A Matter of Great Magnitude: The Conflict over Arithmetization in 16th-, 17th-, and 18th-Century English Editions of Euclid's Elements Books I Through VI (1561–1795)

English editions of Euclid's Elements clashed over the arithmetization of mathematics. The editions of Henry Billingsley, Claude Dechales, and Isaac Barrow from the 16th and 17th centuries paid relatively little attention to mathematical primacy. In the 18th century, however, William Whiston as...

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Bibliographic Details
Published inHistoria mathematica Vol. 27; no. 1; pp. 36 - 53
Main Author Goldstein, Joel A.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.02.2000
Subjects
arithmetization
Robert Keill
Isaac Barrow
Robert Simson
John Playfair
geometry
Euclid of Megara
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Summary:English editions of Euclid's Elements clashed over the arithmetization of mathematics. The editions of Henry Billingsley, Claude Dechales, and Isaac Barrow from the 16th and 17th centuries paid relatively little attention to mathematical primacy. In the 18th century, however, William Whiston asserted that algebraic representations, demonstrations, and proportions were more convenient than, yet as rigorous as, geometry. John Playfair's algebra adapted the Elements to modern audiences. Edmund Scarburgh, John Keill, Edmund Stone, and Robert Simson, however, attacked editions for alterations. Some editors tried to recover Euclid's original text. Most passages on this issue appeared in the editors' prefaces, Book II, Book V, or their notes. Copyright 2000 Academic Press. Des éditions anglaises des Éléments d'Euclid ne s'accordaient pas sur l'arithmétization de mathématiques. Les éditions d'Henry Billingsley, Claude Dechales, et Isaac Barrow des seizième et dix-septième siècles n'ont guère fait attention à la primatie mathématique. Cependant, au dix-huitième siècle, William Whiston a affirmé que les représentations, démonstrations, et proportions algébriques étaient plus commodes que, pourtant aussi rigoureuses que, la géométrie. L'algèbre de John Playfair a ajusté les Éléments aux lecteurs modernes. Edmund Scarburgh, John Keill, Edmund Stone, et Robert Simson cependant, ont attaqué les éditions pour les modifications. Quelques éditeurs ont essayé de retrouver le texte originel d'Euclid. La plupart des passages sur cette question se sont présentées dans les préfaces des éditeurs, Livre II, Livre V, ou leurs notes. Copyright 2000 Academic Press. MSC 1991 subject classifications: 01A20, 01A40, 01A45, 01A50
ISSN:0315-0860
1090-249X
DOI:10.1006/hmat.1999.2263