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Book I   Proposition 12
For
    let any point D have been taken on the other side of the straight line AB,
and, with center C and distance CD,
    let the circle EFG have been described, [Post.3]
and
    let the straignt line EG have been bisected at H, [I.10]
and
    let the straight lines CG, CH, CE have been joined. [Post.1]

I say that
    CH has been drawn perpendicular to the given infinite straight line AB from the given point C which is not on it.
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