## Opera Mathematica

SCARCE FIRST EDITION OF THE COLLECTED WORKS of one of Newton’s most important precursors, John Wallis, Savilian Professor (1649-1703), containing the first printed appearance of Newton’s ideas on fluxions.

A staunch promoter of English mathematicians, Wallis repeatedly urged Newton to publish his theories before others laid claim to he work, for the sake of “your Reputation (& that of the nation)” (Gjertsen, *Newton Handbook*, 605). While Newton resisted for many years, in 1693 Wallis published several letters from Newton in Vol. II of his *Opera*, thereby introducing the concept of fluxional notation—pricked and dotted letters. In the preface to Vol. I (1695), Wallis refers briefly to Newton’s claim to the discovery of Fluxions, while Vol II (1693) has the first full account of Newton’s invention of calculus.

The third volume of Wallis’s *Opera* contains previously unpublished correspondence between Newton and Leibniz, the most important items of which are Newton’s *Epistola prior* and *Epistola posterior*. “These two lengthy letters were sent to Leibniz in 1676 to acquaint him with the main lines of Newton’s mathematical development… *Epistola prior*, beginning with the binomial theorem, went on to describe Newton’s work on series… The second letter also contains much discussion on infinite series. It is best known, however, for Newton’s reference to powerful and general methods he had developed for the drawing of tangents, the determination of maxima and minima, and the quadrature of curves. These, he added, he preferred to conceal within a quite insoluble anagram. A second, and even longer, anagram concealed Newton’s claim to be able to solve fluxional equations… The solutions to both were publicly disclosed by Wallis (1699)” (*ibid*, 189).

Vol. 2 of the *Opera* also contains (pp. 669-78) *De Postulato Quinto; et Definitione Quinta; Lib. 6. Euclidis; disputatio geometrica*, Wallis’s important attempt to prove the parallel postulate of Euclid, also published here for the first time. “John Wallis gave a lecture on this topic… on the evening of 11 July 1663. He had been inspired by Nasr-Eddin’s attempt on it, which he referred to in his lecture, to examine the question himself, and his analysis is remarkable both for its originality and its caution. Indeed, his view of the matter was to be much more profound than many a later writer’s” (Fauvel & Gray, *The History of Mathematics*, 510).

This magnificent and comprehensive edition of Wallis’s collected works was financed by and printed at Oxford University. In addition to several ‘firsts’, including those described above, these volumes contain reprints of virtually all of Wallis’s great books, including the *Arithmetica infinitorum and Mechanica* (Vol. 1), an augmented Latin edition of the *Treatise of Algebra* (Vol. II), and bilingual editions of a number of ancient Greek texts including Ptolemy’s *Harmonics*, Aristarchus’s *On the magnitudes and distances of the sun and moon* and Archimedes’s *Sand-reckoner *(Vol. III). In addition to numerous other mathematical works, the four volumes include his most popular work, *Grammaticae lingua anglicanae*, his “Treatise of Speech [which] formed a useful theoretical foundation for his pioneering attempts to teach deaf-mutes how to speak” (*DSB*), as well as an important tract on cryptography in which he records the methods he developed while deciphering for Cromwell the coded messages of Charles I.

Wing W596, W566, W597. Babson 184. Roberts and Trent, 345. see J.F. Scott, The Mathematical Work of John Wallis, London 1938; M. Baron, The Origins of the Infinitesmal Calculus, Oxford, 1969, 205-213; Richard Westfall, The Life of Isaac Newton, Cambridge, 1993, 207-209ff.

Opera Mathematica. Volumen primum [-Tertium – Opera quaedam miscellanea]. Oxford: Sheldonian Theatre [University Press], 1695, 1693, 1699. Four volumes, bound in three. Folio, contemporary full paneled calf rebacked to style. Complete with four engravings (on three leaves) and three portraits (Vols. I & II with the same portrait by Loggan dated 1678 and engraved by Burghers; Vol 3 by Sonmans dated 1698 and engraved by Burghers). With large bookplate inside each front cover reading “The Gift of Mr. Thomas Heatley, Citizen and Iron-monger of London, to the Mathematical School in Christ’s Hospital, Anno Dom. 1700”. A very clean copy with only occasional light browning and foxing, very handsomely bound.

ONE OF THE MONUMENTS IN THE HISTORY OF MATHEMATICS. RARE.
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Price: $48,000 .