“Reading Euclid” recently inspected its hundredth copy of the Elements, and we’ve now recorded more than three thousand separate items in our summaries of the marks that early modern readers left in these books. With visits to London and Cambridge planned, we’re well on our way to our goal of seeing a representative sample of the early modern copies of the Elements surviving in Britain.
Most of the copies we’ve seen so far are held in Oxford libraries, although their earlier homes have been all over Britain. We’ve seen copies owned by university professors, teachers and students, by doctors, lawyers, merchants and even a saint (Thomas More). Some of the most fascinating copies come from the university context, where we’ve seen evidence of students copying annotations from a teacher’s book into their own. We’ve also seen a fascinating series of notes relating to a proposed new edition of the text: a group of scholars copied in textual variants, amended the Latin translation and compiled thousands of cross-references and commentary items, as well as providing algebraic equivalents for some of the theorems. Sadly that project came to nothing.
The books give a real sense of how the cultural profile of mathematics was changing in the early modern period, and how people’s use of texts and ownership of books was changing too. Those two processes led to a huge range of ways of engaging with the Euclidean text, and we’re beginning to discern some of the patterns and the ways that worked. Now for the next hundred copies!
The Reading Euclid project recently passed the milestone of having worked through fifty copies of Euclid’s Elements as part of the search for annotations and other marks made by readers. Principal Investigator Benjamin Wardhaugh writes:
We’re just a few months into our project on reading Euclid in Early Modern Britain and Ireland, and we’re eventually hoping to work through two or three hundred copies of Euclid’s Elements. We’ve now completed the first fifty, and recorded our two thousandth mark made by an early modern reader. A few patterns are starting to emerge.
Most of the books have been written in by their early readers: not just bookplates, signatures, names and dates, but also detailed – even obsessive – corrections of the mathematics and the language in which it’s expressed. I’ve now seen about twenty-five thousand printed pages, and around one in ten of those pages bears readers’ marks of some kind. Wrong labels are corrected, missing lines are added to diagrams and missing steps are inserted into proofs. More adventurous readers – or those whose responsibilities included teaching – marked up the book in still more detail, selecting and rearranging, supplementing one edition of the Elements with passages from another, or copying in long explanations and discussions from other geometrical works.
What we’re starting to see is a rich and fascinating world of reading and studying, that can help us understand how mathematics was learned in the early modern period. It’s background to the scientific changes of the seventeenth century and the revolutions that shook mathematics in that period. There’s lots more to do, but I’m optimistic about what we’re finding out.
Guest post by Renae Satterley, Librarian, Middle Temple Library
Middle Temple is one of the four Inns of Court, alongside Inner Temple, Gray’s Inn and Lincoln’s Inn. The Inns were traditionally responsible for educating barristers and calling them to the Bar. Since the mid-19th century they have been responsible for calling lawyers to the Bar and ensuring continuing professional standards as well as providing scholarships and support to the Bar.
Middle and Inner Temple trace their origins to the Knights Templar. It is not known when the Inns became two separate entities, but it was at some point before 1500. Members generally lived and worked at their Inn, some throughout their whole lives. As such the Inns were cosmopolitan places, especially during the early modern period. Many illustrious men were called to the Bar as honorary members. Some notable members of Middle Temple include Sir Walter Raleigh, Sir Martin Frobisher and Henry Atkins, physician to the King in 1604.
‘Ordinary’ members were also significant men of their time. Robert Ashley (1565-1641) is one such member. His bequest of over 3,700 books re-established the library at Middle Temple. Ashley was a lawyer, although by his own admission, not a successful one; he describes the ‘ebbs and tides’ of his law practice. Thus Ashley spent most of his life collecting and reading books- he was a true bibliophile. He also translated six works during his lifetime, from French, Italian, Latin and Spanish. The breadth of his collection is characteristic of the learned men of the Inns of Court, that is to say, far-reaching and covering a wide range of topics. The collection is also interesting for being one of the few of its size to have remained relatively intact in central London, where it originated.
One of the areas of particular interest to Ashley was science- including mathematics, geometry, algebra, music and astronomy. There are two works by Euclid in the collection: Elementorum libri XV (printed in Cologne in 1607) and Elementorum libri XIII (printed in Wittenberg in 1609). There is one other Euclid work in the collection without marginalia in Ashley’s hand, Elementorum libri XV, a two volume work printed in Frankfurt in 1607. However, given the paucity of book acquisitions made by the Inn after Ashley’s death, this set most likely belonged to his bequest as well.
The two books that do have Ashley’s marginal notes in them are shown in the images here; both feature fairly extensive manuscript notes about Euclid on the pages preceding the title page:
Unfortunately Ashley did not leave behind any personal papers or manuscripts, apart from two versions of an original work entitled ‘Of Honour’. One version of this manuscript is at Trinity College Cambridge (R.14.20 664) and the other at the Huntington Library (MS EL 1117). He also wrote an autobiography, Vita (MS Sloane 2131) now held at the British Library.
It is difficult to know how well Ashley would have understood the principles presented in these scientific works, but as a trained lawyer, he had been taught to read and cross-reference works closely. Reading and practising law meant being able to reference a wide range of legal precedents and statutes, from Magna Carta onwards. Many of his scientific books are heavily annotated and cross-referenced to other works.
After two full days of compelling papers on all aspects of mathematical teaching in the early modern world, we have wrapped up our first project workshop. We thank all the participants for making it such a lively and engaging event! Click here for more information on the workshop.
Following the 1570 Billingsley edition, today we made a trial print of the first block of text of Proposition 47 in Book 1, i.e. the Pythagoran theorem. We are happy with the results so far though more experimentation will be needed to get an even distribution of ink on the page.
The first rough draught of the diagram, however, turned out more modernist (cf. German expressionism) than early modernist! Now that we are more aware of the challenges involved in working with linoleum, we will be giving it another try.
In the next instalment of our experiment we began to consider the issue of illustrations. As we sat down to take a stab (rather literally) at the Pythagorean diagram, it soon became obvious just how difficult it must have been to print relief drawings with intersecting lines.
Using linoleum rather than wood for our trial, and lacking the fine skills of an experienced woodcut artist, this seemed an almost impossible task. However one need only to consider Albrecht Dürer’s Rhinoceros (1515), or to give more geometric examples, Renaissance architect Sebastiano Serlio’s architectural illustrations (e.g. in Regole generali di architetvra, 1537) to realise that great precision in woodcutting is indeed possible. But the cost of producing the 400-odd diagrams in Euclid’s Elements by this method would necessarily have been high, making the economics of mathematical printing this period something of a puzzle.
While our research concentrates on printed editions of Euclid up to 1700, it bears mentioning that the Bodleian Library at the University of Oxford is home to some spectacular Euclid manuscripts. Among them is MS. D’Orville 301, written in 888 by the scribe ‘Stephanos the clerk’ with annotations added between 10th and 14th centuries. It is based on the Elements edited by Theon of Alexandria in the 4th century. Here is a detail of the Pythagorean theorem on the verso of folio 31; click to view it on the Digital Bodleian website.