## Sir Henry Savile's Lectures on Euclid

### E. M. Wright and E. P. Wright

According to Rouse Ball, in *History of the Study of Mathematics at Cambridge* [1, p. 29] published in 1889,

Christopher Wordsworth, inWhen Sir Henry Savile(born1549and died in1622)became warden of Merton he seems to have felf that the practical abandonment of science to Cambridge was a reproach on the ancient and immenseley more wealthy university of Oxford. Accordingly about1570he began to give lectures on Greek geometry, which, contrary to the almost universal practice of that age, he opened free to all members of the university. These lectures were published in Oxford in1621. He never however succeeded in taking his class beyond the eighth proposition of the first book of Euclid. 'Exolvi,' says he, 'per Dei gratiam, domini auditores, promissum; liberarvi fidem meam; explicavi pro meo modulo definitiones, petitiones, communes sententias et octo priores propositiones Elementorum Euclidis. Hic, annis fessus, cyclos artemque repono.' In spite of this discouraging result Savile hoped to make the study a permanent one, and in1619he founded two chairs, one of geometry and one of astronomy.

*Scholae Academicae*[3, p. 72] in 1877, says

In a footnote, Wordsworth quotes precisely the same Latin sentences as Ball.If Cambridge desired to retort upon her sister[to certain Oxford attacks on Newton]she might with advantage of truth on her side proclaim, that the learned and generous founder of the lectureships of geometry and astronomy at Oxford, the warden of Merton and provost of Eton, Sir Henry Savile, publicly confessed that a course of lectures on the definitions, postulates, axioms and first eight propositions of Euclid was a task which almost overwhelmed him. Dr. Whewell however, takes a more liberal view of his words, and attributes them to the absorbing process of the commentatorial spirit working in a critic long and earnestly employed on one author.

These statements (apart from Whewell's) seem somewhat improbable. Savile was a celebrated scholar, responsible for part of the Epistles, the Acts, and Revelations in the 1611 "Authorised Version" of the English Bible and for a famous edition of St. Chrysostom.

Ball implies that Savile became Warden of Merton before 1570 (at the age of 20); this did not occur until 1585. The very extract quoted by both Wordsworth and Ball raises doubts. Savile could not have been annis fessus in 1570. At the age of 20, one may sometimes, ir rarely, be worn out, but not with years.In1570, our author Savile proceeded in his faculty, and read his ordinaries on 'The Almagest of Ptolemy'[Anthony à Wood(1632-1695)[2, Bliss(1815), Vol.2, p.310]].

When we refer to Savile's published lectures (*Prealectiones tresdecim in principium elementorum Euclidis, Oxonii habitae MDCXX*, Oxford 1621), from which the above Latin quotation is taken, it is at once apparent that they were a set of lectures given in 1620 (when Savile was 70) to inaugurate the Savilian chair of geometry. In his preface Savile warns the reader to expect only the most elementary of Elements. He begins by saying that his plan is, if strength and health allow, to explain the definitions, postulates, axioms and first eight propositions and to leave the rest to his successor. The first lecture (delivered to a large general audience) contains no geometry but confutes the standard error that the geometer Euclid was Euclid of Megara. (Mathematicians who have had to give lectures to learned but non-mathematical audiences will appreciate Savile's strategy.) Subsequently he examines his limited subject matter in the most critical detail and with the fullest account of the views of ancient commentators. To the present generation, who have read Whitehead, Russell and Hilbert, it will not seem absurd to spend seven lectures on definitions, postulates and axioms.

On the last page, Savile uses the words quoted by Ball. *Cyclos artemque repono* (I lay down my compasses and my art) is a parody of *caestus artemque repono* (Aeneid V, 484), the words used by the old boxer when he retires unbeaten and hangs up his gloves on the temple wall. Savile goes on to say that others will succeed him, stronger in body and livelier in mind. As the body ages, the powers of the mind age also. In short, he will never again ascend the lecturing platform. (Our rendering does not do his sonorous and moving Latin full justice.)

He says that his most learned successor [in fact, Henry Briggs] will take his audience further into the mysteries of geometry. As a final word Savile especially commends to them the fifth book on irrational proportion.

This leads to a juster view of Savile's mathematical ability. He found the course of lectures, elaborate and detailed as they were, all he could accomplish at his advanced age. But he was sufficiently modern in outlook to appreciate the profound importance of Eudoxus' theory of irrational proportion, the modern equivalent of which is Dedekind's theory of irrationals.

In the statutes drawn up by Savile for his professor of geometry, the latter is required to lecture on the thirteen books of Euclid's element, on the conics of Appollonius and on all the books of Archimedes. He is also to teach speculative and practical arithmetic, practical geometry or geodesy, music and mechanics.

[University of Aberdeen, Scotland; received by the editor, 7:VIII:1959. Published: *Scripta Mathematica*, **25** (1960), 63 65.]

## References

[1] W. W. R. Ball, *History of the Study of Mathematics at Cambridge* (Cambridge University Press, Cambridge, UK, 1889).

[2] A. à Wood, *Athenae Oxoniensis: An exact history of all the writers who have had their education in the University of Oxford* (2v., 1691 1692; rev. and enl. ed., 1721; 4v., Bliss, London, 1813 1820).

[3] C. Wordsworth, *Scholae Academicae: Some Account of the Studies at the English Universities in the Eighteenth Century* (Cambridge University Press, Cambridge, UK, 1877; rpt., Frank Cass, London, UK, 1968; Augustus M. Kelley, New York, NY, 1969).

JOC/EFR January 2019

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