Reading Euclid: Euclid's Elements of Geometry and its reception in Britain and Ireland, 1570-1700

Lead Research Organisation: University of Oxford
Department Name: History Faculty

Abstract

Euclid's Elements of Geometry was written in about 300 B.C. in Alexandria on the north coast of Egypt. Its long history of active use and re-use passes through the Arabic and Latin Middle Ages as well as the European Renaissance, and it has been a touchstone for mathematical training as well as a spur to new mathematical research for more than two thousand years. This project looks at Euclid's Elements in Britain and Ireland during the century of the Scientific Revolution, when standards of geometrical proof were being actively questioned by mathematicians, but when geometrical methods were also being deliberately brought into other fields, most obviously natural philosophy.

In the period from 1560 to 1700 dozens of new editions of the Elements were printed, and it was certainly the most widely read mathematical book of the time. We will study these editions and the choices they made - about the content and layout of the Elements, which topics to include and which versions of the proofs to print - to help understand the unique position the book occupied and how that position was shaped and maintained.

We will also study the things people did when they had the Elements in their hands. Some wrote in it; some cut out the diagrams; some pasted in extra material. By looking at many examples we will build up a picture of the kinds of ways early modern people engaged with the Elements - schoolchildren, working men, teachers and scholars - which will help to understand the book's role in their lives and in culture.

No mathematical book had such an impact on early modern culture, yet the Elements in this period has never been the subject of a dedicated study. The proposed project will involve two years of work on archival and printed sources in Oxford and London.

Planned Impact

The project addresses three themes that are of perennial public interest: early modern British life, history of science, and how to teach and learn mathematics. The project will prove important new information about neglected aspects of early modern British culture such as mathematical practice and the growth of scientific knowledge. It will fill a gap in our knowledge about the history of science by looking at how mathematics was part of culture in the past and why it mattered so much. And it will provide rigorous background for discussions about mathematics education and the use of Euclidean geometry in the classroom.

The public will be able to engage directly with the project through our project blog and Twitter feed, and we will use the website of the British Society for History of Mathematics to reach an audience including teachers and interested lay people with news about the project. We will also actively seek opportunities to raise the profile of the project with contributions to other blogs, websites and magazines.

The two planned workshops will attract participants from a range of backgrounds including members of the BSHM, museum curators and popularizers, providing a route for the results of our work to be disseminated more widely still to the general public.

Finally the public will be able to visit the display we will organise in Blackwell Hall at the Bodleian Library: a popular city-centre space that attracts a lot of footfall. Here the story of Euclid's Elements will be told using images and objects based on the results of our work.

Publications

10 25 50
 
Description Our research has added detail to the often-repeated image that Euclidean geometry was studied throughout early modern schools and universities. We have been able to show that engagement with Euclid's Elements in the British universities was patchy, ranging from deep and sustained to shallow or - frequently - nonexistent. We have been able to describe a similar pattern in schools, with some institutions teaching geometry effectively and in detail and others ignoring the subject altogether. We have also been able to construct a more detailed narrative of the publication of Euclid's Elements in this period : nearly 300 separate editions of the text appeared between 1482 and 1700, and by cataloguing these and investigating their present locations and readers' annotations in them we have built up a picture of how these books were used, where and by whom. Finally we have investigated a number of particular stories such as the failed project to re-edit Euclid's text at Oxford in the 1690s and the use of Euclid's geometry at the Royal Mathematical School and Westminster School in the Restoration period.
Exploitation Route There is much more that might be investigated about geometry in the early modern period, and our project has only looked at Britain in the sixteenth and seventeenth centuries. It would be possible and worthwhile to extend our methods and results into the 18th century and onto the European continent. It will also be possible to make them part of a larger narrative about the unique impact of Euclid's Elements and Euclidean geometry on European culture.
Sectors Culture, Heritage, Museums and Collections

 
Description Through guest blog posts, our own website and a forthcoming nationwide network of exhibitions the project has raised the profile of Euclid's geometry in views and understanding of the cultural past.
First Year Of Impact 2018
Sector Culture, Heritage, Museums and Collections
Impact Types Cultural

 
Title Catalogue of early modern British book catalogues 
Description Project Post-Doc has developed a digital catalogue of catalogues relating to the book trade in early modern Britain. This novel resource has generated interest among colleagues from the history of the book community, and is the subject of ongoing funding applications aimed at developing it further and making it available to other scholars. 
Type Of Material Improvements to research infrastructure 
Provided To Others? No  
Impact This tool has enabled the research team to study the historical trajectories of certain copies of Euclid's Elements as well as trends in the price of different editions of the book, supplementing our work on the modern locations of the text and the marks made in copies by early modern readers. 
 
Title Catalogue of Euclidean copies 
Description A catalogue of the pre-1700 copies of Euclid's Elements of Geometry and related works presently located in Britain and Ireland. Created and maintained as a MySql relational database, with cross-references to editions, editors, locations, etc. Marks made by early modern readers are also recorded, enabling provenance and patterns of use to be researched in detail. 
Type Of Material Database/Collection of data 
Provided To Others? No  
Impact This data set is a key part of our research on the early modern dissemination of Euclidean texts, and enables us to track the distribution of particular works, editions or versions of a text geographically. It also enables us to efficiently compare patterns of ownership and use for different editions or groups of editions, and to discern chronological changes in those patterns. It is intended to release this data publicly before the end of the project. 
 
Title Catalogue of Euclidean editions, 1482-1700 
Description A bibliographic catalogue, exhaustive in intention, of the editions of works by Euclid printed between 1482 and 1700. Created and maintained as a MySql database with a web front-end scripted in PHP by the PI. It is intended to release this data publicly later in 2017. 
Type Of Material Database/Collection of data 
Provided To Others? No  
Impact This resource is a key part of our research on the printing and dissemination of Euclidean texts during the early modern period, and allows us to record the relationships between editions and discover the roles of individuals such as editors, printers and patrons in multiple editions serving (sometimes) different intellectual agendas. 
 
Description Printing Euclid 
Organisation University of Oxford
Department Bodleian Library
Country United Kingdom 
Sector Academic/University 
PI Contribution Over the course of several informal sessions our research team provided samples of early modern mathematical print and set up and printed replicas of certain of these using moveable type.
Collaborator Contribution The Bodleian Hand Press provided the venue, materials and equipment (hand presses and type) as well as several hours of small-group coaching in their use.
Impact The outcomes of the project were a greatly increased understanding of the processes of printing in the hand-press period for our research team, which have materially affected our understanding and interpretation of the printed materials we are working on.
Start Year 2016
 
Description Defacing Euclid (talk, December 2016) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact The PI gave a talk in Oxford titled "Defacing Euclid: studying and annotating geometry in Britain, c. 1650-1750" to a mainly academic audience.
Year(s) Of Engagement Activity 2016
 
Description Defacing Euclid (talk: February 2017) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Professional Practitioners
Results and Impact The PI gave a talk titled "Defacing Euclid: Printing and annotating the Elements of Geometry in early modern Britain" to the Oxford Bibliographical Society.
Year(s) Of Engagement Activity 2017
 
Description Reading Euclid in Early Modern Britain 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Professional Practitioners
Results and Impact The three members of the project team gave a presentation to the Oxford History of Mathematics Forum on different aspects of their work on 'Reading Euclid in the Early Modern World"
Year(s) Of Engagement Activity 2017
 
Description Reading Euclid in the early modern world 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact This workshop considered how early modern people - from schoolchildren and artisans to teachers and scholars - engaged with Euclid's works and attempt to understand the role they played in their lives and culture. It will examine the unique cultural position Euclidean geometry occupied and how that position was shaped and maintained.

Speakers: Philip Beeley, Mattia Brancato, Vincenzo De Risi, Robert Goulding, Laura Kotevska, Catherine Jami, Sebastien Maronne, Yelda Nasifoglu, Paolo Rossini, JB Shank, Kevin Tracey, Gerhard Wiesenfeldt.
Year(s) Of Engagement Activity 2017
 
Description Reading Euclid website 
Form Of Engagement Activity Engagement focused website, blog or social media channel
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact A website and blog were set up describing and chronicling the work the research team undertook on this award. Responses were solicited and received from a number of scholars and owners of early modern copies of Euclid's Elements, leading in some cases to guest posts on the blog.
Year(s) Of Engagement Activity 2016,2017
URL http://readingeuclid.org
 
Description Rehearsing in the margins: marginal evidence and the culture(s) of mathematical reading in the early modern period 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Postgraduate students
Results and Impact ~25 participants attended a one-day workshop on early modern marginalia, led by graduate students at Canterbury Christ Church University.
Year(s) Of Engagement Activity 2017
 
Description Teaching mathematics in the early modern world 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact About 30 academics and other audience members attended a two-day workshop on "Teaching mathematics in the early modern world". Fourteen talks were given, and there was full and lively discussion throughout the two days.
Year(s) Of Engagement Activity 2016
URL http://www.benjaminwardhaugh.co.uk/workshops/