T
H
E

E
L
E
M
E
N
T
S
Book III   Proposition 11
Then, since
    AG, GF are greater than FA,
that is,
    greater than FH, [F is the center of ABC]

    let FG be subtracted from each;
therefore
    the remainder AG is greater than the remainder GH.

But
    AG is equal to GD; [G is the center of ADE]
therefore
    GD is also greater than GH
the less than the greater: which is impossible.
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