DE MAXIMIS IN FIGVRIS RECTILINEIS. 139 



Lemma I. 



Area Trianguli ABC aequatur dimidio Retfangulo ex 

 duobus quibusuis Lateribus AB, AC v. gr. tn finum an- 

 guli intercepti A dutto (pofito finu toto zz 1 ) 



Demonitratio. 



Sit Triangulum ABC et ducatur v. gr. BD perpcn- psg.i.eti 

 dicularis in AC, fitque finus anguli BACzzx, area Tri- 

 anguli ABC aequalis erit facto ex dimidia BD in AC, 



feu * c ' 2 * D . Quid autem fubftituendum fit loco BD , repe- 

 rietur faciendo hanc analogiam , vt A B ad B D \ ita fi- 

 nus totus, ad finum anguli BAC, feu AB: BD~i:l 

 Ergo AB. k \~BD et proinde area Trianguli, ponen- 



do AB. x pro BD, ^: AC, f' x , Cum autem finus an- 

 guli cuiuscunque acuti, pofitiuus fumtus, pofitiuus quo- 

 que maneat, fi in alteram partem cadat, id eft fi angu- 

 lus fiat obtufus, fequitur aream Trianguli femper e(Te — 



+ A -^P. Q. E. D. 



Lemma II. 



In Trianguh quocunque ABC, quadratum cuiusuis Figum 1; 

 lateris aequale efi quadratis reliquorum laterum , minus du- 

 plo retfangulo eorundem laterum in cofmum anguli intercepti, 

 Jcil. v.gr. BOzz AB 2 4-AO~ 2AB. AC in cof. A 

 {pofito fmu toto zz 1 ). 



Demonftratio. 



Dudh, v. gr. BD normali in AC, vt fupra, et 

 finu anguli BAC vocato x, erit BC 2 ^BD 2 H-AC 2 - 



S 2. cAC. 



