T
H
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S		 Book VI   Proposition 8
Therefore
    as BD which subtends the angle BAD in the triangle ABD is to DA which subtends the angle at C in the triangle ADC equal to the angle BAD,
    so is AD itself which subtends the angle at B in the triangle ABD to DC whcih subtends the angle DAC in the triangle ADC equal to the angle at B,
and
    so also is BA to AC, these sides subtending the right angles; [VI.4]
therefore
    the triangle ABD is similar to the triangle ADC. [VI.Def.1]
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