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Translating Euclid’s diagrams into English, 1551–1571. (English) Zbl 1255.01006
Heeffer, Albrecht (ed.) et al., Philosophical aspects of symbolic reasoning in early modern mathematics. Selected papers of the conference, Ghent, Belgium, August 27–29, 2009. London: College Publications (ISBN 978-1-84890-017-2/pbk). Studies in Logic 26, 125-163 (2010).
The paper discusses the first translations of Euclid’s Elements in early modern England starting in 1551 with R. Record’s first surveying textbook. It focuses on the role and variety of diagrams, i.e., “all manner of visual para-text – including illustrations of definitions, constructions, proof figures, and drawings of instruments – designed to facilitate geometric understanding” (p. 127). Its core question is, how “the visual vocabulary of the Elements [was] made meaningful” for the new audience of vernacular readers (p. 130).
After two introductory sections the third section presents Robert Recorde’s Pathway to Knowledge (1551): “His images establish the legitimacy, meaningfulness, and familiarity of everything from simple geometric objects to relatively complex assertions, constructions, theorems” (p. 136).
The next section is devoted to Henry Billingsley’s compendious edition of the Elements (1570). Here the paper’s focus is on the “means by which it deploys its very unoriginal illustrations to serve an utterly original audience” (p. 138) and on a comparison with the former author: “Record prizes instructiveness, Billingsley completeness” (p. 138). Some remarks on John Dee’s sparsely illustrated preface are added.
The following section discusses the completely different style and purpose of illustration in Thomas Digges’ edition of his farther Leonard’s Pantometria (1571) which is “richly illustrated with conventional geometric figures and examples, plans for surveying instruments, and, above all, detailed scenes of geometry in practice” (p. 145), i.e., surveying and warfare.
Using the different illustrations for parallels and points as a paradigm the two concluding sections compare the above presented approaches to “glimpse the contrasts between the Euclidean translators, and ultimately gain a better insight into what it means to translate Euclid” (p. 159).
The paper itself is richly illustrated by many reproductions of diagrams, figures, and pictures from the original sources.
For the entire collection see [Zbl 1202.03010].

01A40 History of mathematics in the 15th and 16th centuries, Renaissance
01A20 History of mathematics in Ancient Greece and Rome
51-03 History of geometry
00A30 Philosophy of mathematics
97-03 History of mathematics education
62H35 Image analysis in multivariate analysis