The role of the ruler and the compass in Euclid’s Elements: A practice interpreted as a rule
Abstract
In this text we analyze the sources referred to in traditional historiography of mathematics in order to state that there existed a restriction regarding the instruments used in Euclid’s Elements, often emphasized as due to an influence by Platonism. Our principal aim is to analyze whether the exclusivity in the use of ruler and compass as construction methods was a practice or prescribed as a norm in the geometric context of Euclid’s epoch. We follow the study published by Arthur Donald Steele in 1936, scarcely cited by historians. Taking also other works as references, we propose the thesis that the sources do not suggest that such a restriction constituted a norm. The fact that constructions in Euclid’s Elements are done, in practice, using only the ruler and the compass do not allow us to conclude that this was a rule, or a standard procedure in the time. We also explain how the cited version was historically produced.
Keywords: ruler and compass, Euclidean geometry, history of Greek mathematics.
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