‘Much necessary for all sortes of men’: 450 years of Euclid's Elements in English

Abstract

This talk, given at the BSHM Textbooks Meeting in September 2005, is in two parts. First it looks at some of the English editions of the Elements published over the last 450 years. Then, to show how various editors differed in the way they approached the text, it looks at their treatments of Pythagoras’ Theorem (Book I, Proposition 47). Finally, it draws attention to some texts from the Fauvel Collection that either derive from the Elements or are closely connected with it.

Notes

¹Later Recorde refers to the missing parts ‘… the other two books which shoulde have been sette forth with these two, yf misfortune had not hindered it …’ Pathway, sign. z. ii^v, the dedicatory Epistle to King Edward VI.

²John Bale, Index britanniae scriptorum, (ed R C Poole), Oxford, 1902. See Joy B Easton, ‘A Tudor Euclid’, Scripta Mathematica, 27 (1966), 339–355, 340.

³S Lilley, ‘Robert Recorde and the Idea of Progress’, Renaissance and Modern Studies, 2 (1958), 3–37, 26.

⁴It has been conjectured that these errors occurred because in May 1551, around the time of the book's printing, Recorde was embroiled in controversy in connection with his current position as General Surveyor of Mines and Monies in Ireland, and so was unable to see the proofs of the book. See Easton, 1966. There is also confusion over the date of the book's publication. The book itself is dated 28 Jan 1551 but at that time the New Year began on the 25 March. Thus by our system of dating (with the New Year beginning on 1 January) the date of publication would be 1552.

⁵For a more detailed discussion of Billingley's Euclid, see R C Archibald ‘The First Translation of Euclid's Elements into English and its Source’, American Mathematical Monthly, 57 (1950), 443–452.

⁶Henry Billingsley matriculated at St John's College, Cambridge in 1550 and became a scholar there in 1551. He is also said to have studied at Oxford, although he did not take a degree at either University. He was afterwards apprenticed to a London haberdasher and rapidly became a wealthy merchant. He was elected Lord Mayor of London in 1596 and he was knighted the following year. He was married five times and died in 1606. See: A McConnell, ‘Billingsley, Sir Henry (d. 1606)’, Oxford dictionary of national biography (ODNB), Oxford: Oxford University Press, 2004.

⁷Two examples of ‘pop-up’ diagrams are reproduced at: http://www.math.ubc.ca/~cass/Euclid/dee/dee.html.

⁸Sir Thomas Heath, A history of Greek mathematics I, New York: Dover Publications, 1981, 355.

⁹Siegfried Kracauer, Von Caligari bis Hitler, Hamburg: Rowohlts, 1958. I am grateful to Volker Remmert of the University of Mainz for supplying me with this information.

¹⁰John Day[e] has been described as ‘one of the titans of the Elizabethan book world’ and ‘one of the London book trade's most innovative and adept members’. See Andrew Pettegree, ‘Day, John (1521/2–1584)’, ODNB.

¹¹Archibald (1950), 445.

¹²For a commentary on Dee's Praeface and a reproduction of the original, see: John Dee ‘The Mathematical Praeface to the Elements of Geometrie of Euclid of Megara’ with an introduction by Allen G Debus, Science History Publications, 1975.

¹³E G R Taylor The mathematical practitioners of Tudor and Stuart England, Cambridge, 1967, 358.

¹⁴Andrew Saunders, ‘Rudd, Thomas (1583/4–1656)’, ODNB.

¹⁵Books XIV and XV are continuations of Book XII (construction of the five regular solids) but are not by Euclid. Book XIV is the work of Hypsicles who lived in the second half of the second century BC; Book XV is much inferior to Book XIV and is attributed, in part, to Isidorus of Miletus 6th Century AD.

¹⁶See Archibald (1950), 450–451.

¹⁷EL Furdell ‘Sawbridge, George, the elder (b. in or before 1621, d. 1681)’ ODNB.

¹⁸Claude-François Milliet Dechales, Huict livres des Eléments d’Euclide rendus plus faciles, Lyon, 1672.

¹⁹See E G R Taylor (1967), 278.

²⁰Philip Lea (fl. 1666–1700) was a notable cartographer, globe- and instrument-maker. See E G R Taylor (1965), 253.

²¹For reproductions of the Oxford University Press engravings, see J Fauvel, R Flood, R Wilson, Oxford figures: 800 years of Oxford mathematics, Oxford: Oxford University Press, 2000, 53, 129, 161 respectively.

²²See E G R Taylor (1967), 289.

²³From an advertisement in W Alingham Thesaurarium mathematicae, by John Taylor, gent … Enlarged by W. A., London, 1707.

²⁴S D Snobelen, ‘Whiston, William (1667–1752)’, ODNB.

²⁵Whiston had lectured as Newton's deputy when Newton was called to the Mint and so was the natural successor to Newton's chair. His conflict with the Church derived from his support for the anti-trinitarian doctrine.

²⁶For further information about Oliver Byrne and to view the entire book see the University of British Columbia website: http://www.sunsite.ubc.ca/DigitalMathArchive/Euclid/byrne.html.

²⁷Isaac Todhunter ‘Elementary Geometry’, The conflict of studies, and other essays on subjects connected with education, Macmillan, 1879. For a discussion of Todhunter's work see J Barrow-Green ‘Isaac Todhunter and his Mathematics Textbooks’, Teaching and Learning in 19^th-Century Cambridge (ed. J Smith, C Stray), Boydell, 2001.

²⁸By way of comparison, Henry Smith, Savilian Professor of Geometry at Oxford who died in 1883, was only worth about £3,000, and Arthur Cayley, Sadlerian Professor of Pure Mathematics at Cambridge, who died just over a decade later was worth about £23,000.

²⁹Letter from Dodgson to Todhunter, 20 March 1876, Todhunter manuscripts (Notes I), St John's College Archives, Cambridge.

³⁰Euclid, Euclid's Elements, tr. Thomas L Heath (ed. D Densmore), Green Lion Press, 2002.

³¹See, for example, W Knorr ‘The wrong text of Euclid: on Heiburg's text and its alternatives’, Centaurus, 38 (1996), 208–276; D Fowler, The mathematics of Plato's Academy: a new reconstruction, Oxford: Clarendon Press, 1999 (second edition).