To describe a rectilinear figure similar, and similarly laid down, to a given rectilinear figure on a given straight line. * Let $AB$ be the given straight line, and $CE$ the given rectilinear figure. * So it is required to describe a rectilinear figure similar, and similarly laid down, to the rectilinear figure $CE$ on the straight line $AB$.
Given a segment $\overline{AB}$ and an arbitrary rectilinear figure it is possible to construct a similar figure containing the segment $\overline{AB}$ as one of its sides.
Proofs: 1