T
H
E

E
L
E
M
E
N
T
S
Book I   Proposition 20
Then, since AD is equal to AC,
    the angle ADC is also equal to the angle ACD; [1.5]
therefore
    the angle BCD is greater than the angle ADC. [C.N.5]

And, since BCD is a triangle having the angle BCD greater than the angle BDC, and the greater angle is subtended by the greater side, [1.19] therefore
    BD is greater than BC;

But
    AD is equal to AC;
therefore
    BA, AC are greater than BC.
Previous Page    Return to Propositions    Next Page