Dimensioning of ancient buildings for spectacles through stereometrica and De mensuris by Heron of Alexandria

Vitruvius explains in detail how to design Latin and Greek theatres through a geometrical approach that does not involve the problem concerning cavea’s capacity which is the starting requirement of every building for spectacles. Two treatises, Stereometrica and De mensuris, written during the first century A.D. by Heron of Alexandria, explain through numerical examples some relevant formulas aimed at calculating the capacity of buildings like theatres, as well as circuses and amphitheatres. Thanks to new and accurate surveys of some buildings for spectacles, we will show some applications of these formulas and how the dimensioning problem was converted by Heron into a particular case of squaring the circle.