Nexus Network Journal

, Volume 17, Issue 1, pp 23–54

Dimensioning of Ancient Buildings for Spectacles Through Stereometrica and De mensuris by Heron of Alexandria


DOI: 10.1007/s00004-014-0230-8

Cite this article as:
Bianchini, C. & Fantini, F. Nexus Netw J (2015) 17: 23. doi:10.1007/s00004-014-0230-8


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.


Building type (theatre, amphitheatre) Design analysis Design theory Geographical area (Italy, Spain, Algeria, Jordan) Historical era (classical age) Historical treatise Algorithms Arithmetic progressions Circles Geometry Geometric analysis Grids History of mathematics (Heron of Alexandria) Measurement/measuring systems Modules Proportional analysis Shapes (circular ring) Squaring the circle (quadrature of the circle) Symmetry 

Copyright information

© Kim Williams Books, Turin 2014

Authors and Affiliations

  1. 1.Dipartimento di Storia, Disegno, Restauro dell’Architettura, Facoltà di ArchitetturaUniversità degli Studi di Roma “La Sapienza”RomeItaly
  2. 2.Dipartimento di Architettura, Facoltà di IngegneriaUniversità degli Studi di BolognaRavennaItaly