At vero eft 



fin. B 2 = (i — cof. B) (i •+- cof. B) , 

 vnde quoniam, denotante k femifummam omnium laterum, 

 fit 



I COl. _> 2(a& _ f _ cd) ab-hcd * 



r _J_ rr£ "R _!__ b]2 ~ (c ~ d I 2 2(k — c)(k — d) 



I -1- COl. _> 2i a&H-cd) ab-i-cd ' 



confequenter 



/• TD2 __ 4(fe — tt__ — &]__% — c)(fe — -d) "" 



(a fc -+- c d)2 ' 



hoc valore fubftituto radius quaefitus circuli quadrilatero 

 A B C D circumfcripti ita exprimetur : 



t> i ,/ (g b -+- c d)[a c-f- 6 d 1 i a d -+- & c ) 



4 " (fe — a)(fe — fchfe— c) U — d) * 



Corollarium i, 



$. 3. Cum fuperficies trianguli ADC fitfcdfin. D 

 _= l c d fin. B, fuperficies vero triarguli A B C — \ a b fin. B; 

 fi fuperficiem totius quadrilateri littera _^ defignemus, ha- 

 bebimus 



2 =_ j(a b -f- c d) fin. B 

 fiue, fubftituto loco fin. B valore fupra inuento, 



2 — y (h — a) (k — b)(k — c) (k — d), 

 haecque fuperficies eft maxima quam quatuor reftae a 9 b, 

 c, d 9 includere poffunt, ideo quod quadrilaterum circulo eft 

 infcriptum. 



Corollarium 2. 



§. 4. Quod ambas diagonales noftri quadrilateri at- 

 tinet, eas fequenti modo fatis commode per latera exprime- 

 re licet: 



Noua Atta Acad. Imp. Scient Tom. X. O A C 



