addressed to third parties. In a letter to Conti, April 9, 1716, Leibniz again reminded Newton of the admission he had made in the scholium, which he was now desirous of disavowing; Leibniz also states that he always believed Newton, but that, seeing him connive at accusations which he must have known to be false, it was natural that he (Leibniz) should begin to doubt. Newton did not reply to this letter, but circulated some remarks among his friends which he published immediately after hearing of the death of Leibniz, November 14, 1716. This paper of Newton gives the following explanation pertaining to the scholium in question: "He [Leibniz] pretends that in my
book of principles I allowed him the invention of the calculus differentialis, independently of my own; and that to attribute this invention to myself is contrary to my knowledge there avowed. But in the paragraph there referred unto I do not find one word to this purpose." In the third edition of the Principia, 1726, Newton omitted the scholium and substituted
in its place another, in which the name of Leibniz does not appear.
National pride and party feeling long prevented the adoption of impartial opinions in England, but now it is generally admitted by nearly all familiar with the matter, that Leibniz really was an independent inventor. Perhaps the most telling evidence to show that Leibniz was an independent inventor is found in the study of his mathematical papers (collected and edited by C. I. Gerhardt, in six volumes, Berlin, 1849–1860),
which point out a gradual and natural evolution of the rules of the calculus in his own mind. "There was throughout the whole dispute," says De Morgan, "a confusion between
the knowledge of fluxions or differentials and that of a calculus of fluxions or differentials; that is, a digested method with general rules."
This controversy is to be regretted on account of the long and bitter alienation which it produced between English and Continental mathematicians. It stopped almost completely all interchange of ideas on scientific subjects. The English adhered closely to Newton's methods and, until about 1820,
remained, in most cases, ignorant of the brilliant mathematical discoveries that were being made on the Continent. The loss in point of scientific advantage was almost entirely on the side of Britain. The only way in which this dispute may be said, in a small measure, to have furthered the progress of mathematics, is through the challenge problems by which each side attempted to annoy its adversaries.
The recurring practice of issuing challenge problems was inaugurated at this time by Leibniz. They were, at first, not intended as defiances, but merely as exercises in the new calculus. Such was the problem of the isochronous curve (to
find the curve along which a body falls with uniform velocity), proposed by him to the Cartesians in 1687, and solved by James Bernoulli, himself, and John Bernoulli. James Bernoulli
proposed in the Leipzig Journal the question to find the curve (the catenary) formed by a chain of uniform weight
suspended freely from its ends. It was resolved by Huygens,