Geometry

As Euclid is such an important figure in the history of geometry, it is not surprising that he is well represented in New College Library's collections. Indeed, even Henry Savile himself lectured on Euclid, as you can see pictured on the left here. The book preserves Henry Savile’s lecture series on Euclid in one volume. Savile’s interest in biographical study is apparent in his demonstration that Euclid who wrote the Elements was not the same as the philosopher Euclid of Megara, a contemporary of Plato. At the time, they were widely believed to be the one and the same. 

Savile began these lectures on 12 July 1620 to mark the inauguration of his two professorships in geometry and astronomy. His final lectures only covered the first book of Euclid, after which he handed over to Henry Briggs, who had secured the geometry professorship after Savile’s first choice for the post had a disastrous interview. His final recorded lecture points to the future work of the professorships he endowed, ending with the words ‘Quod superset, auditores mei, valete et studete’. (‘All that remains, my listeners, is to say farewell, and get to work!’) This closing remark, as we saw in the previous page, was taken seriously by many Savilian chairs, many of whom published several volumes.

As Euclid was so influential, all undergraduates studying for the BA in the medieval and early modern periods were supposed to master at least the first six books of Euclid. Not much, though, is known about how geometry was actually taught in the university. The two books pictured here provide us with a glimpse into this teaching. Both were owned by the same man, Daniel Appleford, who studied in the college in 1645.

The first, pictured on the right, is the London 1570 translation of Euclid into English, The Elements of Geometrie. The second, pictured below left, is the London 1620 parallel Greek-Latin edition of the first six books of the Elements, the work of Henry Briggs, the first Savilian Professor of Geometry. Appleford has transferred by hand from the latter to the former each of the ‘definitions’ in the original Greek and Latin, adding them to the English headings. Like many student annotators, he lost interest in this exercise fairly quickly, but he did enter a cross-reference to Savile’s 1620 lectures on Euclid, featured directly above.

Appleford left some books in his will to his college friend John Lamphire; and our copy of Savile’s lectures was given by the same Lamphire. This surely, was how both studied Euclid in New College in the 1630s—with the original text, a Latin gloss, an English edition with a commentary, and with Savile’s lectures to give them direction.

The first full mathematical theory following Euclid’s tradition was Apollonius’s, around a century after Euclid. His work, entitled The Conics, though, has come down to us in a battered state. A derived Greek text survives for the first four books, there is an Arabic version of the next three books, but the eight and final book is lost.

Achieving a complete edition using the newly-recovered Arabic sections was a major aspiration for early-modern Oxford scholars. Edward Bernard, Savilian Professor of Astronomy, had acquired a manuscript copy of the missing Arabic books in Leiden in the late 1660s, and hoped to edit the entire text. He failed, and the task was taken up, at least in the Greek portion, by his Savilian successor David Gregory, who died in 1708 before he could complete it. Edmund Halley, Savilian Professor of Geometry, then took on the entire project, teaching himself Arabic. His 1710 edition, pictured to the right, is the result of his work—even including a reconstruction of the missing eighth book. 

At the other end of the eighteenth century is Abram Robertson, an impecunious Scot who had been taken under the wing of his countryman John Smith, Savilian Professor of Geometry from 1766 to 1791—despite Smith’s not being a mathematician at all. But Robertson, who eventually succeeded his mentor, was, and published not only the major work pictured on the left on conics, but also assisted in this year too with Giuseppe Torelli’s posthumous edition of Archimedes. 

Geometry is, perhaps, the branch of mathematics that is most closely linked to art. Both involve the close study of different lines, shapes, and forms—and both attempt to use what can be depicted to convey meaning to the viewer. This link between science and art is personified in the book pictured below. 

The work of Richard Haydocke (1569/70–c. 1642), a clergyman and physician, it is a partial translation of Giovanni Paolo Lomazzo's Trattato dell'arte de la pittura (1584), entitled A Tracte containing the Artes of curious Paintinge Caruinge Buildinge. It was published in Oxford in 1598 and Haydocke executed all the engravings contained within it. As it is the first appearance in English of any porition of an Italian treatise on painting, it is a good example of the link between mathematics and visual art.

This book, pictured on the right, is arguably the most outstanding work of John Wallis, Savilian Professor of Geometry for fifty-four years in the seventeenth century (see the previous page for more information on his life). Published in his seventieth year, A Treatise of Algebra, both Historical and Practical, this work is unusual as it has both a theoretical and practical focus. The last 28 chapters are dedicated to the practical applications of algebra, focusing on the building block of calculus—an area greatly developed by Isaac Newton. Essentially the mathematics of measuring change, calculus has a wide range of practical uses today, from structural engineering to patient diagnosis, credit card payment structures to predicting weather patterns.

This book, whose first page and pull out is depicted below, is the first edition of many—in English—of the Exercitatio geometrica de dimensione figurarum (1684), the earliest publication of the Aberdonian mathematician and astronomer, David Gregory. Gregory was born into a family of illustrious medics and mathematicians; his father, David Gregorie (original Scots spelling), was a physician and also librarian of Marischal College, Aberdeen. David Gregory also studied at Marischal College (one of two universities existing in Aberdeen at that time) as well as at the University of Leiden. He succeeded in 1683 to the Matheson professorship in mathematics at the University of Edinburgh, a chair which his uncle, James Gregorie, had earlier held. Exercitatio geometrica was, in fact, based on his uncle’s work. Gregory sent the original Latin copy of his treatise to Isaac Newton, which in turn galvanized Newton into writing up his own work on infinite series.

David Gregory benefited greatly from Newton’s patronage, and with the support of both Newton and the English astronomer, John Flamsteed, Gregory was elected in 1691 to the Savilian Professorship in Astronomy. Gregory delivered his inaugural Savilian lecture (in Latin) on 21 April 1692, in which he insisted on the necessity of applying geometry in matters astronomical and, though, a Scot, accorded fulsome praise to the achievements of the English. Newton's Principia is a touchstone throughout his lecture and he ends by calling John Wallis, Savilian Professor of Geometry from 1649 to 1703, ‘prince of geometers’.

Published in Edinburgh, this 1745 English translation of Gregory’s Exercitatio geometrica is rendered by an unnamed ‘ingenious Gentleman when a Student here’ (i.e. Edinburgh) and includes ‘several Additions’ to the Treatise ‘in order to render it more useful at this time’. New College’s copy, in its original plain sheep binding, carries various contemporary inscriptions, as can be seen on the right. Whilst these are inconclusive, ‘Earl of Find’ (i.e. the Earl of Findlater) is clearly decipherable. The Library purchased this copy of the Treatise in May 2019.