Definition: 4.2: Rectilinear Figure Circumscribed about Another Rectilinear Figure

And, similarly, a (rectilinear) figure is said to be circumscribed about a(nother rectilinear) figure when the respective sides of the circumscribed (figure) touch the respective angles of the (figure) about which it is circumscribed.

Modern Formulation

A rectilinear figure \(A\) is said to be circumscribed about another rectilinear figure \(B\), if and only if all the sides of \(A\) pass through the vertices of \(B\). In this case, \(B\) is inscribed in \(A\).


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


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  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"