6i VJRIAE LEMONSTRAT. GEOMETK. 

 (AD-f-BC-f-CD-AB) vnde fadlonim §. 17 exhi- 



, . TTT (AD-f-BC)(BC-t-BE — CE) a f-k 



bitoriim tertius erit : 111. . . ^ q Z=: A Ur 



h-bc-hcd-ab. 



Theorema. 



§. 24.. Quadrilateri circulo infcripti ABCD arc» 

 inuenitur , fi a femifumma omnium eius laterum fingula 

 latera feorfim fubtrahantur , haec quatuor refidua in fe in ■ 

 vicem multiplicentur , atque ex produdo radix quadrata 

 cxtraliatur, 



Demonftratio. 



Si duo latera oppofita AB, CD ad concurfum vs- 

 que in E producantur , atque quadrilateri ABCD area 

 ponatur =Q^, vidimus §. 17 valorem 16 QQ^ aequari 

 produdo ex quatuor fadloribus , quos eosdem faftores in 

 ^. §. 19. 20 et §. §. 22. 23 (uccindius expreflimus , ita 

 vt nunc valor ipfius 16 Q^Q^ aequetur produdo ex his 

 quatuor &(S:oribus. 



j^ fiEz:^^^ki±:2£2-AB-f-CD-hAD-BC 



jj^ (ADH-BC)(BE-4-CE-BC) ^^ AB>{- CD- AD^-BC 



ni. l^:°±?£l^.BE^£l)-ADH-BC-f-CD-AB 



JV. (AD. H-BC)(BC-BEH-C E)_^3^^p_^3C-CD 



Hinc ergo erit 16 QQ^ aequale huic produdlo (AB-f- 

 CDH-AD-BC)(AB-i- CD-|-BC-AD)(AD-|-B 

 C-i-CD-AB)(AB-i-AD-j-BC-CD). Quod fi 

 iam ponatur fumma omnium laterum A B -f- B C 

 H-CD-4-DA=2S vc lemifununa fit ;=: S. criti 



2g 



