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Book IV   Proposition 13
Then, since
    the angle HCF is equal to the angle KCF,
and
    the right angle FHC is also equal to the angle FKC,
FHC, FKC are two triangles having two angles equal to two angles and one side equal to one side, namely FC which is common to them and subtends one of the equal angles; therefore
    they will also have the remaining sides equal to the remaining sides; [I.26]
therefore
    the perpendicular FH is equal to the perpendicular FK.

Similarly it can be proved that
    each of the straight lines FL, FM, FG is also equal to each of the straight lines FH, FK.
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