Search Results: opuscula analytica by euler leonhard

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 First edition, rare, of this collection of 28 previously unpublished papers by Euler, the majority of which deal with topics in number theory (e.g., papers 3, 5, 7-11, 14, 19 - see the listing below), of which the most important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… Read More

Petropoli: Academiae Imperialis Scientiarum, 1783. FIRST EDITION. With 2 folding plates of figures. Contemporary half-calf and marbled boards, spine label; a clean and crisp copy with the small book label of the Physikalische Biblioteek der Königl. Landesschule on the paste-down.