FJRIJE DEMONSTRAT. GEOMETR, 6t 



te has proportiones : BE:DEz=BC;AD et CE:AE^ 

 BC:AD ex quarum vtraque elicitur componendo 

 BE : DE -i- BE =: BC : AD -|- BC 

 CE : AE + CE =r: BC : AD -H BC 

 Cum ergo tam BE ad DE-f-BE quam CE ad AE 

 -4-CE eandem teneat rationem , etiam differentia antece» 

 dentium CE— BE ad differentiam conlequentium AE 

 -l-CE demto DE-j-BE eandem habebit rationem \t 

 BC ad AD-I-BC erit fcilicet : 



CE-BE : AE-i-CE-DE-BE=BC : AD-j-BC 

 At ell AE[-|-CE-DE-BE=AE-BE-DE-hC 

 E=:AB-CD ficque erit CE-BE-AB-CD — BC : 

 AD-hBC et alternando CE-BE : BC^AB-CD ; 



ADH-BC Q. E. D. r . O' -:ir ■■■:,! 



Coroll. I. - 



§. 22. Cum igitur hinc fit inuertendo BC : CE 

 -BE=iADH-BC: AB-CD , erit componendo BC 

 -HCE-BE: BC=:AD-i-BC-i-AB-CD: AD-H 



BC, Atque aequatis redangulis extremorum et medio- 

 rum fiet (AD-f-BC)(BC-}-CE-BE)=BC(AD-H 

 BC-l-AB— CD) vnde fadlorum §. 17. exhibitorum 

 quartus erit : IV. . . .I^?£H|^±H^-M,) -AB^-AD 

 4-BC-CD. 



Coroll. 2. 



§. 23. Simili modo ex proportione BC : CE-BE 

 = AD-f-BC :AB-CD orietur diuidendo 



BC-CE-i-BE:BC=:AD-4-BC-AB-HCD:AD-H 

 BC hincque erit (AD-i-BC)(BC-i-BE-CE}=:BC 



H 3 (AB 



