Perspectives on Euclid and Geometry

We are happy to announce a series of public lectures tying in with the ‘Seeing Euclid’ display. The lectures will start at 7pm on Wednesdays through the month of June, and take place in Lecture Theatre 3 (lower floor) at the Mathematical Institute, University of Oxford (Andrew Wiles Building, Woodstock Road, Oxford OX2 6GG).

6 June: Jeremy Gray (The Open University)
“Non-Euclidean geometry and the historian of mathematics”

13 June: Vicky Neale (University of Oxford)
“A mathematician reads Euclid”

20 June: Stephen Johnston (University of Oxford)
“The Body Beautiful: Euclid and Geometrical Solids in Renaissance Europe”

27 June: Lynn Gamwell (School of Visual Arts, New York)
“Geometry in Modern and Contemporary Art”

the schedule is available for download in pdf format or as a jpeg

2nd Digital Approaches to the History of Science Workshop: 23 March 2018 @ the History Faculty, University of Oxford

Registration is now open for the second Digital Approaches to the History of Science Workshop, which will take place at the History Faculty, University of Oxford, on 23 March 2018 (9:30 to 17:00) .

Confirmed speakers include:

  • Richard Dunn: the Board of Longitude Project
  • Christy Henshaw: the Wellcome Collection
  • Miranda Lewis, Howard Hotson, Arno Bosse: Cultures of Knowledge
  • Robert McNamee: Electronic Enlightenment Project
  • Tobias Schweizer, Sepideh Alassi: Bernoulli-Euler Online (BEOL)
  • Sally Shuttleworth: Diseases of Modern Life or Constructing Scientific Communities
  • with lightning talks by Grant Miller and Yelda Nasifoglu

The event is free but due to limited space, registration is required; see the Eventbrite page for more information.

On this workshop series, see the Bodleian Digital Library blog and our page on the DAHS Workshops.

Image: René Descartes, Principia philosophiae (Amsterdam, 1644), ‘Cartesian network of vortices of celestial motion’, p. 110. Bodleian Library Savile T 22. Edited in Photoshop by Yelda Nasifoglu.

Robert Hooke’s Euclid? | Guest post by Elizabeth Wells

Guest post by Elizabeth Wells, Archivist and Records Manager at Westminster School

‘he went to Mr. Busby’s, the schoolemaster of Westminster, at whose howse he was; and he made very much of him…There he learnd to play 20 lessons on the organ. He there in one weeke’s time made himselfe master of the first VI bookes of Euclid, to the admiration of Mr. Busby (now S.T.D.), who introduced him’

‘Biography of Robert Hooke’, John Aubrey’s Brief Lives.

Dr Richard Busby (1606-1695), Head Master of Westminster School 1638-1695, and his pupil Robert Hooke (1635-1703) both deserve greater notoriety than they currently enjoy.  Busby remained a household name until fading from the public consciousness in the 20th Century.  His fame was due to his great stature as a pedagogue: other pupils of his include John Locke, Christopher Wren and John Dryden; and to the strict discipline he enforced – Busby once boasted of having birched sixteen of the bishops on the bench in the House of Lords. Hooke’s reputation has been on the rise, thanks in part to Lisa Jardine’s biography, published to mark his tercentenary. However, his contemporary and friend, Wren, with whom he collaborated on so many projects following the fire of London, still eclipses him. It doesn’t help that there is no surviving picture of Hooke, although the popular story, that Isaac Newton destroyed the sole portrait as an act of revenge, is unlikely to be true.

Portrait of Dr Busby

Westminster School is fortunate to hold a substantial number of rare books, the bulk of which were accumulated by Dr Busby during his Head Mastership.  A library for the pupils had been founded by donations from Mildred and William Cecil in the 16th Century.  Busby, a keen bibliophile, developed the collection.  In 1648, the year before Hooke started at Westminster, the school reacquired a space to the south of the main schoolroom to use as a library.[1] . It was a room which Busby let selected pupils use for private study, and it may well have been where Hooke learnt his Euclid, for a contemporary remarked that he ‘seldome sawe him in the schoole’.

Today nineteen editions of Euclid’s work remain in the school’s collection, dating from 1533 until 1678.  Could one of these have been the copy that Hooke pored over?  We can discount those published after 1654, at which point Hooke had certainly left the school for Oxford, which takes us down to twelve contenders. A further five volumes which are listed in the manuscript library catalogue of the mathematician John Pell (1611-1685) can also be eliminated.  These books were purchased by Dr Busby in 1687, following Pell’s death, too late for Hooke to have made use of them.  Pell’s books are often easy to spot in the library; his preferred binding style in velum with a green spine label stands out.  He was also an attentive, pedantic, reader and regularly annotated and corrected his books.

John Pell corrected this diagram in his 1546 edition of Euclid’s Elements

So what of the remaining seven works in the library? It is improbable that Hooke used the Arabic edition in Busby’s Library which was printed in Rome in 1594.  Dr Busby did teach pupils at the school Arabic during his time as Head Master  – John Evelyn records that he ‘heard and saw such exercises at the election of scholars at Westminster School to be sent to the University in Latin, Greek, Hebrew, and Arabic, in themes and extemporary verses, as wonderfully astonished me in such youths, with such readiness and wit, some of them not above twelve or thirteen years of age.’  However, Michael Hunter has suggested that it is unlikely that Hooke had much knowledge of the language, and there were certainly no examples of Arabic books amongst Hooke’s own library when it was sold following his death.[2]

Title page to the Arabic edition of Euclid’s Elements with a manuscript Latin translation below

Bound as one whole are the three tracts concerning Euclidean geometry edited by Conrad Dasypodius (Rauchfuss), printed in Strasburg in 1564.  Dasypodius only included the first two books in full and the third tract contains the ‘enuciations’ of the Euclid’s books III-XIII.  In a later edition he explained that he added the enuciations as he did not wish to leave the book unfinished, but that including Euclid’s full work would make the book unwieldy for students.  Therefore, if we believe that Hooke fully mastered the first six books we must discount this particular translation.

Our earliest Euclid dates from 1533: Simon Grynaeus’ edition published in Basel.  This was the first edition of the Greek text and was based on several rather poor manuscript copies. Hooke might have used this volume, but the binding is very ornate and I wonder if Dr Busby might have held this fine copy in reserve.

Fine blind-tooled binding on Grynaeus’ 1533 edition of Euclid

A stronger contender is Henry Briggs’ 1620 edition.  It is a pleasing folio volume with the first six books in Greek with Latin translation, based on Frederico Commandino’s translation from the Greek.

Dr Busby owned a 1627 copy of the German mathematician, Christopher Clavius’, edition. Clavius did not produce an original translation, but compiled copious notes from previous editors and added his own comments.  It was a popular version, first printed in 1574, but with new editions every decade until the mid 17th Century. This version has rather distracting flowers and leaves pointlessly ornamenting the diagrams. Another German edition, this time printed in Wittenberg in 1634, was produced by the mathematician Ambrosius Rhode. This may also have made an unappealing study, as it is a small book with dense type.

Ornate foliage floats around the diagrams in this 1627 edition

Whilst Hooke might have already mastered Euclid after two years at the school, a tempting book to study would have been Thomas Rudd’s edition, printed in London in 1651. This work, unlike the others listed, was an English translation and had the benefit of an additional mathematical preface of John Dee.

Of course, Hooke may have studied any one of these five works, or indeed, a combination of the texts. Perhaps the most interesting point to take away from this exercise is the popularity of Euclid’s work and the range of translations and editions available to pupils at the school.

Hooke and Busby collaborated on a number of building projects in later life, including the ‘beautyfieing of the School & College’.  Hooke appears to have acted as the architect and overseer for the redesign of the room Dr Busby called his ‘Museum’, which we now know as the Busby Library.[3]   The room was badly damaged by an incendiary bomb in 1940, but has been reconstructed as a faithful replica, based on drawings and photographs in the school’s archive. The majority of Busby’s library survived the blast as the bulk of his collection was evacuated to Christ Church, Oxford, his former college. It is pleasing to think of Hooke employing his Euclidean geometry to construct this beautiful space as a legacy for his former Head Master and a gift to generations of future pupils.

The Busby Library c. 1840

[1] Smith, Eddie, “Westminster School Buildings, 1630–1730” in Westminster: The Art, Architecture and Archaeology of the Royal Abbey and Palace (British Archaeological Association: 2015) pp. 381-2.

[2] Hunter, Michael, Robert Hooke: Tercentennial Studies (Routledge: 2006) p. 14.

[3] Smith, Eddie, “Westminster School Buildings, 1630–1730,” p. 382.

Digital Approaches to the History of Science – Workshop I

Click here for more information on the DAHS workshops.

Digital Approaches to the History of Science, the first of two planned workshops on this topic, was held at the History Faculty in Oxford on 28 September 2018. A total of nearly sixty attendees assembled to hear presentations from a selection of the most exciting current projects in this field from around the UK. Professor Rob Iliffe, representing the Newton Project, addressed the ongoing challenges and complexity of digitizing and presenting the manuscript writings of Isaac Newton, and Alison Pearn spoke of the related issues faced by the digital side of the ongoing Darwin Correspondence project. Lauren Kassell, of the Casebooks Project, introduced a very different type of material and spoke of the need to find new ways of representing, encoding and searching the mass of information contained in early modern medical-astrological casebooks.

After lunch two speakers discussed from complementary perspectives the opportunities represented by the very rich archive of the Royal Society. Louisiane Ferlier discussed the digitization of Royal Society journals and the work needed to clean and link the metadata about the articles in them. Pierpaolo Dondio described his work modelling and visualising the network of authors, editors and referees who controlled the content of those papers, and provided examples of the kinds of research outcomes such work can produce. A final talk turned to the use of digital humanities resources in the university classroom: Kathryn Eccles and Howard Hotson described the Cabinet project, which has made a rich ecology of digital images and objects available to students on a growing list of Oxford undergraduate papers.

Rich discussions took place both around the individual presentations and over lunch and coffee, and this sell-out event has certainly stimulated interest and ongoing discussion about the distinctive opportunities for history of science created by digital scholarship and resources. The event was supported by the Centre for Digital Scholarship (Oxford), ‘Reading Euclid’, the Royal Society and the Newton Project, and was organised jointly by the Centre for Digital Scholarship and ‘Reading Euclid‘.

Many thanks to all the participants — we are already looking forward to the next workshop!

Augustus de Morgan and Euclid | Guest post by Karen Attar

Guest post by Dr Karen Attar, Curator of Rare Books at Senate House Library and a Research Fellow at the Institute of English Studies, both of the University of London. She has published widely on library history, and the library of Augustus De Morgan is one of her areas of interest.

Senate House Library, University of London—known until 2004 as the University of London Library—serves students from all the Colleges and schools of the federal University of London as a library for the humanities and social sciences. One might not, therefore, expect mathematics to feature. But its remit used to be larger; and the founding collection was the mathematical library of the mathematician and mathematical historian Augustus De Morgan (1806-1871), some 4,000 titles purchased shortly after De Morgan’s death by Samuel Loyd, Baron Overstone, for the University, as ‘the first fruits of a Library which shall ere long become such in all respects as the London University ought to possess’.

De Morgan’s Euclids

De Morgan collected as comprehensively as he could on a limited budget on all areas of mathematics: arithmetic (on which he published), geometry, functions, probability, and astronomy, with some related biographies, bibliographies, encyclopaedic works, and works on music thrown in. He had multiple editions of books by various writers. Of these, Euclid stands out. De Morgan’s copies range chronologically from the two productions of the incunable period to Isaac Todhunter’s textbook of 1862, in editions issued throughout Europe, from Venice to Amsterdam and from Basel to Dublin among others. Their format ranges from folio to duodecimo; their languages cover English, French, Italian and German alongside the original Greek and the predominant Latin.

As De Morgan was eminent in his field and a known collector and annotator of mathematical books, his own association with the Euclids bestows cachet upon them. Yet provenance interest does not rest on De Morgan alone.

Annotations on Euclidis Megarensis philosophi acutissimi mathematicorumq[ue] omnium sine controuersia principis op[er]a, ed. Campano da Novara (Venice: Paganino Paganini, 1509), p. 59. SHL classmark: [DeM] L.6 [Euclid - Elementa - Latin] fol. SSR
Annotations on Euclidis Megarensis philosophi acutissimi mathematicorumq[ue] omnium sine controuersia principis op[er]a, ed. Campano da Novara (Venice: Paganino Paganini, 1509), p. 59. SHL classmark: [DeM] L.6 [Euclid – Elementa – Latin] fol. SSR. © Senate House Library
The version published in Venice in 1509 is annotated in Italian; that from Paris in 1527 in Latin, in an early hand.  More tangibly, the astronomer Francis Baily (1744-1844), a prominent member of the Royal Society, annotated his copy (Edinburgh, 1799), both in the margins of the printed text and on interleaved pages.  We have some record of a few other former owners, such as Sir Thomas Knyvett (1539-1618; edition published in Padua in 1560), much of whose library of some 70 manuscripts and 1,400 printed books ended up via John Moore, Bishop of Ely, in Cambridge University Library, and the antiquary and literary scholar James Orchard Halliwell-Phillips (1820-1889), at whose sale of mathematical books in 1840 De Morgan bought extensively.  A Maltese architect, George Grognet, acquired in 1806 the edition published in Basle in 1550. A woman, one Abigail Baruh Lousada (c.1772-1833), a London scholar who translated the mathematical works of Diophantes into English and published some mathematical papers, owned the 1644 Paris edition; De Morgan patronised the sale of her library in 1834.  Most recently, Dionysius Lardner (1793-1859), London University’s first professor of natural philosophy and astronomy, edited his text of Euclid (1828) for the use of students in and preparing for the University of London and inscribed it to Augustus De Morgan.

De Morgan’s annotations are often bibliographical, place the book within its intellectual context, refer to rarity, or concern provenance. That on Lardner’s edition moves bibliography into the realm of the anecdotal:

“This was one of the first copies issued and was sent out before the unfortunate slip in page 244 was cancelled. Of course that slip was very sharply criticized particularly by Peter Nicholson, who foretold the ruin of the University of London from it.”

(Peter Nicholson (1765-1844) was a Scottish mathematician and architect who wrote about architecture, and who spent some of his life in London. De Morgan was connected with University College London (the ‘University of London’ referred to), as its first professor of mathematics.)

Giovanni Alfonso Borelli’s Euclides restitutus, siue, Prisca geometriae elementa, breuiùs, & faciliùs contexta (Pisa: Francesco Onofri, 1658). © Senate House Library
Giovanni Alfonso Borelli’s Euclides restitutus, siue, Prisca geometriae elementa, breuiùs, & faciliùs contexta (Pisa: Francesco Onofri, 1658). © Senate House Library

An intriguing example of a provenance annotation concerns the inscription ‘Edmond Waller’ on the half-title of Giovanni Alfonso Borelli’s Euclides restitutus, siue, Prisca geometriae elementa, breuiùs, & faciliùs contexta (Pisa: Francesco Onofri, 1658). Was this the seventeenth-century poet and politician Edmund Waller (1606-1687)? De Morgan was at pains to find out, writing both to the British Museum and to the literary critic and antiquary Bolton Corney (1784-1870) in a quest for other examples. He tipped their replies into the book, and summarised their messages in his handwritten notes.

Giovanni Alfonso Borelli’s Euclides restitutus, siue, Prisca geometriae elementa, breuiùs, & faciliùs contexta (Pisa: Francesco Onofri, 1658). © Senate House Library
Edmond Waller’s inscription on the half-title of Giovanni Alfonso Borelli’s Euclides restitutus, siue, Prisca geometriae elementa, breuiùs, & faciliùs contexta (Pisa: Francesco Onofri, 1658). © Senate House Library

An author search under De Morgan as former owner on Senate House Library’s online catalogue brings up a list of all De Morgan’s books here. To learn more about De Morgan’s interaction with Euclid and other writers, see my article on ‘Augustus De Morgan and his Reading’ in The Edinburgh History of Reading: A World Survey, edited by Mary Hammond and Jonathan Rose (Edinburgh University Press, forthcoming).

Karen Attar
Curator of Rare Books
Senate House Library, University of London