Proposition XI.27 — On a given straight line to construct a parallelepipedal sol…

Proof

Apply the face-angle construction of XI.26 at each vertex; by VI.18 the resulting faces are similar to the corresponding faces of the given solid.

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Depends on (3)

VI.18Proposition VI.18On a given straight line to describe a rectilineal figure similar and similarly situated to a given rectilineal figure.
XI.24Proposition XI.24If a solid be contained by parallel planes, the opposite planes in it are equal and similar parallelograms.
XI.26Proposition XI.26At a given point on a given straight line to construct a solid angle equal to a given solid angle contained by three…

Required by (dependents) (1)

XII.17Proposition XII.17Given two spheres about the same centre, to inscribe in the greater sphere a polyhedral solid which does not touch the…

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