62 



INDEX FIGURAE PR OPRIET AT UM. 



Tlieor. Xir. Fig. 5. R= 



AD X BE X CF = BD X CE X AF = ^^ (a^+ÄHc* - SÄ^). (2) 

 ACx\0+BCxBG ABxAG+BCxCG ABxBG+ACxCG. 



Thcor, XIIL Fig. 3. 



Coroll. 1. 



Coi'oll. 2, 



Tlieor. XIV. Fig. 3. 



Theor. XV. Fig. 5. 



Coioll. 1. 



Coroll, 2. 



Theor. XVI. Fig. 5. 



Coroll. 



Scholion. 



Theor. XVII. Fig. 3. 



Coroll. 



Theor. XVIII. Fig. 3. 



Theor. XIX. Fig. 3. 



Covoll. 1. 



Coi ull. 2. 



Coioll. 3. 



Coroll. 4. 



Theor. XX. Fig. 3. 



Theor. XXI. Fig. 3. 



2AB ~" 2AC ~ 2BG 



4Ä^ = AB' + CG'' = AC'' + BG'' = BC^ + AG^ 

 AG^ + BG^ 4- CG^ = i2Ä^ — (a= + 6^ -}- c^). 

 OE' = iAG, OF' = iBG, OD' = ICG. 

 2Ä — AG X BG X CG : CG X DG. 

 4Ä^ = AG^ + BG^ + CG* + 2CG X DG. 

 CG X DG = BG X FG = AG X EG = l{a^- + 6^ + c^ - 8/7 = ). 

 AG X BG X CG = R(a^ + b' + c' — 8Ä»). 

 AG X BG X CG : EG X FG X DG = 8 /?=■ : (a:- -H b'-hc'- 3R'). 

 EG X FG X DG = (a= + 6= + c' — 8R-y : 8R. 



AG="-^'-ig=^'\ BG=^^--'+;;-^'^ CG== <-'f-^' . (3) 



EG = 



DG = 



„4 _ ^,4 _ c4 _)_ 21,^^ ' 



c* — a* — b'^ + 2a'l)^ 

 uc/ 



FG: 



b* — n'^ — c* + 2a=t» 

 ■ Qbl 



CO 



R + r = '(AG + BG + CG). 



5R = ci+ß+y — |(AG + BG + CG). 



DF : AG = BC : 2R. 



DF X FE X ED : AG X BG X CG = / : 2«^ 



FD X DE X EF = AD X RE x CF = BD x CE x AF 



= ~^i''' + ^^- + <''-^^'> 

 ABxACxBC!FDxDExEF=AGxBGxCG:EGxFGxDGi 

 ABxAGxBC:FDxDExEF = 3Ä^:(a=' + i'' + c2 — 8Ä^). 

 CD X BF X AE : FD x DE xEF = FD x DE xEF : EGxFGxDG. 

 DE X EF X FD : CG X DG = / : TZ. 

 7xCG = iZxCDxEF. 



DFxEG+FExDG + EDxFG 



Theor. XXLI. Fig. 5. AB + AC+BC = =2ßx 



CG X DG 



Coroll. 



Theor. XXIII. Fig. 3. 



Scholion 1, 



/An Ar nr^ /'^^ ^D DF\ 

 (AB, AC,BC):: (^cG' BG' ÄG> 



.;i.:;ioJ:. 



FD + DE + EF = 2/ : R. 



FD 3,"_(Ü±±=f!), DE =^_(f!±£!zi!), EF=^if:±^^^. (5) 



sac 



2ab 



Theor. 



