THE BRACHISTOCHRONE PROBLEM

LEIBNIZ, GOTTFRIED & JOHANN BERNOULLI & JAKOB BERNOULLI & EHRENFRIED WALTHER VON TSCHIRNHAUS.

Supplementum defectus geometria Cartesianae circa inventionem locorum. [Joh. Bernoulli] + [Two other papers]. Notatiuncula ad acta decemb. 1695. [LEIBNIZ].

Leipzig, Grosse & Gleditsch, 1696. 4to. Entire volume present. Nice contemporary full vellum. Small yellow paper label pasted to top of spine and library-label to front free end-papers. Internally some browning and brownspotting. Overall a nice and tight copy. [Bernoulli paper:] pp. 264-69. [Leibniz-paper:] pp. 45-47. [Entire volume: (2), 603, (1) pp. + plates].

First printing of the famous 1696-edition of Acta Eruditorum in which Johann Bernoulli published a challenge to the best mathematicians:

"Let two points A and B be given in a vertical plane. To find the curve that a point M, moving on a path AMB , must follow such that, starting from A, it reaches B in the shortest time under its own gravity."

Johann adds that this curve is not a straight line, but a curve well known to geometers, and that he will indicate that curve, if nobody would do so that year. Later that year Johann corresponded directly with Leibniz regarding his challenge. Leibniz solved the problem the same day he received notice of it, and almost correctly predicted a total of only five solutions: from the two Bernoullis, himself, L'Hospital, and Newton. Leibniz was convinced that the problem could only be solved by a mathematician who mastered the new field of calculus. (Galileo had formulated and given an incorrect solution to the problem in his Dialogo).

But by the end of the year Johann had still not received any other solutions. However, Leibniz convinced Johann that he should extend the deadline to Easter and that he should republish the problem. Johann now had copies of the problem sent to Journal des sçavans, the Philosophical Transactions, and directly to Newton. Earlier that year Johann had accused Newton for having filched from Leibniz' papers. Manifestly, both Johann and Leibniz interpreted the silence from June to December as a demonstration that the problem had baffled Newton. They intended now to demonstrate their superiority publicly.

But Newton sent a letter dated Jan. 30 1697 to Charles Montague, then president of the Royal Society, in which he gave his solution and mentioned that he had solved it the same day that he received it. Montague had Newton's solution published anonymously in the Philosophical Transactions. However, when Bernoulli saw this solution he realized from the authority which it displayed that it could only have come from Newton (Bernoulli later remarked that he 'recognized the lion by its claw').

The present volume contains the following articles of interest:
Jakob Bernoulli:
1, Observatiuncula ad ea quaenupero mense novembri de Dimensionibus Curvarum leguntur.
2, Constructio Generalis omnium Curvarum transcendentium ope simplicioris Tractoriae et Logarithmicae.
3, Problema Beaunianum universalius conceptum.
4, Complanatio Superficierum Conoidicarum et Sphaeroidicarum.

Johann Bernoulli
5, Demonstratio Analyticea et Syntetica fuae Constructionis Curvae Beaunianae.
6, Tetragonismus universalis Figurarum Curvilinearum per Construitionem Geometricam continuo appropinquantem.

Tschirnhaus
7, Intimatio singularis novaeque emendationis Artis Vitriariae.
8, Responsio ad Observationes Dnn. Bernoulliorum, quae in Act. Erud. Mense Junio continentur.
9, Additio ad Intimationem de emendatione artis vitriariae.

Order-nr.: 42863