T
H
E

E
L
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M
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N
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Book I   Proposition 44
Then, since
    the straight line HF falls upon the parallels AH, EF,
    the angles AHF, HFE are equal to two right angles. [I.29]
Therefore
    the angles BHG, GFE are less than two right angles;
and straight lines produced indefinitely from angles less than two right angles meet; [Post.5]
    therefore HB, GB, when produced, will meet.

    Let them be produced and meet at K;
through the point K
    let KL be drawn parallel to either EA or FH [I.31]
and
    let HA, GB be produced to the points L, M.
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