Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-10T20:44:11.757Z Has data issue: false hasContentIssue false
  • English
  • Français

Fractional Arithmetic in the Tabula Alimentaria of Veleia

Published online by Cambridge University Press:  04 July 2019

Charles Stewart
Charles Stewart*
Affiliation:
University of Reading
*
c.stewart3@reading.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

The Tabula Alimentaria of Veleia records the details of two second-century a.d. imperial alimentary schemes at the northern Italian town of Veleia, providing a rare insight into the workings of these schemes. Imperial loans are made to local landowners in exchange for pledges of specified property. Interest paid by landowners is used to fund cash subsidies for the upbringing of selected local children. In the early twentieth century, the French scholar Félix de Pachtere came close to demonstrating a consistent arithmetical relationship between a landowner's declared property value and the loan received. However, anomalies remained. This article proposes a revised formula which establishes a precise and consistent linkage between loan amounts and property declarations. Based on this arithmetical dataset, the paper proposes some hypotheses about how these fractional computations might have been performed in second-century Rome.

Keywords

alimentade PachtereRoman arithmeticRoman fractionsVeleia
Type
Articles
Information
The Journal of Roman Studies , Volume 109 , November 2019 , pp. 89 - 102
Copyright
Copyright © The Author(s) 2019. Published by The Society for the Promotion of Roman Studies 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

I would like to thank the Editor of JRS and its anonymous readers, whose comments greatly improved the quality and clarity of this paper.

References

BIBLIOGRAPHY

Criniti, N. 1991: La Tabula alimentaria di Veleia. Introduzione storica, edizione critica, traduzione, indici onomastici e toponimici, bibliografia veleiate, Parma.Google Scholar
Criniti, N. 2016: La Tabula alimentaria di Veleia. Edizione critica, versione italiana, fortuna (5th edn) (05/09/2016; most recent update 02/06/2018). Available at: http://www.veleia.it/download/allegati/fn000897.pdf (accessed 01/10/2018).Google Scholar
Criniti, N. 2018: Dalla tabula alimentaria all’ ager Veleias. Bibliografia veleiate 1739–2017 (most recent update 13/03/2018). Available at: http://www.veleia.it/download/allegati/fn000890.pdf (accessed 01/10/2018).Google Scholar
de Lama, P. 1819: Tavola alimentaria velejate detta Trajana, restituita alla sua vera lezione da P. de Lama, Parma.Google Scholar
de Masdeu, J. F. 1788: Historia critica de España y de la cultura española, Madrid.Google Scholar
de Pachtere, F. G. 1920: La Table hypothécaire de Veleia. Étude sur la propriété foncière dans l'Apennin de Plaisance (Bibliothèque de l’École des hautes études IVe section, sciences historiques et philologiques 228), Paris.Google Scholar
Duncan-Jones, R. 1982: The Economy of the Roman Empire: Quantitative Studies (2nd edn), Cambridge.Google Scholar
Friedlein, G. 1869: Die Zahlzeichen und das elementare Rechnen der Griechen und Römer und des christlichen Abendlandes vom 7. bis 13. Jahrhundert, Erlangen.Google Scholar
Hultsch, F. 1866: Metrologicorum Scriptorum Reliquae, Lausanne.Google Scholar
Jongman, W. 2002: ‘Beneficial symbols: alimenta and the infantilization of the Roman citizen’, in Jongman, W. and Kleijwegt, M. (eds), After the Past: Essays in Ancient History in Honour of H. W. Pleket, Leiden and Boston, 47–80.10.1163/9789004350915Google Scholar
Lo Cascio, E. 2000: ‘Alimenta Italiae’, in González, J. (ed.), Trajano Emperador de Roma. Atti del Congresso. Siviglia 1998, 14–17 settembre, Rome, 287–312.Google Scholar
Maffei, S. 1749: Museum veronense. Hoc est antiquarum inscriptionum atque anaglyphorum collectio cui taurinensis adiungitur et vindobonensis, Verona.Google Scholar
Maher, D., and Makowski, J. 2001: ‘Evidence for Roman arithmetic with fractions’, Classical Philology, 376–99.10.1086/449557Google Scholar
Pullan, J. M. 1968: The History of the Abacus, London.Google Scholar
Schärlig, A. 2001: Compter avec des cailloux. Le calcul élémentaire sur l'abaque chez les anciens Grecs, Lausanne.Google Scholar
Soricelli, G. 2001: ‘Le prime obligationes a Veleia ed il ruolo di T. Pomponio Basso’, Zeitschrift für Papyrologie und Epigraphik 136, 289–97.Google Scholar
Turner, J. H. 1951: ‘Roman elementary mathematics: the operations’, Classical Journal 47, 63–74, 106–8.Google Scholar
Woolf, G. 1990: ‘Poverty and patronage: the significance of the epigraphy of the Roman alimentary schemes in early imperial Italy’, Papers of the British School at Rome 58, 197–228.10.1017/S006824620001165XGoogle Scholar