) ^4 ( i:4-- 



{ff-\-xx){ac-\-bdy'aacc-bbdd)+ff{aabb-\-ccdd)-{-xx{aadd-^bbcc)-) 

 +aacc{aa + cc~bb-dd)~{ac-\-bdy-{aa-\'bb-\-cc-\-dd) C-o 



•i-bbdd ^bb-\-dd—aa -cc) 3 



quare cum huiiis aeqnationis primum membrum contrahatur in 



na b c d {ff-\- X x)y 

 tota aequatio fequentcm accipiet formam : 



ff{ab-hcdy-\-xx{ad-\-bcy-2bd(ac-\-bd){aa + cc)_ 



-2ac{ac-hbd){bb-\-dd)-^' 



cuius poftremum membrum in fuos fadores refolutum 

 producet: 



ffCab -\- c dy -\-x x{ad -{■ bcy - 2[ac -{-bd)(ab -{- c d){ad-\- b c)~o, 

 in qua acquatione fi loco a c -{- b d itcrum fcribatur/.v, prodibit 

 ffiab-^-cdy + xxiad-^-bcy—^fxQab-i-cd^^ad-^-bc^z^oy 

 quae forma manifefto eft quadratum^ vnde fequitur fore 

 f^ab-^-cd^-xiad-^-bc^ — o, 



quae aequatio ergo praeter aflumtam fx ~ a c -\- b d et- 

 iam exprimit infignem proprietatem quadrilaterorum cir- 

 culo infcriptorum. 



Corollarium. 



§. 18. Pro omnibus igitur quadrilateris circulo 

 infcriptis non folum valet proprietas notifllma fxzac-{-bd, 

 fed etiam haec altera - — ". f "^ - ^ , quibus duabus aequa- 



X a b -f- e a ' 1 t • 



tionibus demum natura horum quadrilaterorum exhauritur. 

 Hinc autem fi prior per poftcriorem vcl multiphcetur vel 

 diuidatur, ambae diagonales feorfim determinabuntur fe- 

 qucntibus formulis: 



f f — f<i c -t- 6 d)(a d H- td ) _^ .. ^ {ac -^bd)(ab ^ cd ) 



Scho- 



