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Diophantus geometra siue Opus contextum ex arithmetica et geometria simul : in quo quæstiones omnes Diophanti, quæ geometrice solui possunt, enodantur tum algebricis, tum geometricis rationibus. Adiectus est Diophantus geometra promotus, in quo subtiles propositiones non absimili methodo pertractantur, & via noua ad eiusmodi praxes inueniendas aperitur.Paris: Michel Soly, 1660.
Rare first edition of this work on the indeterminate problems of Diophantus' Arithmetica. Billy corresponded actively with Fermat on number theory, and it is mainly through his collection of letters from Fermat, published as 'Doctrinae Analyticae Inventum Novum' in the 1670 edition of Bachet's Diophantus, that we know of Fermat's methods for solving Diophantine equations. This work, published a decade before the 'Inventum Novum', also deals with Diophantine problems, in which both arithmetical and geometrical solutions are given. The second part is devoted to 59 algebraic problems that are not found in Diophantus.

"From 1631 to 1633 Billy taught mathematics at the Jesuit college at Rheims. He became a close friend of Bachet, who was one of his pupils at Rheims. After this Billy taught in Grenoble and then was rector of a number of Jesuit Colleges in Chalons, Langres and in Sens. From 1665 to 1668 he was professor of mathematics at the College of Dijon. One of his pupils in Dijon was Ozanam but this was before he was appointed to the chair of mathematics so, since there were no formal mathematics classes at the College, he taught Ozanam privately. Billy corresponded with Fermat and produced a number of results in number theory which have been named after him. Billy had collected many problems from Fermat's letters and, after the death of his father, Fermat's son appended de Billy's collection under the title Doctrinae analyticae inventum novum (New discovery in the art of analysis) as an annex to his edition of the Arithmetica of Diophantus (1670). Itard writes in [DSB]:-

'It is an elaborate study of the techniques of indeterminate analysis used by Fermat and, on the whole, it explains them correctly. From it one can guess at Fermat's general line of activity in a field in which there are few pertinent documents.'

He also published astronomical tables such as 'Tabulae Lodoicaeae seu universa eclipseon doctrina tabulis'. This was a table of eclipses for the years 1656 to 1693 and included solar and lunar tables. Billy is also important in being one of the first to reject the role of astrology in science, along with superstitious notions about the malevolent influence of comets. Among Billy's most important works are: Abrégé des préceptes d'algèbre (1637); Nova geometricae clavis algebra (1643); Tractatus de proportione harmonicae (1658); and Diophantus geometria sive opus contextum ex arithmetica et geometria simul (1660)." (MacTutor History of Mathematics).

Sommervogel I, 1478, no. 7.. 4to: 221 x 170 mm. Pp. (20), 261 [recte 255], (1), [errors in pagination: jumps from 72 to 79, 86 = 89, 130 double, 133 to 135], complete. Near contemporary overlapping vellum, little browned & spotted, some paper flows, one sheet repaired, ownership inscription on title: Cardenay, or Cordemoy

      [Bookseller: Sophia Rare Books]
Last Found On: 2012-12-27           Check availability:      Antikvariat    


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