When the letter of Leibnitz, therefore, was read, Keill appealed to the registers of the society for the proofs of what he had advanced; Sir Isaac also expressed his displeasure at the obnoxious passage in the Leipsic Review, and at the defence of it by Leibnitz, and he left it to the society to act as they thought proper. A committee was therefore appointed on the 11th March, consisting of Dr. Arbuthnot, Mr. Hill, Dr. Halley, Mr. Jones, Mr. Machin, and Mr. Burnet, who were instructed to examine the ancient registers of the society, to inquire into the dispute, and to produce such documents as they should find, together with their own opinions on the subject. On the 24th April the committee produced the following report:—
“We have consulted the letters and letter-books in the custody of the Royal Society, and those found among the papers of Mr. John Collins, dated between the years 1669 and 1677, inclusive; and showed them to such as knew and avouched the hands of Mr. Barrow, Mr. Collins, Mr. Oldenburg, and Mr. Leibnitz; and compared those of Mr. Gregory with one another, and with copies of some of them taken in the hand of Mr. Collins; and have extracted from them what relates to the matter referred to us; all which extracts herewith delivered to you we believe to be genuine and authentic. And by these letters and papers we find,—
“I. Mr. Leibnitz was in London in the beginning of the year 1673; and went thence, in or about March, to Paris, where he kept a correspondence with Mr. Collins by means of Mr. Oldenburg, till about September, 1676, and then returned by London and Amsterdam to Hanover: and that Mr. Collins was very free in communicating to able mathematicians what he had received from Mr. Newton and Mr. Gregory.
“II. That when Mr. Leibnitz was the first time in London, he contended for the invention of another differential method properly so called; and, notwithstanding that he was shown by Dr. Pell that it was Newton’s method, persisted in maintaining it to be his own invention, by reason that he had found it by himself without knowing what Newton had done before, and had much improved it. And we find no mention of his having any other differential method than Newton’s before his letter of the 21st of June, 1677, which was a year after a copy of Mr. Newton’s letter of the 10th of December, 1672, had been sent to Paris to be communicated to him; and above four years after, Mr. Collins began to communicate that letter to his correspondent; in which letter the method of fluxions was sufficiently described to any intelligent person.
“III. That by Mr. Newton’s letter of the 13th of June, 1676, it appears that he had the method of fluxions above five years before the writing of that letter. And by his Analysis per Æquationes numero Terminorum Infinitas, communicated by Dr. Barrow to Mr. Collins in July, 1669, we find that he had invented the method before that time.
“IV. That the differential method is one and the same with the method of fluxions, excepting the name and mode of notation; Mr. Leibnitz calling those quantities differences which Mr. Newton calls moments or fluxions; and marking them with the letter d—a mark not used by Mr. Newton.
“And therefore we take the proper question to be not who invented this or that method, but who was the first inventor of the method. And we believe that those who have reputed Mr. Leibnitz the first inventor knew little or nothing of his correspondence with Mr. Collins and Mr. Oldenburg long before, nor of Mr. Newton’s having that method above fifteen years before Mr. Leibnitz began to publish it in the Acta Eruditorum of Leipsic.
“For which reason we reckon Mr. Newton the first inventor; and are of opinion that Mr. Keill, in asserting the same, has been no ways injurious to Mr. Leibnitz. And we submit to the judgment of the society whether the extract and papers now presented to you, together with what is extant to the same purpose in Dr. Wallis’s third volume, may not deserve to be made public.”
This report being read, the society unanimously ordered the collection of letters and manuscripts to be printed, and appointed Dr. Halley, Mr. Jones, and Mr. Machin to superintend the press. Complete copies of it, under the title of Commercium Epistolicum D. Johannis Collins et aliorum de analysi promota, were laid before the society on the 8th January, 1713, and Sir Isaac Newton, as president, ordered a copy to be delivered to each person of the committee appointed for that purpose, to examine it before its publication.
Leibnitz received information of the appearance of the Commercium Epistolicum when he was at Vienna; and “being satisfied,” as he expresses it, “that it must contain malicious falsehoods, I did not think proper to send for it by post, but wrote to M. Bernouilli to give me his sentiments. M. Bernouilli wrote me a letter dated at Basle, June 7th, 1713, in which he said that it appeared probable that Sir Isaac Newton had formed his calculus after having seen mine.”[67] This letter was published by a friend of Leibnitz, with reflections, in a loose sheet entitled Charta Volans, and dated July 29, 1713. It was widely circulated without either the name of the author, printer, or place of publication, and was communicated to the Journal Literaire by another friend of Leibnitz, who added remarks of his own, and stated, that when Newton published the Principia in 1687, he did not understand the true differential method; and that he took his fluxions from Leibnitz.