Reading Euclid at the Edward Worth Library
Dr Edward Worth (1676-1733), and Euclid
in early eighteenth-century Dublin.
Fig. 1: Portrait of Dr Edward Worth
Dr Edward Worth was an early eighteenth-century Dublin physician who bequeathed a library of some 4,400 volumes to Dr Steevens’ Hospital, Dublin (an institution of which he was a Trustee). The Edward Worth Library remains in situ and contains a particularly fine collection of medical and scientific texts. Worth was a Fellow of the Royal Society and his collection was greatly influenced by the works of Sir Isaac Newton (1642-1727). He clearly agreed with the mathematization of science which Newton had advocated and he was a dedicated collector of mathematical texts. Worth’s mathematical collection is an extraordinarily extensive one, encompassing nearly 100 items and covers a wide range of topics. An important part of his collection relates to ancient sources and first and foremost were his editions of Euclid. Worth owned three editions of Euclid and a number of other works which contained sections on Euclid’s Elements. These books are the subject of this online exhibition and the books themselves will be on display at the Edward Worth Library during June and July 2018 as part of the University of Oxford project Seeing Euclid. An Open Day will be held on Thursday 21 June 2018 for the Euclid exhibition and, in addition, the Librarian will be delighted to provide tours by appointment between Monday 18 June and Tuesday 31 July. To arrange a tour please e-mail firstname.lastname@example.org or phone 00353 1 635 2215.
Fig. 2: Euclid, Elementorum Euclidis libri tredecim. Secundum vetera exemplaria restituti. Ex versione Latina Federici Commandini aliquam multis in locis castigate (London, 1620), p. 1.
Worth’s earliest edition of Euclid’s Elements was by Federico Commandino (1506-1575), and was published in London in 1620. Commandino, like Worth, had been trained as a physician, and he too was deeply interested in mathematics. He was drawn to the works of ancient mathematicians and was responsible for editions of other famous mathematicians – his 1568 edition of the works of Archimedes may also be found in the Worth Library. Commandino’s edition of Euclid was first published in 1572 and went through a number of subsequent editions, being translated into Italian in 1575, another Latin edition in 1619, and the 1620 London bi-lingual edition (in Latin and Greek), which Worth purchased. Euclid’s Elements became a best-seller because of the clarity of his thought, and in this image of page 1 of Commandino’s edition we can see why, for Euclid begins with his most basic definition: ‘A Point is that which hath no part’.
Fig. 3: Euclidis Elementorum libri xv. breviter demonstrati, opera Is. Barrow, Cantabrigiensis, Coll. Trin. Soc… (London, 1659), provenance.
Worth’s second edition of Euclid was one of the most famous textbooks of its day. Barrow’s textbook was popular for a number of reasons: it was portable, designedly contained as many demonstrations as possible, and was succinct but at the same time left nothing out. The editor, Isaac Barrow (1630-1677), a Fellow (and later Master) of Trinity College, Cambridge, produced his compact edition of the Elements in 1656. Unlike other contemporary editions of the Elements such as that by André Tacquet (1612-1660), Barrow chose to include all the books of the Elements. Barrow was first and foremost a teacher and his edition was clearly written with his students in mind: we can see this not only in the dedication of the book to them but also in the manner in which Barrow sought to make the Elements as accessible as possible. Worth’s edition bears an interesting provenance note: Peter Forth had been admitted to Trinity College, Cambridge, on 31 July 1672 and was awarded his B.A. in 1677 and his M.A. in 1680, before going on to Grays Inn to study law. He was, therefore, a student at the same college as Barrow.
Fig. 4: Euclidis quæ supersunt omnia. Ex recensione Davidis Gregorii … (Oxford, 1703), frontispiece.
The editor of Worth’s third edition of the Elements, the Newtonian David Gregory (1656-1708), was elected to the Savilian Chair of Astronomy at Oxford in 1691. He proved to be as anxious as Isaac Barrow had been in Cambridge to extol the virtues of Euclid and in 1703 his seminal edition of the Elements was published by the University Press. The seventeenth-century mathematical curriculum at the University of Oxford had invariably started with Euclid’s Elements so Gregory’s decision to produce another edition was unsurprising. Its paramount position in the curriculum is reflected by Gregory’s choice of image for the frontispiece: here we see the Socratic philosopher Aristippus discovering signs of civilization following his shipwreck: he points to the ground where geometrical signs are clearly visible and the message is driven home by the caption from Vitruvius ‘We can hope for the best for I see the signs of men’. For Gregory, being a mathematician was intrinsic to being a civilised human being.
Fig. 5: Peter Ryff’s Quaestiones geometricae : in Euclidis et P. Rami Stoicheiosin. in vsum scholae mathematicae collectae à doctore Petro Ryff … quibus Geodaesiam, adjecimus per vsum radii geometrici (Frankfurt, 1621), title page.
Peter Ryff (1553-1629) was, like Worth and Commandino, a physician. He had been trained at the University of Basel by one of the most famed physicians of the sixteenth-century, Felix Platter (1536-1614), and Ryff gained his MD there in 1584. Two years later, in 1586, he was appointed Professor of Mathematics at the same university and he continued to pursue both careers for the rest of his life. Ryff spread his intellectual net wide, producing works on history, astronomy, astrology and, of course, mathematics. His Quaestiones geometrica, was initially published by the prestigious Wechel press at Frankfurt in 1600, and the spread of subsequent editions is an indication of the popularity of his text: 1602 Frankfurt, 1621 Frankfurt, 1649 Frankfurt, and 1665 Oxford. The seventeenth-century Oxford edition reflects the fact that Ryff’s text was used by seventeenth-century Oxford students to supplement their editions of the Elements. Hotson notes that Ryff’s edition restored demonstrations that had been previously excluded by Petrus Ramus (1515-1572).
Fig. 6. Christophori Clauii Bambergensis e Societate Iesu Opera mathematica V. tomis distributa : ab auctore nunc denuo correcta, et plurimis locis aucta, 3 vols (Mainz, 1611), i, title page.
Christopher Clavius (1538-1612), was one of the most famous scientists in early modern Europe and a leading light in the Society of Jesus. As Smolarski notes, Clavius’ position as professor of mathematics at the Jesuit Collegio Romano for over 45 years insured that he was immensely influential in championing the teaching of mathematics, not only at the Collegio Romano, but also (and perhaps more importantly), in the extensive Jesuit school system. His influence may be seen in the various drafts of the core Jesuit curriculum document, the Ratio Studiorum (1599), which advocated the study of Euclid in Jesuit schools. Clavius’ influence spread far and wide: his student at the Collegio Romano, Matteo Ricci (1552-1610), who, with his colleague Xu Guangqi (1562-1633), was responsible for producing the first Chinese edition of Euclid’s Elements, chose as his text Clavius’ 1574 Roman edition.
Worth owed a 1608 Genevan edition of Clavius’ famous commentary on the Sphaera of Sacrobosco and this opera omnia edition produced in 1611, which included Clavius’ 1574 commentary on Euclid’s Elements. As the title page of the 1574 text made clear, Clavius was concerned with 15 books by Euclid. Swertz and Katz note that the last two books were actually texts by Hypsicles of Alexandria (ca.190 BCE—ca 120 BCE) and Isidore of Miletus (fl.ca. 532). The 1574 text proved popular, and was reprinted on many occasions. In fact, as Sigismondi (p. 232), reminds us, ‘Clavius’ Euclid became the standard geometry textbook for the seventeenth century’.
Worth’s edition of Clavius’ collected works is one of a number of texts in the Worth Library which include commentaries on the Elements in conjunction with other mathematical and scientific texts. The title page draws attention to this: in the lower part we see Clavius at work; the two main figures represent Geometry (on the left) and Astronomy (on the right), but these two areas of the quadrivium, while the main focus of the work, are accompanied by texts on arithmetic, algebra, horology and, unsurprisingly given Clavius’ important role in the Gregorian reform of the calendar in 1582, calendar reform. This work contains sporadic annotations and the name of a previous owner, whose signature and date may be seen in the lower right hand corner of the page: ‘Bernard à Mallinckrot An. 1626.’ This undoubtedly refers to Bernhard von Mallinckrodt (1591-1664), Dean of Münster Cathedral, who converted from Protestantism to Catholicism in 1616. He, like Worth, was a renowned bibliophile.
Fig. 7. Marin Mersenne, Universae geometriae, mixtaeque mathematicae synopsis (Paris, 1644), Sig. 2 [cross] 4v.
Marin Mersenne (1588-1648), was a French Minim who played a vital role in the seventeenth-century Republic of Letters. His seventeen-volume correspondence gives us some idea of his scholarly friendship network and of the wide range of his intellectual interests. Mersenne was a polymath but is probably best known for his work on prime numbers. As Stedall notes, Euclid’s Book VII had defined perfect numbers as ‘(whole) numbers that are the sum of their parts’ and he had added a further theorem in Book IX: if 2n – 1 is prime then (2n – 1) x 2n-1 is perfect. In 1644 Mersenne argued that ‘perfect numbers are indeed rare, so that it has so far been possible to find only eleven’, but, as Stedall notes, Mersenne’s list was not accurate. Grosslight argues that, paradoxically, Mersenne’s lack of mathematical acumen enabled him to be a more attractive ‘mathematical intelligencer’ in seventeenth-century Europe. As this image from Worth’s copy of Mersenne’s Universae geometriae demonstrates, Mersenne did not provide a complete edition of Euclid but instead included selected parts of the Elements alongside mathematical texts by both ancient mathematicians, such as Archimedes, and more modern commentators, such as Ramus. Unlike all the other works in this exhibition, no diagrams were included.
Fig. 8. R. P. Claudii Francisci Milliet Dechales Camberiensis è Societate Jesus Cursus seu Mundus mathematicus, 4 vols (Lyon, 1690), i. Sig. †1v, detail.
Claude François Milliet Dechales (1621-1678), continued in Clavius’ mould for he too was a Jesuit mathematician who promoted not only the teaching of mathematics but, more specifically, the study of Euclid. His earliest exploration of Euclid, was his Euclidis Elementorum libri octo, ad faciliorem captum accommodate (Lyon, 1660), which had been translated into French in 1672 as Huict Livres des Elemens DEuclide (Lyon, 1672), and into English as The Elements of Euclid Explain’d (London, 1685). In this Dechales justified his decision to omit books 7, 8, 9 and 10 because he considered them to be ‘of little or no use in any part of the Mathematics. And I had oft wondred how they obtein’d a place amongst the Elements, since ‘tis evident Euclid compil’d them for no other end but to settle the doctrine of Incommensurables; which being little better than a vain curiosity, ought not to be receiv’d into the books which treat of the First Principles of the Science, but to make a particular Treatise by itself.’ As De Risi notes, this eliminated ‘the arithmetical treatises (VII–IX), the tenth book on irrational magnitudes, and the thirteenth book on the Platonic solids’.
At this image of the summary of the Cursus makes clear, by 1674, the year his Cursus seu Mundus mathematicus was published at Lyon (which Worth bought in the posthumous Lyon edition of 1690), Dechales had changed his mind and included not eight but fourteen books of Euclid. In this multi-volume work Dechales sought to provide a guide not only to Euclid but to the courses which he had given at Jesuit colleges at Marseille, Lyon and Turin. As he had been appointed professor of hydrography at Marseille, the four-volume work thus had a much broader scope than that of his initial extremely popular edition of Euclid which it incorporated. In this broad curriculum approach it mirrors Clavius’ earlier work.
Fig. 8. Oeuvres posthumes de Mr Rohault 2 vols (The Hague, 1690-95), i, p. 1.
Worth owned another posthumously published compilation volume of mathematical and more generally scientific works by a famous French natural philosopher, Jacques Rohault (1620-1672). Rohault is best known as a proponent of Cartesian natural philosophy, and his most famous work, Traité de physique (1671), became a popular textbook on the subject. Worth collected this octavo edition of his collected works, which included his shortened version of the Elements. Rohault had been given the task of teaching mathematics to Louis, Le Grand Dauphin (1661-1711), and the pedagogical nature of his text is clearly apparent.
To find out more about Worth as a collector of mathematical books see our online exhibition ‘Mathematics at the Edward Worth Library’.
Dechales, Claude François Milliet, The Elements of Euclid Explain’d (London, 1685).
De Risi, Vincenzo, ‘The development of Euclidean axiomatic. The systems of principle and the foundations of mathematics in editions of the Elements in the Early Modern Age’, Arch. Hist. Sci. 70, no 6. (2016), 591-676.
Euclid, Elementorum Euclidis libri tredecim. Secundum vetera exemplaria restituti. Ex versione Latina Federici Commandini aliquam multis in locis castigate (London, 1620), edited by Commandino.
Euclid, Euclidis Elementorum libri xv. breviter demonstrati, opera Is. Barrow, Cantabrigiensis, Coll. Trin. Soc… (London, 1659), edited by Barrow.
Euclid, Euclidis quæ supersunt omnia. Ex recensione Davidis Gregorii … (Oxford, 1703), edited by Gregory.
Feingold, Mordechai (ed.), Before Newton: The Life and Times of Isaac Barrow (Cambridge University Press, 1990).
Feingold, Mordechai, ‘Newton, Leibniz, and Barrow Too. An Attempt at a Reinterpretation’, Isis, 84, no.2 (1993), 310-338.
Feingold, Mordechai, ‘The Mathematical Sciences and New Philosophies; in Nicholas Tyacke (ed.) The University of Oxford Vol IV: The Seventeenth Century (Oxford University Press, 1997).
Feingold, Mordechai, ‘Barrow, Isaac (1630–1677)’, Oxford Dictionary of National Biography, Oxford University Press, 2004; online edn, May 2007 [http://www.oxforddnb.com/view/article/1541].
Grattan-Guinness, Ivor, The Fontana History of the Mathematical Sciences (London, 1997).
Grosslight, Justin, ‘Small Skills, Big Networks: Marin Mersenne as Mathematical Intelligencer’, History of Science 51 (2013), 337-74.
Guicciardini, Niccolò, ‘‘Gigantic implements of war’: images of Newton as a mathematician’, in Eleanor Robson and Jacqueline Stedall (eds.) The Oxford Handbook of The History of Mathematics (Oxford University Press, 2010), 712.
Hotson, Howard, Commonplace Learning. Ramism and its German ramifications, 1543-1630 (Oxford, 2007).
Mersenne, Marin, Universae geometriae, mixtaeque mathematicae synopsis (Paris, 1644).
Mersenne, Marin, Correspondance du P. Marin Mersenne, edited by Paul Tannery, Cornelis de Waard and Armand Beaulieu (Paris, 1945-88).
J J O’Connor and E F Robertson, Federico Commandino, MacTutor History of Mathematics, (University of St Andrews, Scotland, February 2000):
Saito, Ken, ‘Reading ancient Greek mathematics’, in Eleanor Robson and Jacqueline Stedall (eds.) The Oxford Handbook of The History of Mathematics (Oxford University Press, 2010), 801-826.
Sigismondi, C., ‘Christopher Clavius astronomer and mathematician’, Il Nuovo Cimento, 1 no. 1 (2013), 231-236.
Smolarski, Dennis, C. ‘The Jesuit Ratio Studiorum, Christophe Clavius, and the Study of Mathematical Sciences in Universities’, Science in Context, 15, no. 3 (2002), 447-457.
Stedall, Jacquelin, Mathematics Emerging. A Sourcebook 1540-1900 (Oxford, 2008).
Swetz, Frank J. and Victor J. Katz, ‘Mathematical Treasures: Christopher Clavius’ edition of Euclid’s Elements available at https://www.maa.org/press/periodicals/convergence/mathematical-treasures-christopher-claviuss-edition-of-euclids-elements [accessed 22 May 2018].
Swetz, Frank J., ‘Mathematical Treasures: Euclid in China: https://www.maa.org/press/periodicals/convergence/mathematical-treasure-euclid-in-china [accessed 22 May 2018].
Venn, John and J. A. Venn (eds) Alumni Cantabrigiensis (Cambridge University Press, 1922), Part II volume I, 169.
Text: Dr Elizabethanne Boran, Librarian, The Edward Worth Library, Dublin.