TY - JOUR

T1 - Geometry and arithmetic in the medieval traditions of Euclid's Elements

T2 - A view from Book II

AU - Corry, Leo

PY - 2013/11

Y1 - 2013/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84883798984&partnerID=8YFLogxK

U2 - 10.1007/s00407-013-0121-5

DO - 10.1007/s00407-013-0121-5

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AN - SCOPUS:84883798984

SN - 0003-9519

VL - 67

SP - 637

EP - 705

JO - Archive for History of Exact Sciences

JF - Archive for History of Exact Sciences

IS - 6

ER -