Id rARIAE DEMON-STRAT. GEOMETR, 



— CE-I- AB ficque erit BE-hCE : AB-4-CD=BC ; 

 AD-BC etalternando BE-i-CE ; BC=:AB-i-CD : 

 AD~BC. (^ E. D. 



Coroll. I. 



§. 19. Cum igitiir fit BEH-CE:BC=AB-H 

 CD:AD-BC erit componendo BE-t-CE-f-BC : BC 

 ^ABH-CD-f-AD-BC : AD- BC vnderedangiilum 

 extremonim aequale erit redangulo mediorum , fcilicet : 

 (AD-BC)(BE-f-CE-|-BC)— BC(AB-f-CD-i-A 

 D— BC) hincque fadorum in §.17 exhibitorum pri- 

 mus erit I. . (a^-bc )(beh-c e.^bc, -AB-t-CD-HAD-BC 



Coroll. 2. 



§. 20. Simili modo ex proportione BEH-CE:BC 

 I^AB-t-CD : AD— BC orietur diuidendo : 

 BE-i-CE-BC : BCr^AB-i-CD-AD-^BC : AD- 



BC vnde fequentia redangula inter le erunt aequalia : 

 (AD-BC)(BE-f-CE-BC) — BC(AB-+-CD-AD 

 -4-BC) hincque fadorum in §. 17 exhibitonim (ecun- 

 dus erit: IL . . ^^^^^^^^^^^zz AB-i-CD-AD 



Theorema. 



§. ai. lisdem pofitis , fcilicet fi quadrilateri circu- 

 16 infcripti ABCD duo latera AB>DC ad concurftan 

 Vsque in E producantur , erit : 



CE-BE : AB-DC 1= BC : AD-i-BC 



Demonftratio. 



Triangula fimilia BCE et DEA praebent vt an= 



te 



