Article ID: CBB001213490

Geometry and Arithmetic in the Medieval Traditions of Euclid's Elements: A View from Book II (2013)


This article explores the changing relationships between geometric and arithmetic ideas in medieval Europe mathematics, as reflected via the propositions of Book II of Euclid's Elements. Of particular interest is the way in which some medieval treatises organically incorporated into the body of arithmetic results that were formulated in Book II and originally conceived in a purely geometric context. Eventually, in the Campanus version of the Elements these results were reincorporated into the arithmetic books of the Euclidean treatise. Thus, while most of the Latin versions of the Elements had duly preserved the purely geometric spirit of Euclid's original, the specific text that played the most prominent role in the initial passage of the Elements from manuscript to print---i.e., Campanus' version---followed a different approach. On the one hand, Book II itself continued to appear there as a purely geometric text. On the other hand, the first ten results of Book II could now be seen also as possibly translatable into arithmetic, and in many cases even as inseparably associated with their arithmetic representation.

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Authors & Contributors
Berggren, John Lennart
Brummelen, Glen Van
De Young, Gregg
Takahashi, Ken'ichi
Høyrup, Jens
Zenner, Marie-Thérèse
Historia Mathematica
Sciamvs: Sources and Commentaries in Exact Sciences
Science in Context
Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften
Revue d'Histoire des Sciences
Revue d'Histoire des Mathématiques
Ashgate, Variorum
Franz Steiner Verlag
Edizioni Cadmo
University of Pennsylvania Press
Arab/Islamic world, civilization and culture
Transmission of texts
al-Quhi, Abu Sahl Wayjan ibn Rustam
Oresme, Nicole
Regiomontanus (Jahannes Mueller)
Campano, Giovanni
Al-Mu'taman ibn Hūd, Yūsuf, King of Saragossa
Time Periods
14th century
11th century
Early modern
16th century
Middle and Near East
Mediterranean region
Pisa (Italy)

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