP = S-ACet CQ^— S-AB 

 quibus valoribus ftibftitutis erit. 

 Area A ABC— VS (S-AB) (S-AC) (S-EC). 



Q. E. D. 



CoroU. I. 



§. 10. Hinc etiam concinna expreflio pro radio 

 circuU triangulo infcripti OP exhiberi poteft. Cum enim 

 fit S.OP':=AR.BP.Cq eritOP'=^^, ideoque 

 OPmV ^iCQ, j.^j^ ^j.g^ pj.^ AR, BP, CQ_ fcriptis 

 valoribus ante indicatis habebitur. 

 Radius ciicuh infcripti Qp-y (•^-^bxs-acx.s ^^ , 



Coroll. 2. 



§. II. Qiiia S denotat femifiimmam laterum triaa- 



gnh,ita YtfitSzzUB-hlAC-i-iBC— -(AB-I-AC 



-l-BC) crit hoc valore lubftituto : 

 S-ABzr^AC-i-lBC-UBzr i(AC-f-BC-AB) 

 S-ACz=:iAB-h^BC-'ACz= i(AB-f-BC-AC) 

 S-BC=:^AB-+-iAC-iBC=: i(AB-+-AC-BC) 



fic erit: S(S-AB)(S-AC)(S-BC ) — 



A(AB-+-AC-f-BC)(AC-hBC-AB)(AB-|-BC-AC) 



(AB-l-AC-BC) 



ideoque area trianguh quoque ita exprimetur. 



iy(AB-hAC-|-BC)(AC-hBC-AB)(AB-HBC-AC) 



(AB-hAC-BC). Scho- 



