Reconstruction of Heron's formulas for calculating the volume of vessels

In: Posluschny, A. ; Lambers, K. ; Herzog, I. (Hrsgg.): Layers of Perception. Proceedings of the 35th International Conference on Computer Applications and Quantitative Methods in Archaeology (CAA), Berlin, 2.-6. April, 2007 (Koll. Vor- u. Frühgesch. 10). Bonn 2008 376 (Abstract)

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Abstract

Heron’s formulas for “pithoid” and “spheroid” pithos, as formulas of volume of the truncated paraboloid and 3/4 of ellipsoid of revolution, have been reconstructed in the present study. Research has proven that the ovoid body of Roman narrow-necked light-clay D-type amphorae is a special case of “pithoid”. With the help of geometrical approximation by conic sections of the profile of these amphorae, it is shown that in antiquity there really were amphorae projected on the basis of conic sections. Their volumes could be calculated with the help of ancient mathematical formulas. The results obtained testify to the influence of antique mathematics on morphology and technology of amphorae design. Formulas for the volume of simple solids of revolution defined by conic sections can be applied in modern calculations of volumes of some types of antique amphorae and in reconstructing their profiles.