LEIBNITZ, GOTTFRIED WILHELM., JOHANN BERNOULLI, JACOB BERNOULLI & ISAAC NEWTON - SOLVING THE BRACHISTOCHRONE PROBLEM.

Communicatio suae pariter, duarumque alienarum ad edendum sibi a Dn. Jo. Bernoulli, deinde a Dn Marchione Hospitalio communicatarum solutionum problematici curvae..descensus a Dn. Jo. Bernpulli....propositi solutione... (Leibniz). + Curvatura Radii in Diaphanis non uniformibus, Solutioque Problematis a se in Acta 1696, propositi, de invenienda Linea Brachystochrona, id est, in qua grave a dato puncto ad datum punctum...temporere decurrit, & de curva Synchrona seu radiorum unda construenda. (Johann Bernoulli). + Solution Problematum Fraternorum, Peculiari Programmatis ...., nec non Actorum Lips.... propositorum: una cum Propositione reciproca aliorum. (Jacob Bernoulli). + Excerpta ex Transactionibus Philos. Anglic...Epistola missa ad ...D. Carolum Mountague .... in qua solvuntur duo problemata Mathematica a Johanne Bernpulli...proposita. (Newton).

Leipzig, Grosse & Gleditsch, 1697. 4to. No wrappers. In: "Acta Eruditorum Anno MDCXCVII", No V, May-issue. Pp. 193-240 (entire issue offered). With titlepage to the volume 1697. Leibniz: pp. 201-205. Johann Bernoulli: pp. 206-211. Jacob Bernoulli: pp. 211-214. Newton: pp. 223-224. As usual, some leaves with browning.

First appearance of the famous issue of Acta Eruditorum in which the 4 solutions by the 4 most eminent mathematicians at the time, were printed together. There were in all 5 solutions to the posed problem, and Newton's solution was first printed in the Philosophical Transactions (January 1697) and reprinted here. The solution proposed by L'Hopital, not printed here, was not published until 1988.

The brachistochrone problem was posed by Johann Bernoulli in Acta Eruditorum in June 1696. He introduced the problem as follows: "I, Johann Bernoulli, address the most brilliant mathematicians in the world. Nothing is more attractive to intelligent people than an honest, challenging problem, whose possible solution will bestow fame and remain as a lasting monument. Following the example set by Pascal, Fermat, etc., I hope to gain the gratitude of the whole scientific community by placing before the finest mathematicians of our time a problem which will test their methods and the strength of their intellect. If someone communicates to me the solution of the proposed problem, I shall publicly declare him worthy of praise."

Johann Bernoulli and Leibniz deliberately tempted Newton with this problem. It is not surprising, given the dispute over the calculus, that Johann Bernoulli had included these words in his challenge:-
...."there are fewer who are likely to solve our excellent problems, aye, fewer even among the very mathematicians who boast that [they]... have wonderfully extended its bounds by means of the golden theorems which (they thought) were known to no one, but which in fact had long previously been published by others."

According to Newton's biographer Conduitt, he solved the problem in an evening after returning home from the Royal Mint. Newton:
... "in the midst of the hurry of the great recoinage, did not come home till four (in the afternoon) from the Tower very much tired, but did not sleep till he had solved it, which was by four in the morning."

Newton send his solution to his friend Charles Montague and Montague published anonymously in the Transactions. Newton's solution, presented here in the Acta, is also anonymous. The episode did not please Newton, as he later wrote: "I do not love to be dunned [pestered] and teased by foreigners about mathematical things ..."

After the competition Johann Bernoulli said ".... my elder brother made up the fourth of these (after Leibniz, himself and Newton), that the three great nations, Germany, England and France, each one of their own to unite with myself in such a beautiful search, all finding the same truth."

Struik (Edt.) "A Source Book in Mathematics, 1200-1800, pp. 391 ff.

Order-nr.: 45644