‎"EULER, LEONHARD.‎
‎De numeris amicabilibus. - [EULER ON AMICABLE NUMBERS.]‎

‎Leipzig, Grosse & Gleditsch, 1747. 4to. Contemp. full vellum. Faint handwritten title on spine. Two small stamps to title page and pasted library label to pasted down front free end-paper. In: ""Nova Actorum Eruditorum Anno MDCCXLVII"". (4), 720, (27) pp. + 6 engraved plates. The entire volume offered. [Euler's paper:] Pp. 267-9.‎

Reference : 42976

‎First edition of Euler's paper in which he describes the work that European mathematicians have done on amicable numbers and shows how to find pairs of amicable numbers. He gives the first 30 pairs of which some, but not all, were found with his method.When Euler began his studies only three pairs of amicable numbers were known. In the present and early Euler-paper he mentions the technique that Descartes and Fermat had used ""and listing 30 amicable pairs, including the three already known, and including one ""pair"" that was not actually amicable. Nevertheless, in one paper, Euler lengthened the list of known amicable pairs by a factor of almost ten. Euler gives us almost no clue about how he found these numbers"" (Sandifer, Charles Edward. How Euler did it, 2007, p. 50). ""At this time in which mathematical Analysis has opened the way to many profound observations, those problems which have to do with the nature and properties of numbers seem almost completely neglected by Geometers, and the contemplation of numbers has been judged by many to add nothing to Analysis. Yet truly the investigation of the properties of numbers on many occasions requires more acuity than the subtlest questions of geometry, and for this reason it seems improper to neglect arithmetic questions for those. And indeed the greatest thinkers who are recognized as having made the most important contributions to Analysis have judged the affection of numbers as not unworthy, and in pursuing them have expended much work and study."" (Translation of the introduction of the present paper by Jordan Bell of Carleton University).Enestroem E100.Many other papers by influential contemporary mathematicians, philosophers and historians are to be found in the present volume. ‎