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Definition: 4.1: Rectilinear Figure Inscribed in Another Rectilinear Figure

A rectilinear figure is said to be inscribed in a(nother) rectilinear figure when the respective angles of the inscribed figure touch the respective sides of the (figure) in which it is inscribed.

Modern Formulation

A rectilinear figure (\(n\)-sided figure, \(n \ge 3\)) is said to be inscribed in another when all its vertices are on the sides of the figure in which it is said to be inscribed.

Example

The \(4\)-sided figure \( E F G H \) is inscribed in the \(4\)-sided figure \( A B C D \):

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References

Bibliography

1. Byrne, O.: "The First Six Books of the Elements of Euclid, in Which Coloured Diagrams and Symbols are used Instead of Letters", London William Pickering, 1847

Adapted from (subject to copyright, with kind permission)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

1. Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016