Proposition VI.18 — On a given straight line to describe a rectilineal figure si…

Proof

Triangulate the given polygon by joining a vertex to all others. On the new base copy each angle (I.23) and use VI.4 to fix the side ratios; assemble the triangles into the similar polygon.

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Depends on (2)

I.23Proposition I.23On a given straight line and at a point on it to construct a rectilineal angle equal to a given rectilineal angle.
VI.4Proposition VI.4In equiangular triangles the sides about the equal angles are proportional, and those are corresponding sides which…

Required by (dependents) (3)

VI.20Proposition VI.20Similar polygons are divided into similar triangles, equal in multitude and in the same ratio as the wholes; and the…
VI.25Proposition VI.25To construct one and the same figure similar to a given rectilineal figure and equal to another given rectilineal…
XI.27Proposition XI.27On a given straight line to construct a parallelepipedal solid similar and similarly situated to a given…

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