T
H
E

E
L
E
M
E
N
T
S
Book IV   Proposition 12
Therefore
    the straight line KC is equal to CL, and the angle FKC to the angle FLC.
And, since KC is equal to CL, therefore
    KL is double of KC.
For the same reason it can be proved that
    HK is also double of BK.
And
    BK is equal to KC;
therefore
    HK is also equal to KL.

Similarly
    each of the straight lines HG, GM, ML can also be proved equal to each of the straight lines HK, KL;
therefore
    the pentagon GHKLM is equilateral.
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