### Diophantus of Alexandria.

## Arithmeticorum libri sex, et de numeris multangulis liber unus.

Cum commentariis C.G. Bacheti V.C. & observationibus D.P. de Fermat senatoris Tolosani … Accessit doctrinae analyticae inventum novum, collectum [by J. de Billy] ex varijs ... Fermat epistolis [ed. Samuel de Fermat].

**Description:**
FIRST EDITION OF FERMAT'S RECENSION, large engraved vignette on title, several finely engraved headpieces and initials, and a few woodcut diagrams in the text, damp-stain in the inner margin of the first 20 odd leaves, occasional browning and spotting as usual, nothing severe,
pp. [xii], 64, 341, 48, folio (350 x 230 mm),
contemporary vellum (probably Italian), green morocco label on spine (partly defective), upper corners worn, a little worming to the insides of the boards,

**Publication Details:**
Toulouse: Bernard Bosc, 1670

**Notes:** First edition of Fermat's annotated edition of Diophantus' Arithmetica, a large copy, and also the first printing of Fermat's contributions to the theory of numbers, of which he is the undisputed founder, including his famous statement of 'Fermat's last theorem.' Since most of Fermat's work in number theory remained unpublished in his lifetime, 'it was neither understood nor appreciated until Euler revived it and initiated the line of continuous research that culminated in the work of Gauss and Kummer in the early nineteenth century' (DSB). Fermat showed little interest in publishing his work,...moreFirst edition of Fermat's annotated edition of Diophantus' Arithmetica, a large copy, and also the first printing of Fermat's contributions to the theory of numbers, of which he is the undisputed founder, including his famous statement of 'Fermat's last theorem.' Since most of Fermat's work in number theory remained unpublished in his lifetime, 'it was neither understood nor appreciated until Euler revived it and initiated the line of continuous research that culminated in the work of Gauss and Kummer in the early nineteenth century' (DSB). Fermat showed little interest in publishing his work, which remained confined to his correspondence, personal notes, and to marginal jottings in his copy of the 1621 editio princeps, edited by Claude Bachet, of Diophantus' Arithmetica. Fermat's marginalia included not only arguments against some of Bachet's conclusions, but also new problems inspired by Diophantus. After his death, Fermat's eldest son Clement-Samuel published his father's marginalia in this new edition. Most famous of the 48 observations by Fermat included here is the tantalizing note that appears on fol. H3r 'regarding the impossibility of finding a positive integer n > 2 for which the equation xn + yn = zn holds true for the positive integers x, y, and z' (Norman). Fermat noted that he had discovered a 'truly marvellous demonstration' of this proposition, but that the margin was too narrow to transcribe it. This simple statement became known as the single most difficult problem in mathematics, and for over 300 years no mathematician succeeded in either proving or disproving it. In 1995 Andrew Wiles, professor of mathematics at Princeton, who had been obsessed with Fermat's last theorem since the age of 10, completed a 130-page proof (first presented in 1993, with a flaw that required revision), using the most advanced techniques of modern mathematics. His achievement was described by fellow mathematicians as the mathematical equivalent 'of splitting the atom or finding the structure of DNA' (Singh, Fermat's Enigma (1997), p. 279). Although Fermat's marginal jottings in Diophantus hold a special place in the history of mathematics, much of what we know of Fermat's methods of proof is found in his letters to the French Jesuit Jacques de Billy, a pupil of Bachet, printed for the first time in the present work as Doctrinae Analyticae Inventum Novum. Some copies have a portrait and errata leaf (not present here), both of which were certainly issued later. The Macclesfield copy (possibly large paper) was 360 mm tall: most copies are in the 330-340 range.See Weil, Number Theory: An Approach Through History from Hammurapi to Legendre, 1984. **HIDE**

**Bibliography:** (Honeyman 893; Hoffman II, p.109; Macclesfield 638 (large paper copy); Norman 777; Smith, Rara arithmetica, p. 348)

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**Price:** £35,000

**Subject:** Sciences

**Published Date:** 1670

**Stock Number:** 64285

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