|Book IV Proposition 13|
the angle HCF is equal to the angle KCF,
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]
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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