EULER, LEONHARD. - SOLVING THE "BASEL PROBLEM".

De Summis serierum reciprocarum. (On the sums of series of reciprocals).

(Petropoli, St. Petersburg, Typis Academiae, 1740). 4to. No wrappers. In: "Classes Prima continens Mathematica. Commentarii Academiae Scientiarum Imperialis Petropolitanae", Tomus VII ad Annum 1735, &..... Euler's paper: pp. 123-134 a. 1 engraved plates. A small brownspot in margin of first leaf, otherwise clean.

First printing of a major mathematical paper in Number Theory in which Euler solves the Basel Problem. Euler finds an exact expression for the sum of the squares of the reciprocals of the positive integers, namely pi^2/6. It was "Euler’s first celebrated achievement ... his solution in 1735 of the "Basel Problem"..." (Ed Sandifer).

"This is one of Euler's most celebrated papers, in which he demonstrates formulas such as Pi ^2= sum of the inverse squares of the positive integers, and many more, on equating the sine expansion of a circular arc to the infinite product of the simple factors of the associated multiple arcs." (Ian Bruce).
Enestroem E41.

Order-nr.: 50925