Abstract
We will use the standard term “regular polygon” (or n-gon) for what Euclid calls in particular cases an “equilateral and equiangular polygon.” Convexity is always tacitly assumed. Book IV follows a tight plan and has none of the subdivisions of some other books. We repeat what has been said in the section about the contents of the Elements. Four problems are treated systematically: (i) to inscribe a rectilinear figure in or (ii) to circumscribe it about a given circle; (ii) to inscribe a circle in or (iv) circumscribe it about a given rectilinear figure.
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