EULER, LEONARD. - ON THE ISOCHRONE PROBLEM.

De innumerabilibus Curuis tautochronis in in Vacuo. (On the innumerable tautochrone curves in a vacuum). (+) Curva Tautochrona in Fluido resistentiam faciente secundum Quadrata cerilitatum. (Tautochrone curves in a fluid making a second resistance proportional to the square of the speed).

(Petropoli, St. Petersburg, Typis Academiae, 1735). 4to. No wrappers. In: "Classes Prima continens Mathematica. Commentarii Academiae Scientiarum Imperialis Petropolitanae", Tomus IV ad Annum 1729. The whole section of "Mathematica"offered. Pp 1-118 pp. and 10 engraved plates. Euler's papers: pp. 49-67 a. 2 engraved plates. Pp. 67-89 a. 1 engraved plate. Wide-margined, clean.

Both first editions and some of the earliest mathematical papers by Euler. The first paper is a masterful work, in which Euler first establishes a surprisingly simple geometric condition for tautochronic curves, and then shows how to generate such curves, both analytic and algebraic, starting from the familiar cycloid ; the next paper extends the analysis to a resistive medium where the resistance is in proportion to the square of the speed. - Enestroem E12 and E13.

The section (Mathematica) also contains papers by Jacob Hermann, Christopher Maier, G.W. Krafft and Daniel Bernoulli "Problema astronomicum inneniendi altitudinem poli,....", pp. 89-94.

Order-nr.: 50850