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.
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机译：维特鲁威（Vitruvius）详细说明了如何通过几何方法设计拉丁和希腊剧院，而这种方法不涉及有关洞窟容量的问题，洞窟洞窟的容量是每座眼镜的基本要求。亚历山德里亚（Alexandria）的苍鹭（Heron of Alexandria）在公元一世纪写的两篇论文Stereometrica和De mensuris通过数值示例解释了一些相关公式，这些公式旨在计算剧院，马戏场和露天剧场等建筑的容量。由于对一些眼镜的建筑物进行了新的，准确的调查，我们将展示这些公式的一些应用以及Heron如何将尺寸标注问题转换为对圆进行平方的特殊情况。
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