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St. Petersburg: Academia Imperialis Scientiarum, 1783. First edition. THE LAW OF QUADRATIC RECIPROCITY. First edition, rare, of this collection of 28 previously unpublished papers by Euler, the majority of which deal with topics in number theory (e.g., papers 3, 5, 7-11, 14, 19 - see the listing below), of which the most important is 'Observationes circa divisionem quadratorum per numeros primos' (3), read at the St. Petersburg Academy in 1772. This paper gives the first clear statement of the 'law of quadratic reciprocity,' called the 'golden theorem' by Gauss who gave its first proof in his Disquisitiones Arithmeticae (1801). Euler had studied questions related to quadratic reciprocity for decades, starting with a letter to Christian Goldbach dated 28 August, 1742. He gradually accumulated numerical evidence, but did not feel able to formulate the 'law' until he did so in (3). He continued to work on topics related to quadratic reciprocity - paper (5) is an example - but a proof eluded him, as it…
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Opuscula Analytica
by EULER, Leonhard
- Used
- Hardcover
Two folding engraved plates. 2 p.l., 363 pp.; 2 p.l., 346 pp. Two vols. Large 4to, early 19th-cent. half-sheep & green marbled boards, flat spine gilt, red leather lettering piece on spine. St. Petersburg: Typis Academiae Imperialis Scientiarum, 1783-85. First edition of this collection of 29 mathematical treatises by Euler; the first volume was published in the year of his death. This is a very uncommon book. "Containing important papers on the theory of numbers, including his famous 'Observationes circa Divisionem Quadratorum per Numeros primos', also 'de Criteriis Aequationis fxx + gyy = hzz, utrum ea Resolutionem admittat necne? Considerationes super Theoremate Fermatiano,' etc. etc."-Sotheran, 2nd Supp., 1464. Fine and fresh set from the library of the Dukes of Anhalt with their stamp on verso of each title. ❧ Keynes, A Treatise on Probability. Bibliography, p. 443.
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Opuscula Analytica
by EULER, Leonhard
- Used
- first
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- Used
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- First edition
- Quantity Available
- 1
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Koebenhavn V, Denmark
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£12,246.00
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£12,246.00