INDEX FIGURA.E PROPRIETÄT UM. 



65 



Coroll. 2. 

 CoroU. 5. 

 Coroll. i. 



Theor. XLIII. Fig. i. 



CorolL 1. 

 Coroll. 2. 



Theor. XLIV. Flg. i. 



Coroll. 1. 

 Coroll. 2. 

 Coroll. 3. 

 Theor. XLV. Fig. lo. 



Coroll. 1. 



Coroll. 2. 



Coroll. 3. 



Coroll. 4. 



Theor. XL VI. Fig. i. 



Theor. XLVII. Fig. i. 



Coroll. 



Theor. XL VIII. Fig. i. 



CoroU. 1. 



Coroll. 2. 



Coroll. 5. 



Theor. XLIX. Fig. i. 



Coroll. 1. 

 Coroll. 2. 

 Coroll. 3. 



Theor. L. Fig. i. 



Coroll. 1. 

 Coroll. 2. 



AP : PE"' = b+c : a. 



PE"' X PF'" X PD'" = 4Rr3:(l+„, + „_ ^). 



AP X BP X CP : PE'" X PF"' x PD'" = ^l+^ + „_r) : r. 



AS = 



ß 



__ Vbßcy Kr._Vbßcy 



, AR=, 



ß 7 



CRxBQxAS = CQxBSxAR r= ahc - 

 BQxCRxAS : APxBPxCP = 7 : r=. 



4Ä/. 



AQ 



_\/hc 



BR = 



\/acrß 



CS 



\/ ahry 



QE'" = "^^'I^, RF' 



,T 



AQ X BR X CS = ü(a + i + c)V r, 

 AQxBQxCQ= 4i?^=. 



APxBPxCP : AQxBQxGQ = OP:OQ- 

 AQ : QE'" = 6 + c : fl. 



_ Wacrß gp,„ _ cVairy 

 (a+c)/-' {a+b)r 



QE'"xRF'"xSD'" = 4Ä7= : r(/+,-w + « _r). 

 AQ X BR X CS : QE"'xRF'"x SD'" = (Z + ^ + „-I*^).-7 

 QE"'x RF'" X SD'" : AE'" x BF'" x CD'" z= R. -. o,-. 

 Recta AQ in punctis P et E'" harmonice divisa est. 

 a + r: ar ^ l>+ c : I, et a—r : mr =z a: I. i 



oc + r:a—r = b + c : a = AQ: QE'" = AP : PE'". 

 « + /3: aß = c : 2 , et a — ß : aß = a — b : 1. 

 » + ß:»—ß =1 c:a — b =. AB : D"W. 

 i»-{-ß : aß = y — r:yr. 



R — ^x Oi±ßH^ + yXß±20^ 



aß + ay + ßy 

 PQ = °-V^"''>^ pj^ _ Wacrß pg _ c\/abry 



PQ X PR X PS = i6Ä=/-. 



PQxPRxPS : 4APxBPxCP = Ä:r. 



PQXPRXPS : BQxCRxAS=4ä/:/. 



QR = 



ct/fla5/3 



, QS 



b\/ac>.cy a\/bßcy 



—j— , SR = —j- . 



QR X RS X SQ = i6R'I .. r. 



QR X RS X SQ : AP X BP X CP = 4Ä/ : r3. 



I Coroll. 



