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if in a right-angled triangle a perpendicular be drawn from the right angle to the base,
the triangles adjoining the perpendicular are similar both to the whole and to one another.
Being what it was required to prove.
Porism. From this it is clear that
if in a right-angled triangle a perpendicular be drawn from the right angle to the base,
the straight line so drawn is a mean proportional between the segments.
