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Book VI   Proposition 31
And, since
    ABC is similar to ABD,
therefore
    CB is to BA, so is AB to BD. [VI.Def.1]
And,
    since three straight lines proportional,
    as the first is to the third, so is the figure on the first to the similar and similarly described figure on the second. [VI.19, Por.]

Therefore,
    as CB is to BD,
    so is the figure on CB to the similar and similarly described figure on BA.

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