During the early modern period, hundreds of editions of Euclid’s Elements of Geometry were printed. Individual copies of these editions were often read with pen in hand, resulting in a multitude of physical traces in the books, such as marginalia, notes or marks of ownership. Recent scholarship has emphasized the role of annotation and note-taking in the material history of reading.Footnote1 Owen Gingerich and Renée Raphael have shown that mathematical books were no exception to this, as many of the printed works of Copernicus and Galileo survive in annotated copies.Footnote2 This fascinating new volume of essays combines the material history of the book and the history of mathematical reading by asking how mathematical knowledge ‘got off the printed or manuscript page and into the minds and practices of its readers’ (p. 9). Published in the Material Readings in Early Modern Culture series, the study is based on two workshops organized by the Reading Euclid project at the University of Oxford. The volume focuses on mathematical reading in early modern Europe from the sixteenth to the eighteenth centuries, addressing mathematical texts both in print and in manuscript.
The material use of mathematical books provides the main focus. Vincenzo De Risi’s chapter looks at readers’ diverse responses to Euclid’s Elements of Geometry, while Robert Goulding presents a close reading of the problem of proportion in Euclid’s textbook through the manuscript writings of Henry Savile (1549–1622). Mathematical textbooks in particular were heavily annotated by students, tutors or professionals. Some copies were customized, as readers introduced a table of contents or an index by hand. In a wide-ranging survey, Benjamin Wardhaugh discusses material evidence of mathematical practices in the ‘sociable space’ of the printed page.Footnote3 He concludes that elementary textbooks at school were ‘used most heavily and aggressively’, with pupils ‘adding, translating, marking, copying, and re-using’ handwritten notes (p. 243). Kevin Tracey focuses on useful mathematical knowledge in John Seller’s Pocket Book (1677), which was employed ‘as a theatre in which to rehearse and perform mathematical practices’ (p. 277). Building on the foundational study of William Sherman, Boris Jardine elaborates on a ‘tentative typology of reading’ for practical mathematical texts. Mining the layers of annotation in Leonard and Thomas Digges’ Pantometria (1591), his essay differentiates ‘topical’, ‘extractive’, ‘heuristic’ and ‘corrective’ types of annotation (pp. 261–262). Finally, Philip Beeley presents a study of Edward Bernard (1638–1697), Savilian professor of astronomy at Oxford, who prepared an edition of Euclid’s Elements of Geometry for the university press of John Fell (1625–1686). Publication eventually failed, but David Gregory (1659–1708) later reused Bernard’s editorial notes for his own publication of the textbook in 1703.
This customization of books includes ‘reading by drawing’ (p. 64).Footnote4 Two fascinating chapters by Yelda Nasifoglu and Renée Raphael detail the changing role of mathematical diagrams during the sixteenth and seventeenth centuries. Nasifoglu traces how diagrams were more often grouped together at the end of Euclid’s Elements of Geometry, as geometry grew ‘more algebraic’ over time (p. 87), while Raphael examines readers’ critical responses to a printed diagram of Tycho Brahe (1546–1601). Mordechai Feingold’s excellent contribution details the complex status of mathematical learning at English universities in the seventeenth century.Footnote5 While mathematical knowledge was seen as part of a ‘unified vision of learning’ during the Renaissance, the seventeenth century also encouraged ‘gentlemanly moderation’ (pp. 124–126). But Feingold argues for a ‘more nuanced, and indeed favourable, picture of mathematical instruction within early modern humanist universities’ (p. 138). Specialist communities emerged around the new Savilian professorships established at Oxford. These allowed for more focused teaching within the general curriculum of regent masters. This picture can be supported with evidence from other universities. At St Andrews, the establishment of a Regius professorship of mathematics in 1668 similarly led to the creation of a mathematical community around James Gregory (1638–1675) and William Sanders (1640–1705).
Finally, two engaging studies by Richard Oosterhoff and William Poole deal with the collection of mathematical notes and annotated books. Oosterhoff’s chapter focuses on the antiquarian scholar-collector Brian Twyne (1581–1644) at Oxford. Like Nicolas-Claude Fabri de Peiresc (1580–1637) or Esprit Calvet (1728–1810), Twyne published little, but gathered a vast collection of scholarly notes. His collection reveals an overlap between his historical and his mathematical interests, reflecting the general ‘rise of note-taking’ during the early modern period.Footnote6 It is noteworthy that a major part of these notes was accumulated and ordered in a miscellaneous manner.Footnote7 Some of the notebooks, which were titled schediastica, contained a set of ‘brief, complete miniature treatises carefully written out’, while many of Twyne’s notes on Euclidean geometry were written on loose sheets of paper (p. 152). These loose notes recall other ‘messy’ note-takers like Robert Boyle or Leibniz.Footnote8 The relationship of collecting and note-taking is further explored in Poole’s excellent history of the Savilian library at Oxford. As a resource for learning and teaching, the Savilian library included unpublished notes, printed books and manuscript notes in books. John Wallis (1616–1703) regularly worked with the collection, and he reused Savile’s mathematical marginalia for his own editorial pursuits.
This carefully researched volume reveals how mathematical knowledge was created in the margins of printed books both before and after publication. Emphasizing the materiality of mathematical reading, its chapters illustrate different practices of annotation, based mostly but not exclusively in early modern England. While its contributions underscore the specifics of mathematical note-taking, they provide rich resources to contextualize mathematical reading in the broader history of used books, pointing to the common humanist background shared by note-taking practices across the humanist disciplines. The humanists valued the philological emendations in the books of the late Angelo Poliziano (1454–1494) as much as they reused the mathematical annotations of Henry Savile. Handwriting, in the words of Peter Stallybrass, should be seen as a ‘direct response to the stimulus of print’.Footnote9 This volume shows that this is just as true of mathematical books as it is of the fields of the trivium, on which the study of annotation has generally focused.Footnote10
Correction Statement
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Notes
1 William H. Sherman, Used Books: Marking Readers in Renaissance England (Philadelphia: University of Pennsylvania Press, 2008).
2 Renée Raphael, Reading Galileo: Scribal Technologies and the Two New Sciences (Baltimore: Johns Hopkins University Press, 2017); Owen Gingerich, An Annotated Census of Copernicus’ De revolutionibus (Nuremberg, 1543 and Basel, 1566) (Leiden: Brill, 2002).
3 For the term, see Jason Scott-Warren, ‘Reading Graffiti in the Early Modern Book’, Huntington Library Quarterly, 73/3 (2010), pp. 363–381, here p. 381.
4 On diagrams, see Matthew Eddy, ‘How to See a Diagram: A Visual Anthropology of Chemical Affinity’, Osiris, 29/1 (2014), pp. 178–196; and Matthew Eddy, ‘The Interactive Notebook: How Students Learned to Keep Notes during the Scottish Enlightenment’, Book History, 19 (2016), pp. 86–131.
5 See Anja-Silvia Goeing, Glyn Parry and Mordechai Feingold (eds.), Early Modern Universities: Networks of Higher Learning (Leiden: Brill, 2021), for a recent study on the history of universities.
6 Ann Blair, ‘The Rise of Note-Taking in Early Modern Europe’, Intellectual History Review, 20/3 (2010), pp. 303–316.
7 See Angus Vine, Miscellaneous Order: Manuscript Culture and the Early Modern Organization of Knowledge (Oxford: Oxford University Press, 2018).
8 See Richard Yeo, ‘Loose Notes and Capacious Memory: Robert Boyle’s Note-Taking and its Rationale’, Intellectual History Review, 20/3 (2010), pp. 335–354.
9 Peter Stallybrass, ‘Printing and the manuscript revolution’, in Barbie Zelizer (ed.), Explorations in Communication and History (London: Routledge, 2008), pp. 111–118, here p. 115.
10 I am grateful to Ann Blair for her helpful comments on this review.