58 VARIAE LEMONSTRAT. CEOMETR. 



crunt fim'lia ^ eorumque ergo areae fe habebunt vt qua- 

 drata latenim homologorum, veluti AD et BC: erit itaque 

 aAED:aCEB — AD':BC' et diuidendo 

 aAED-aCEB:aCEB — AD' - BC* hoc eft 

 DABCD. aCEB=iiAD*-BC*:BC*. Q. E. D. 



Coroll. I. 



§. 14. Ex cognita ergo area trianguli CEB inuc- 

 nietur area quadrikiteri ABCD ; erit namque 

 P A B C D — ^^^— . A B E C 

 feu fi area trianguli BEC defignetur breuitatis gratia lit- 

 tera T , et area quadrilateri ABCD littera Q^, erit 



AP»— BC» T, 

 ^^— — 8C»'^' *• 



Coroll. 2. 



§. 15. Tum vero quia eft differentia quadratorum 

 AD'-BC*=:(AD-f-BC)(AD-BC), erit "^^^^ 

 ^TT^ . - ^^^^ hincque habebitur haec aequatio 

 Q^— ^^^^^ . ^^^^^ , quae fumendis quadratis abit in hanci 



f) f\ AP — BC AD — BC AP-f-BC AD-4-BC rr- q» 



>C^ BC • BC BC • BC • * • ' 



Coroll. 5. 



§. 16. Ex fuperiori autem §. ii. colligltur effe 

 aream trianguli BECi::T=: J V (BE-f-CE-hBC) (B 

 E-f-CE-^BC) (BE-CE-j-BC) (CE-BE-hBC) 

 vnde TT— ^(BE-4-CE-f-BC)(BE-+-CE-BC) 

 (BE-CE-hBC)(CE-BE-|-BC). Hinc ergo pro- 

 dibit valor quadrati areae quadrilateri A B C D feu 

 ipfius QQ combinandis his fadoribus ipfius TT cum 

 sinte inuentis ita expreifus 



