<36>

CHAPTER XV.

NICOLAS FACIO DE DUILLIER ATTACKS LEIBNITZ — LEIBNITZ APPEALS TO NEWTON — HE REVIEWS NEWTON'S 'QUADRATURE OF CURVES,' AND ACCUSES HIM OF PLAGIARISM — NEWTON'S OPINION OF THE REVIEW — DR. KEILL DEFENDS NEWTON AS THE TRUE INVENTOR OF FLUXIONS, AND APPARENTLY RETORTS THE CHARGE OF PLAGIARISM ON LEIBNITZ, WHO COMPLAINS TO THE ROYAL SOCIETY — KEILL EXPLAINS HIS DEFENCE — THE ROYAL SOCIETY APPROVES OF HIS EXPLANATION — LEIBNITZ CALLS KEILL AN UPSTART, AND BEGS THE ROYAL SOCIETY TO SILENCE HIM — THE SOCIETY APPOINTS A COMMITTEE TO INQUIRE INTO THE CLAIMS OF LEIBNITZ AND NEWTON — THE COMMITTEE REPORT TO THE SOCIETY, WHO PUBLISH THE RESULT IN THE 'COMMERCIUM EPISTOLICUM' — INSTIGATED BY LEIBNITZ, JOHN BERNOULLI ATTACKS THE REPORT, AND ASSERTS, IN A PRIVATE LETTER TO LEIBNITZ, THAT HE WAS THE FIRST INVENTOR OF THE NEW CALCULUS — LEIBNITZ CIRCULATES THIS LETTER IN A CHARTA VOLANS, AND GIVES UP BERNOULLI AS THE AUTHOR OF IT — KEILL REPLIES TO THIS LETTER, AND ATTACKS BERNOULLI AS ITS AUTHOR, WHO SOLEMNLY DENIES IT TO NEWTON — LEIBNITZ ATTACKS NEWTON IN A LETTER TO THE ABBÉ CONTI — NEWTON REPLIES TO IT — THE CONTROVERSY EXCITES GREAT INTEREST — LEIBNITZ URGES BERNOULLI TO MAKE A PUBLIC DECLARATION IN HIS FAVOUR — BERNOULLI SENDS TO LEIBNITZ THE CELEBRATED LETTER 'PRO EMINENTE MATHFMATICO,' EN CONDITION OF HIS NAME BEING KEPT SECRET — LEIBNITZ AND WOLF ALTER THIS LETTER IMPROPERLY, AND PUBLISH IT IN SUCH A FORM, THAT BERNOULLI IS PROVED TO BE ITS AUTHOR — BERNOULLI IS ANNOYED BY THE DISCOVERY, AND ENDEAVOURS, BY IMPROPER MEANS, TO EVADE THE TRUTH — THE ABBÉ VARIGNON RECONCILES NEWTON AND BERNOULLI — DEATH OF LEIBNITZ — NEWTON WRITES A HISTORY OF THE CALCULUS — GENERAL VIEW OF THE CONTROVERSY, AND OF THE CONDUCT OF THE PARTIES.

NICOLAS FACIO DE DUILLIER, a Genevese by birth, came to England in the spring of 1687, and with the exception of a visit to Switzerland in 1699, 1700, and 1701, re <37> mained there during the rest of his life. He had become acquainted with the celebrated Huygens at the Hague in 1686, and had attained to such a proficiency in mathematics, that he was introduced to Sir Isaac Newton, and visited him at Cambridge in the month of November 1692. Though only in the 28th year of his age, his health was precarious, and he seems to have consulted Newton on the subject of his spiritual as well as of his bodily condition. On his return from Cambridge, he caught a severe cold, which affected his lungs, and gave him great alarm. In communicating to Sir Isaac an account of his symptoms, he says, "I thank God that my soul is extremely quiet, in which you have had the chief hand;" and fearing that his illness would prove fatal, he expresses the "wish that his eldest brother, a man of an extraordinary integrity, shoidd succeed him in his friendship." Sir Isaac answered this letter in course of post, making inquiries about his brother, and telling Facio that he remembered him in his prayers; and Facio in reply gave him his most humble thanks, both for his prayers and his kindness, requested him thus to remember him as long as he lived, and assuring him that he always remembered him in a similar manner.[1]

<38>

Having been elected a Fellow of the Royal Society in 1687, he took an active part in its proceedings, and communicated papers to its Transactions. In the year 1699 he published a tract entitled a "Geometrical Investigation <39> of the Solid of least Resistance," in which he made the following reference to the history of the new calculus.[2]

"The celebrated Leibnitz may perhaps inquire how I became acquainted with the calculus which I use. About the month of April, and the following months in the year 1687, and subsequent years, when nobody, as I thought, used such a calculus but myself, I invented its fundamental principles, and several of its rules. Nor would it have been less known to me if Leibnitz had never been born. He may, therefore, boast of other disciples, but certainly not of me. And this would be sufficiently evident if the letters which passed between me and the illustrious Huygens were given to the public.[3] Compelled by the evidence of facts, I hold Newton to have been the first inventor of the calculus, and the earliest by several years: And whether Leibnitz, its second inventor, has borrowed anything from him, I would prefer to my own judgment that of those who have seen the letters of Newton and copies of his <40> other manuscripts. Nor will the silence of the more modest Newton, or the active exertions of Leibnitz in everywhere ascribing the invention of this calculus to himself, impose upon any person who shall examine these documents as I have done."[4]

Strong as these expressions are, they cannot be regarded as charging Leibnitz with plagiarism. He is styled the second inventor, the title with which he, on many occasions, expressed himself satisfied, and he is blamed only for everywhere ascribing the invention to himself. In replying to Duillier,[5],Leibnitz appealed to Newton himself as having stated, in the celebrated scholium, that the new calculus was common to them both, and that neither had received any light from the other;[6] and, without disputing or acknowledging the priority of Newton's claim, he asserted his own right to the discovery of the differential calculus. Facio sent a reply to the editors of the Acta Eruditorum, but they refused to print it on the ground of their aversion to controversy.[7] The controversy therefore terminated for the present, and the contending parties laid down their arms, ready to resume them on the slightest provocation.

When Newton published his Treatise on the Quadrature ot Curves, along with his Optics in 1704, he mentioned in his introduction that he had gradually found the method of fluxions in the year 1665 and 1666. A review of this <41> work, by Leibnitz,[8] but without his name, was published in the Acta Eruditorum for January 1705. After giving an imperfect analysis of its contents, he compared the method of fluxions with the differential calculus, and, in a sentence of some ambiguity, he states that Newton employed fluxions in place of the difterences of Leibnitz, and made use of them in his Principia in the same manner as Honoratus Fabri, in his Synopsis of Geometry, had substituted progressive motion in place of the indivisibles of Cavalieri. As Fabri, therefore, was not the inventor of the method which is here referred to, but borrowed it from Cavalieri, and only changed the mode of its expression, there can be no doubt that the artful insinuation contained in the above passage was intended to convey the impression that Newton had stole his method of fluxions from Leibnitz. That this was the view of it taken by the friends of Newton will presently appear. That it was the view taken by Newton himself we are fortunately able to prove from the following passage in his own handwriting,[9] which is so important that we copy it without any change.

"In the Acta Eruditorum for 1705,[10] an account of the Introduction to the Book of Quadratures was published in these words: — 'Quæ [Isagogen or Preface] ut MELIUS intelligatur sciendum est cum magnitudo aliqua continue crescit veluti linea, exempli gratia crescit fluxu puncti, quod eam describit, incrementa illa momentanea est producta appellavi DIFFERENTIAS, nempe inter magnitudinem quæ antea erat et quæ per mutationem momentaneam est producta; atque hinc natum esse calculum <42> Differentialem, eique reciprocum summatorium,[11] cujus elementa ab INVENTORE D. Godofredo Guillielmo Leibnitio in his actis sunt tradita, variisque usus tum ab ipso, tum a DD. Fratribus Bernoulliis, tum a D. Marchione Hospitalio sunt ostensi. Pro Differentiis IGITUR Leibnitianis D. Newtonus adhibet, semperque [pro iisdem] adhibuit fluxiones, iisque tum in suis Principiis Naturæ Mathematicis, tum in aliis postera editis [pro Differentiis Leibnitianis] eleganter est usus, QUEMADMODUM ut Honoratus Fabrius in sua synopsi Geometrica motuus progressus Cavallerianæ methodo SUBSTITUIT.' And all this is as much as to say that I did not invent the method of fluxions in the years 1665 and 1666, as I affirmed in this Introduction, but that after Mr. Leibnitz, in his letter of 21st June 1677, had sent me his differential method, instead of that method, I began to use, and have ever since used, the method of fluxions."[12]

That Newton was virtually accused of plagiarism by the reviewer, cannot, we think, admit of a doubt. The indirect and ambiguous manner in which the charge is couched, and the artful reference to the case of Fabri and Cavalieri, make it doubly reprehensible; and we are persuaded that no candid reader can peruse the passage without a strong conviction that it justifies, in the fullest manner, the indignant feelings which it excited among the English philosophers. If Leibnitz, in place of being the author of the review, had been merely a party to it, <43> he merited the full measure of rebuke which was dealt out to him by the friends of Newton, and deserved those severe reprisals which doubtless embittered the rest of his days. He who dares to accuse a man like Newton, or indeed any man holding a fair character in society, of the odious crime of plagiarism, places himself without the pale of the ordinary courtesies of life, and deserves to have the same charge thrown back upon himself. The man who conceives his fellow to be capable of such intellectual felony, avows the possibility of himself committing it, and almost substantiates the weakest evidence of the worst accusers.

Dr. Keill, as the representative of Newton's friends, could not brook this concealed attack upon his countryman. In a letter on the Laws of Centripetal Forces, addressed to Halley, and printed in the Philosophical Transactions for 1708,[13] he stated that Newton was "beyond all doubt" the first inventor of fluxions; and he asserted "that the same calculus was afterwards published by Leibnitz, the name and the mode of notation being changed." If the reader is disposed to consider this passage as retorting the charge of plagiarism upon Leibnitz, he will readily admit that the mode of its expression is neither so coarse nor so insidious as that which is used by the writer in the Acta Eruditorum. In a letter to Hans Sloane, dated 4th March 1711, Leibnitz complained to the Royal Society of the treatment he had received. "Nobody", says he, "knew better than Newton that this charge is false, for certainly I never heard of the name of the Calculus of Fluxions, nor saw with these eyes the characters which Newton used." He expressed his conviction that Keill had erred <44> more from rashness of judgment than from any improper motive. He did not regard the accusation as a calumny; and he requested that the Society would desire Mr. Keill to disown publicly the injurious sense which his words might bear. When this letter was read to the Society, Keill justified himself to Sir Isaac Newton and the other members, by showing them the obnoxious article on the Quadrature of Curves in the Acta Eruditorum, and they all agreed in attaching the same injurious meaning to the passage in the review. The discussion excited so much interest, that, on the 5th April 1711, Newton gave, from the chair of the Society, "a short account of his invention, with the particular time of his first mentioning or discovering it ;[14] upon which Mr. Keill was desired to draw up an account of the matter in dispute, and set it in a just light."[15] This account, contained in a letter to Sir Hans Sloane, was read at the Society on the 24th May 1711, and a copy of it was ordered to be sent to Leibnitz. In this letter, which is one of considerable length, Dr. Keill declares that he never meant to state that Leibnitz knew either the name of Newton's method or the form of notation, and that the real meaning of the <45> passage was, "that Newton was the first inventor of fluxions, or of the differential calculus, and that he had given, in two letters to Oldenburg, and transmitted to Leibnitz, indications of it sufliciently intelligible to an acute mind,[16] from which Leibnitz derived, or was able to derive, the principles of his calculus."

The charge of plagiarism which Leibnitz thought was implied in the former letter of his antagonist, is here greatly modified, if not altogether denied. Keill expresses only an opinion that the letters seen by Leibnitz contained intelligible indications of the fluxionary calculus, from which he either derived, or might derive, the principles of his calculus. Even if this opinion were correct, it is no proof that Leibnitz either saw these indications or availed himself of them; or if he did perceive them, it might have been in consequence of his having previously been in possession of the differential calculus, or having enjoyed some distant view of it. Leibnitz should, therefore, have allowed the dispute to terminate here; for no ingenuity on his part, and no additional facts, could affect an opinion which any other person as well as Keill was entitled to maintain.[17]

<46>

Leibnitz, however, took a different view of the subject, and wrote a letter to Sir Hans Sloane, dated December 29, 1711, which excited new feelings, and involved him in new embarrassments. Insensible to the mitigation which had been kindly impressed upon the supposed charge against his honour, he alleges that Keill had attacked his candour and sincerity more openly than before; — that he acted without any authority from Sir Isaac Newton, who was the party interested; — and that it was in vain to justify his proceedings by referring to the provocation in the Acta Eruditorum, because, in that journal, no injustice had been done to any party, but every one had received what was his due. He asserts, that he discovered the calculus some years before he published it, that is in 1675, or earlier. He brands Keill with the odious appellation of an upstart, and one little acquainted with the circumstances of the case;[18] and he calls upon the Society to silence his vain and unjust clamours,[19] which, he believed, were disapproved by Newton himself, <47> who was well acquainted with the facts, and who, he was persuaded, would willingly give his opinion on the matter.

This unfortunate letter was doubtless the cause of all the rancour and controversy which so speedily followed, and it placed his antagonist in a new and a more favourable position. It may be correct, though few will admit it, that Keill's second letter was more injurious than the first; but it was not true that Keill acted without the authority of Newton, because Keill's letter was approved of, and transmitted, by the Royal Society, of which Newton was the president, and therefore became the act of that body. The obnoxious part, however, of Leibnitz's letter, consisted in his appropriating to himself the opinions of the reviewer in the Leipsic Acts, by declaring that, in a review which charged Newton with plagiarism, every person had got what was their due. The whole character of the controversy was now changed: Leibnitz places himself in the position of the party who had first disturbed the tranquillity of science by maligning its most distinguished ornament; and the Royal Society was imperiously called upon to throw all the light they could upon a transaction which had exposed their venerable president to so false a charge. The Society, too, had become a party to the question, by their approbation and transmission of Keill's second letter, and were on that account alone bound to vindicate the step which they had taken.

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 Acta Eruditorum, and at the defence of it by Leibnitz, and he left it to the Society to act as they thought proper.

<48>

In this emergency, a committee of the Royal Society was appointed on the 6th March 1712, "to inspect the letters and papers relating to the dispute, consisting of Dr. Arbuthnot, Mr. Hill, Dr. Halley, Mr. Jones, Mr. Machin, and Mr. Burnet." Mr. Robarts, a contributor to the Transactions, was added to the committee on the 20th of March, M. Bonet, the Prussian Minister, on the 27th, and Mr. De Moivre, Mr. Aston, and Dr. Brook Taylor, on the 17th of April.[20] The committee, thus constituted, was instructed to examine the registers of the Society, and to lay before it such documents as they might discover, with their own opinions on the subject. This committee, probably from being called consessus arbitrorum, has been supposed to have been a judicial committee; but, as Professor De Morgan has shewn, and as Newton himself has asserted, it had no such character, since none of Leibnitz's friends were placed upon it, and no invitation given him to produce documents in his defence. The committee consisted entirely of Newton's friends; and several of them, though qualified to attest the genuineness of the documents in the report, were not fitted, by their mathematical acquirements, to give an opinion on the subject.[21]

<49>

On the 24th of April the committee gave in the following report, which was in the handwriting of Halley: —

"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. That 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 Mouton's method, he persisted in maintaining it to be his own invention, by reason that he had found it by himself, without <50> knowing what Mouton had done before, and had much improved it. And we find no mention of his having any other differential method than Mouton's, before his letter of 21st June 1677, which was a year after a copy of Mr. Newton's letter, of the 10th 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 correspondents; in which letter the method of fluxions was sufficiently described to any intelligent person.

"III. That by Mr. Newton's letter of the 13th 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 the 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 reasons we reckon Mr. Newton the first inventor; and are of opinion that Mr. Keill, in asserting <51> the same, has been noways injurious to Mr. Leibnitz. And we submit to the judgment of the Society, whether the extracts, and letters, and papers, now presented, 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 and agreed to, the Society unanimously adopted it, 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.[22]

According to Leibnitz, he 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. Bernoulli to give me his sentiments.[23] M. Bernoulli wrote me a letter, dated at Basle, June 7, 1713, in which he said, that it appeared prohable that Sir Isaac Newton had formed his calculus after having seen mine."[24] This letter was published in Latin, by Leibnitz, with reflections, in a loose sheet, entitled Charta Volans, dated July 29, 1713, and <52> was widely circulated, without either the name of the author, printer, or place of publication, and giving the names of N——n and L——z, with their initial and final letters.

The origin of this letter is curious and instructive. In writing to Leibnitz on the 28th February, 1713, Bernoulli says, that he has informed Newton of some of his mistakes,[25] but in a very gentle manner, that he might not give offence to one who had been very kind to him in getting him elected a Fellow of the Royal Society, and as showing much attention to his son when in London. In Leibnitz's reply of the 16th March, he remarks that Newton wishes to ingratiate himself with him, and he adds, we shall see what can be elicited from the correspondence with Collins, which, owing to his absence from home, he may not see so early as he will. Bernoulli had now received from Paris a copy of the Commercium Epistolicum, and in replying to Leibnitz on the 7th of June he gives him a general account of the Report of the Committee, and adds in a couple of pages his own opinion of it, which constitutes the celebrated letter of the 7th June 1713, inserted by Leibnitz in the Charta Volans. He concludes the letter by imploring Leibnitz "to make a right use of what he has written, and not compromise him with Newton and his countrymen, as he was unwilling to be mixed up with these controversies."[26] In spite of this request, Leibnitz not only gave up Bernoulli as the author of the letter, but had insidiously inserted in a parenthesis, and in the same type, as if it had been written by the author, the words, as was long ago remarked by a certain eminent mathematician, which placed Bernoulli in the ridiculous position of praising himself.

<53>

Previous to the publication of the Charta Volans, Dr. Keill sent to the Journal Littéraire for 1713,[27] some remarks on the controversy, with the Report of the Committee, and Newton's important letter to Collins, dated 10th December, 1672. An anonymous answer,[28] but certainly written by Leibnitz, appeared in the same work for November and December 1713. It contained a French translation of the Charta Volans, and of the letter of a very eminent mathematician, dated 7th June 1713, on the subject of the controversy, the same letter which Leibnitz mentions to Count Bothmar, as the production of Bernoulli.[29] In this letter Bernoulli asserts that Newton in his researches confesses that he never even thought of Fluxions, and had not invented them before the differential calculus. He maintains that he was ignorant, when he wrote the Principia, of the true way of taking the fluxions of fluxions, and he accused him of having deprived Hook and Flamsteed of their just honours, the one for his hypothesis of the planets, and the other for the use of his observations.

Newton was indignant at this new attack upon his character, which was sent to him in the autumn of 1713, by Mr. Chamberlayne, who then kept a correspondence with Leibnitz, and he immediately drew up a sharp <54> reply,[30] which was probably sent to Keill, as the groundwork of his long and elaborate answer, which appeared in the Journal Littéraire for July and August 1714.[31] Bernoulli was supposed by both to be the very eminent mathematician[32] who wrote the letter of the 7th June 1713, and but for Leibnitz's indiscretion, his name would never have been known. Never doubting that Bernoulli was the author, Keill endeavoured to prove it, and exposed with great severity the incorrectness and injustice of his charges against Newton. Notwithstanding the repeated declarations of Leibnitz, that Bernoulli was the author of this letter, Bernoulli himself disavowed it to M. Des Maizeaux, to M. Montmort, and to the Abbé Varignon; and in a letter to Newton, dated 3d November 1719, he declared that he was not the author of it, and that too with such solemnity that Newton believed him, and would not <55> listen to Keill and his other friends when they expressed an opposite opinion. "I beseech you," says he,[33] "and I adjure you, by all that is sacred, that you will firmly believe that anything published without a name, in which a sufficiently honourable mention of you has not been made, has been falsely imputed to me. . . . Far be it from me to believe that Leibnitz, that truly excellent man, wished to deceive you by mentioning me. It is more credible that he was deceived either by his own conjecture or that of others, and yet he was not altogether blameless, in so far as he rashly and imprudently committed to writing anything of which he had no knowledge." The dishonesty of Bernoulli, thus placed beyond a doubt, is equalled only by the dishonourable conduct of Leibnitz in betraying his friend.[34] Anxious to obtain the opinion of a great mathematician in favour of his own claims, and against those of Newton, he asked Bernoulli, as we have seen, to do him this favour. This request of his patron and friend was readily granted, but under the obligation that his name should be concealed. Leibnitz, however, was not satisfied with this anonymous tribute to his genius, and did not scruple to obtain for it all its value by violating his word, and exposing his friend to the enmity of Newton, and the keen shafts of Keill, of <56> which we shall presently see he stood in great alarm. During the interval between the date of Bernoulli's letter, namely, the 7th June, and that of the Charta Volans, in which Leibnitz published it, namely, the 29th July 1713, he seems to have felt how little was the value of the anonymous testimony which he had received; he therefore writes to Bernoulli on the 28th June, "that he expects from his justice and candour that he will, as soon as possible, declare publicly among his friends, when the opportunity occurs, that the Calculus of Newton was posterior to his."[35] In replying to this letter Bernoulli assures him, that he will conceal nothing either among his friends or publicly, when the occasion demands it, and he comforts Leibnitz by saying that his fate was like that of his prince, the Elector of Hanover, whom the villanous English wished to deprive of the succession to the kingdom, in the same manner as they wished to deprive him of the possession of his calculus. Leibnitz, however, was very uneasy on the subject. He was anxious to know what the Parisians thought, for though he had no doubt that Varignon would be his friend, he feared that others would take the opportunity of attacking him.[36] He expresses the hope, however,[37] in a letter containing some severe strictures on Newton, that Varignon would take care, Bernoulli prompting him, that nothing was done in France of which he might complain.

<57>

This extreme sensitiveness, on the part of Leibnitz, we can readily excuse, but we can find no apology for his conduct in betraying so ardent a friend as Bernoulli. On a future occasion we shall find him prompting the German mathematician to another act of hostility against Newton and Keill, and a second time divulging the secret under which the favour was granted. And at the very close of his career, when his great powers had been appreciated by the world, and an immortality of reputation was dazzling his failing sight, he did not scruple to conspire with Wolf, another German mathematician of feeble morality, to vitiate a letter of Bernoulli, and leave a shadow upon his name which the lustre of his genius will never be able to efface.

Amid the feelings excited by the letter of the eminent mathematician, Mr. Chamberlayne, whom we have already mentioned as the correspondent of Leibnitz, conceived the design of reconciling the two distinguished philosophers; and, in a letter, dated April 28th, 1714,[38] he addressed himself to Leibnitz, who was still at Vienna. In replying to this letter, Leibnitz declared that he had given no occasion for the dispute; "that Newton procured a book to be published, which was written purposely to discredit him, and sent it to Germany, France, and Italy, as in the name of the Society;" and he stated "that there was great room to doubt whether Newton knew his invention before he had it from him." Mr. Chamberlayne communicated this letter to Sir Isaac Newton, who replied, that Leibnitz had attacked his reputation in 1705, by intimating that he had borrowed from him the method of fluxions; that if Mr. C. could point out to him anything in which he had injured Mr. Leibnitz, he would endeavour <58> to give him satisfaction; that he would not retract things which he knew to be true; and that he believed that the committee of the Royal Society had done no injustice by the publication of the Commercium Epistolicum. In another letter, Leibnitz expressed his entire disapprobation of the Report of the Committee, and of the Commercium, declaring, at the same time, more than a year and a half after two copies had been sent to him, that he had not yet seen the book published against him, and requesting Mr. Chamberlayne to submit his letter to the Society.

When the letter was laid before a meeting of the Society on the 20th of May, 1714, they came to the following resolution: —

" It was not judged proper (since this letter was not directed to them) for the Society to concern themselves therewith, nor were they desired so to do. But if any person had any material objection against the Commercium, or the Report of the Committee, it might be reconsidered at any time."

This resolution was sent to Leibnitz, who, in a letter to Chamberlayne, dated 25th August 1714, justly observes that the Society "did not pretend that the Report of the Committee should pass for a decision of the Society."[39] <59> Along with the resolution, Mr. Chamberlayne sent to Leibnitz, Sir Isaac's letter and Dr. Keill's answer to the papers inserted in the Journal Littéraire, and after perusing them, he replied, "that Sir Isaac's letter was written with very little civility, that he considered it non scripta, as well as the piece printed in French (by Dr. Keill); that he was not in a humour to put himself in a passion against such people; that there were other letters among those of Oldenburg and Collins which should have been published; and that on his return to Hanover he would be able to publish a Commercium Epistolicum, which would be of service to the history of learning." When this letter was read to the Royal Society, Sir Isaac remarked, that the last part of it injuriously accused the Society of having made a partial selection of papers for the Commercium Epistolicum; that he did not interfere in any way in the publication of that work, and had even withheld from the committee two letters, one from Leibnitz in 1693, and another from Wallis in 1695, which were highly favourable to his cause.[40] He stated that he did not think it right for Mr. Leibnitz himself to publish a Commercium Epistolicum, but if he had letters to produce in his favour, that they might be published in the Philosophical Tratisactions, or in Germany.

About this time the Abbé Conti, a noble Venetian, came to England. He was a correspondent of Leibnitz, <60> and in the postscript of a letter which he had received from him soon after his arrival,[41] and written in November or December 1715, he enters upon his dispute with Newton. He charges the English with "wishing to pass for almost the only inventors." He declares "that Bernoulli has judged rightly in saying, that Newton did not possess before him the infinitesimal characteristic and algorithm." He remarks that Newton preceded him only in series; and he confesses that during his second visit to England, "Collins showed him part of his correspondence," or, as he afterwards expresses it, he saw "some of the letters of Newton at Mr. Collins's." He represents the metaphysics of the English as narrow, (borée,) and their mathematics as common or superficial. He then attacks Sir Isaac's philosophy, particularly his opinions about gravity and a vacuum, the intervention of God for the preservation of his creatures; and he accuses him of reviving the occult qualities of the schools. But the most remarkable passage in the letter is the following: "I am a great friend of experimental philosophy, but Newton deviates much from it when he pretends that all matter is heavy, or that each particle of matter attracts every other particle." The letter concludes with a problem, which he requests Conti to propose, "in order to feel the pulse of the English analysts."

Under these cirumstances, and influenced by the advice of Keill, which we have already mentioned, Sir Isaac became anxious that foreigners of distinction should see the original papers which had been preserved in the archives of the Society, and compare them with the other letters of Leibnitz. He therefore requested the Abbé Conti to assemble the ambassadors and other foreign <61> ministers for this purpose, and when they had met in the apartment of the Society and collated the papers, the Baron de Kilmansegg, the Hanoverian minister, remarked that this measure was not a sufficient one, and that the right way of terminating the dispute was that Newton himself should write a letter to Leibnitz, stating to him "his reasons," and demanding a direct answer to them. All the ministers who were present approved of this suggestion, and the king, to whom it was mentioned in the evening, gave it his hearty approbation.

Conti reported these proceedings to Sir Isaac, and in five or six days he received a letter from him, dated February 26, 1715-16, to be sent to Leibnitz, who was then in Hanover. As this letter was addressed to Conti, he enclosed it in one of his own, dated — March 1716, which he had previously read to Newton. Mr. Demoivre had corrected it, and added the part which related to the equivocal manner in which Leibnitz had proposed the problem for the English analysts. The letter of Conti, with Newton's enclosed, which was to be taken to Hanover by the Baron de Discau, remained more than a month in London. Madame de Kilmansegg had it translated into French. The king read it, and approved of it so highly as to say, that the reasons were very simple and clear, and that it would be difficult to reply to the facts.[42]

This letter of Newton's was the first occasion on which he appeared in the controversy in his own person. Reluctantly driven into the field, he did not hesitate to give utterance to the opinions which had been maintained by Keill. In a tone of dignified severity he gave a brief <62> notice of the controversy, and triumphantly refuted the allegations of his adversary. "Finding it impossible," he says, "to reply to matter of fact, Leibnitz invoked the opinion of a mathematician or pretended mathematicians, dated 7th June 1713, and inserted it in an anonymous defamatory letter of the 29th July, which he circulated in Germany," — a letter which had been answered by Keill, and to which no reply had been returned. He charges Leibnitz with trying to engage him in philosophical disputes, and challenging him to the solution of problems which have no relation whatever to the question in dispute; and he makes some severe observations on Leibnitz's doctrine of the Preestablished Harmony, which he pronounces a true miracle, and contrary to all experience. He cites a passage from Leibnitz's letter to himself, dated March 7, 1693, in which he acknowledges the value of Newton's discoveries; and he makes the following observations on that branch of the dispute which relates to Leibnitz's having seen part of Newton's letters to Mr. Collins. "He (Leibnitz) complains of the committee of the Royal Society, as if they had acted partially in omitting what made against me; but he fails in proving the accusation. He quotes a passage concerning my ignorance, pretending that it was omitted in the Commercium Epistolicum, and yet you will find it there in p. 74, lines 10, 11, and I am not ashamed of avowing it. He says that he saw this paragraph in the hands of Mr. Collins when he was in London the second time, that is in October 1676; and as this is in my letter of the 24th of October 1676, he therefore then saw that letter. And in that and some other letters writ before that time, I described my method of fluxions; and in the same letter I described also two general methods of series, one of which is now claimed <63> from me by Mr. Leibnitz." The letter concludes with the following paragraph: "But as he has lately attacked me with an accusation which amounts to plagiary; if he goes on to accuse me, it lies upon him by the laws of all nations to prove his accusations, on pain of being accounted guilty of calumny. He hath hitherto written letters to his correspondents full of affirmations, complaints, and reflections, without proving anything. But he is the aggressor, and it lies upon him to prove the charge."

In transmitting this letter to Leibnitz, the Abbé Conti informed him that he himself had read with great attention, and without the least prejudice, the Commercium Epistolicum, and the little piece[43] that contains the extract; that he had also seen at the Royal Society the original papers of the Commercium Epistolicum, and some other original pieces relating to it. "From all this," says he, "I infer, that, if all the digressions are cut off, the only point is, whether Sir Isaac Newton had the method of fluxions or infinitesimals before you, or whether you had it before him. You published it first, it is true, but you have owned also that Sir Isaac Newton had given many hints of it in his letters to Mr. Oldenburg and others. This is proved very largely in the Commercium, and in the extract of it. What answer do you give? This is still wanting to the public, in order to form an exact judgment of the affair." The Abbé adds, that Mr. Leibnitz's own friends waited for his answer with great impatience, and that they thought he could not dispense with <64> answering, if not Dr. Keill, at least Sir Isaac Newton himself, who had given him a defiance in express terms. In the close of his letter he informs Leibnitz that several geometers in London and Oxford have solved his problem, and he tells him that he will take some other opportunity of speaking to him of Newton's philosophy, which has been greatly misapprehended.

Leibnitz was not long in replying to the request of the Abbé Conti, and the defiance of Newton. He addressed a letter to the former on the 9th of April 1716, but he sent it through M. Remond de Montmort, to be communicated to the mathematicians[44] in Paris, as neutral and intelligent witnesses, and then transmitted to Conti. In the letter to the Abbé, which was dated 14th April, he tells him that he may judge from all this, if "the wicked chicanery of his new friends has greatly embarrassed him," and he closes his letter with a reference to the pro <65> blem, "for feeling the pulse of the English analysts," which he tells him was proposed by Bernoulli.[45]

The letter of Leibnitz of the 9th April is bold and ingenious. He defends the statements in the anonymous attacks upon Newton as if they were his own. He gives an account of his two visits to London, and mentions what he there saw and learned. He charges Newton with retracting his admission in the scholium, and thus considers himself entitled to retract his admission in favour of Newton. He introduces again his metaphysical opinions as having been misrepresented by Newton, and he concludes by denying that he was the aggressor, and had accused Newton of plagiarism.

On the very day when Leibnitz was writing this letter, Bernoulli was engaged in composing his famous Epistola pro Eminente Mathematico, which has formed so curious <66> and instructive an episode in the fluxionary controversy. He had been stung by the poignancy of Keill's reply to the Charta Volans, and the severity of its animadversions on the letter of his own which it contained; and, as will be seen from his own acknowledgment, he was afraid to encounter without a mask so bold and uncompromising an antagonist. He therefore resolved to attack Keill in an anonymous letter, addressed to Christian Wolf, one of the editors of the Acta Eruditorum. This letter, dated April 8, 1716,[46] which Bernoulli, the grandson, admits was particularly directed against Newton, was sent to Wolf on condition of the most inviolable secrecy. It was to be first communicated to Leibnitz with power to change or omit what was necessary, and to print it as a letter from an anonymous person, or as if it were written by some other person with a real or a feigned name; but in whatever way this was done, Wolf was directed to manage the whole matter with his usual skill, lest Keill should suspect Bernoulli to be the author; "for," he adds. "it would be very disagreeable to me to be irritated and contumeliously treated by his bile, as his antagonists usually are, after he has hitherto treated me with sufficient politeness." Wolf expressed his great satisfaction with the attack upon "that trifler Keill," and promised to communicate it to Leibnitz, and decide according to his opinion on the form and manner in which it was to be published. The two critics, Wolf and Leibnitz, made such changes in the epistle as were agreeable to the latter, and every means were taken to keep the secret. Herman suspected that Bernoulli was the author of it, and, when he mentioned his suspi <67> cion, Wolf denied it, as he declares he always did; but though every precaution was taken to keep the secret, it was discovered by means of the phrase meam formulam, which had been either heedlessly overlooked, or, as we believe, willingly left, in order to fix it upon Bernoulli, whose public declaration against Newton, and in favour of himself, Leibnitz had expressed his anxiety to obtain. The changes made on the letter were very considerable. M. Bernoulli, the grandson, who had a copy of the original, has published the two in opposite columns,[47] and, after a careful comparison of them, he observes, "that not a single disobliging expression against Newton and Keill had been omitted or softened. It is true," he continues, "with respect to Keill, who was the more ill-treated, that his name was everywhere suppressed; and when Wolf (and Leibnitz too) calls him an audacious antagonist in one place, where the letter only called him Keill, he did worse than mention him by his name." Without noticing the fulsome praise of Leibnitz and Bernoulli, inserted in the letter, Bernoulli, the grandson, calls our attention to another point, — "to a species of fraud which Leibnitz and Wolf committed against their friend by interpolations, which they ought not to have made without his consent, seeing that they were to his disadvantage, and had principally for their object to claim for Leibnitz discoveries which Bernoulli attributed to himself. There can be no doubt that these interpolations were made by Leibnitz alone, for Wolf would not of his own accord have permitted them; but he was too much devoted to Leibnitz not to adopt what was done by his great patron."[48]

<68>

Although this letter was published in July 1716, yet Bernoulli was not aware, even in the month of March 1717, of the trick that had been played him, or of the injurious interpolations which had been made in it, or, of the worst fact of all, that the words meam formulam proved him to be the author. It was not till he heard of Herman's conjecture that he was the author, that he was induced to read the letter, and discover these unfortunate words. He immediately saw the use which would be made of them. His friends had already been laughing at the mistake, and his enemies accusing him of being the author of the letter; and he expressed his dread that Keill would seize every opportunity of cutting him up, and employing the matter against him for his own purposes. He, therefore, implored Wolf to think of some method of correcting the blunder in the errata, and he suggested that meam should read eam; but seeing that this would not answer the purpose, he begged Wolf to think of some better method, by which the mistake should be laid upon the printer. Wolf did not obey the mandate of his friend, and, on the advice of Montmort, Bernoulli was induced to avow the letter through his son Nicolas, and to make the best apology he could by throwing much of the blame upon the friends who had deceived him. The avowal, which forms the appendix to a mathematical paper, is written in a good spirit, and concludes by expressing the ardent wish of his father, that the disputants would become good friends, and unite their powers, as citizens of the republic of mathematics, in labouring to extend its <69> domains.[49] In concluding this strange history, in which Leibnitz performs the least creditable part, we are scarcely surprised at the fact stated by Bernoulli's grandson, that Wolf had the effrontery, in a histoiy of his life and writings, to claim for himself the authorship of the letter Pro Eminente Mathematico![50]

This celebrated letter, as might have been expected, excited the indignation of Newton and his friends. They had no difficulty in discovering its author;[51] and a long and elaborate reply to it, in the form of a letter to Bernoulli, was immediately prepared by Dr. Keill, and submitted to Newton, who proposed numerous alterations, and made many important additions to it. It is written with Keill's usual boldness, and ends with the following observation: — "If any person shall think that you have been treated too severely, I request them to take the trouble of reading your letter, a worthy effort of your genius, and then let them consider if you have not well deserved it.

"Si pergis dicere quæ vis, audies quæ non vis."[52]

After the death of Leibnitz, which took place on the 14th November 1716, the controversy to a considerable <70> extent ceased.[53] His champion Bernoulli withdrew from the field, when no longer influenced by his patron and friend; and though Newton has been charged with having made an improper attack upon Leibnitz after his death, he did nothing more than publish an answer, which had been previously in circulation among his friends, in the form of Remarks on the letter of Leibnitz to the Abbé Conti.[54] This paper, which is erroneously characterized by Biot as a bitter refutation, is, on the contrary, an argumentative defence of his claims, — an interesting notice of his own mathematical discoveries, — a defence of the Royal Society and of Dr. Keill, — and a frank expression of his feelings in reference to the conduct both of Leibnitz and Bernoulli.

Although Bernoulli felt the severity of Newton's censure, he was now more anxious to explain his own conduct than to retaliate upon his adversaries, and a few months had scarcely elapsed after the death of Leibnitz, before he sent messages of kindness to Newton. We have already seen that in April 1717, he not only threw the blame of the pulse-feeling problems upon Leibnitz, <71> but blamed him highly for betraying the secret under which they were sent to him. In a subsequent letter from Montmort to Newton, dated 7th March 1718, he conveys similar messages from Bernoulli and his son Nicolas, expressing their fears that their disputes with Keill had deprived them of his friendship. In replying to Bernoulli, Montmort pointed out to him the inconsistency of these expressions with the Epistola pro Eminente Mathematico, and seems to have suggested to him the propriety of disowning it. Bernoulli, however, took a middle course. He acknowledges that he had, at Leibnitz's request, sent him the facts necessary to defend himself against Keill, and was not answerable either for the praise given to himself, or the harsh language applied to his antagonists.

When Sir Isaac received Montmort's letter, he enclosed it to Keill,[55] requesting "his sense upon this matter." In his reply,[56] Keill observes that Bernoulli "is sensible that he had burnt his fingers; that he should beg Newton's pardon for saying that he did not understand second differences, — that no notice should be taken of these letters," and that "it lay on Bernoulli to clear himself, and produce the author of the scurrilous paper.

The celebrated Abbé Varignon had been long desirous of reconciling Newton and Bernoulli, and at last succeeded in the attempt. Sir Isaac had in 1718 sent Varignon three copies of the English edition of his Optics, and in 1719, as many of the Latin edition, to be presented to his friends. Varignon sent a copy of each to Bernoulli in the name of Newton,[57] and it was in Ber <72> noulli's reply, dated 10th July 1719, thanking him for these presents, that he gave the solemn denial which we have already quoted, that he was not the author of the celebrated letter to Leibnitz of 7th June 1713. In answering this letter,[58] Newton thus expressed himself, "When I first received your letters, through the mediation of the Abbé Varignon, and understood from them that you were not the author of a certain letter to Mr. Leibnitz, dated 7th June 1713, I at once resolved not only to forget the mathematical disputes which had lately taken place, but to cultivate your friendship, and to estimate highly your great mathematical merits. I have never grasped at fame among foreign nations, but I am very desirous to preserve my character for honesty, which the author of that epistle, as if by the authority of a certain great judge, had endeavoured to wrest from me. Now that I am old, I have little pleasure in mathematical studies, and I have never tried to propagate my opinions over the world, but have rather taken care not to involve myself in disputes on account of them."

The dignified tone of this letter could not fail to disturb the tranquillity of Bernoulli. Conscious of having written the letter which Newton condemns as an attack upon his honesty, he could hardly avoid referring to it in his reply, and we cannot but regret that the terms in which he again denies it are essentially different from those which he had used only a month before.[59] "I am not aware," says he, "of the nature of the letter to Leibnitz, dated 7 th June 1713, of which you speak. I do not remember that I wrote to him on that day, nor do I altogether deny it, as I do not keep copies of my letters. But if, perhaps, <73> among the innumerable letters which I have written to him, one should be found to which the said day and year is prefixed, I dare solemnly assure you, that nothing is contained in it which in any way could injure your character, and that I never gave him leave to publish any of my letters, and especially one which would not be agreeable to you. I implore you, therefore, to be persuaded, that I never intended to speak of you otherwise than as a great man, and never to attack your character and probity."

The letter of Newton, to which this was the reply, was enclosed in one to Varignon,[60] in which he thanks him for having reconciled him to Bernoulli, and mentions as the ground of his embracing him as a friend, his denial of having written the obnoxious letter to Leibnitz. Varignon was much gratified at having brought about this reconciliation, but it was a reconciliation merely nominal, and led only to a few interchanges of civility. — Bernoulli sought an explanation through Varignon, of the charge of knight errantry which Newton had made against Leibnitz and his "army of disciples," for challenging the English to the solution of mathematical problems. Newton explained that the phrase was used in a jocular sense, and applied to Leibnitz ;[61] and we believe that no farther communication took place between them till 1723, when Newton sent Bernoulli a copy of the French edition of his Optics.[62] In returning thanks for this present, Ber <74> noulli takes occasion to introduce for the third time the subject of the celebrated letter of the 7th June 1713. Hartsoecker, a Dutch philosopher, had attacked Newton's Theory of Colours, and had referred to him as his authority for charging Bernoulli with having called himself "an excellent mathematician" in the Charta Volans. After directing the attention of Newton to the attack upon his Theory of Colours, Bernoulli denies the truth of the charge against himself without distinctly denying, as he formerly did, the authorship of the letter, and seems to expect that Newton should take some step in the matter. "Although the fellow," says he, "is unworthy of any answer from me, yet one thing irritates me greatly, namely, that he exposes me to the laughter of every person, and impudently maintains that I took to myself the title of an excellent mathematician; and in order that the crime of calumny should not attach to himself, he makes you the author of it by citing the passage in which you speak of that letter of 7th June 1713, which Leibnitz maintained was written by me, and in which that eulogium, within parentheses, was ascribed to me. Hence the calumniator maliciously concludes that you wished to insinuate that I had been so arrogant as to assume this title to myself. . . . . In the meantime, whatever be the calumny of Hartsoecker, it applies more to you than to me, for he malignantly endeavours to draw it from your express words. What you think should be done therefore, that my innocence may be protected among those who do not see the Collection of Des Maizeaux,[63] I would willingly learn from yourself, if you are disposed to honour me with an answer."[64] It does not <75> appear that Newton answered this letter, or that any further correspondence took place between him and Bernoulli.

In the year 1725, a new edition of the Commercium Epistolicum was published, with notes, a general review of it,[65] and a preface of some length. A question has arisen respecting the authorship of the review and the preface, some ascribing them to Keill, and others to Newton. From similarity of style, but chiefly on the authority of Dr. James Wilson, the friend of Pemberton, Professor De Morgan had made it highly probable that both the review and the preface were written by Newton.[66] Of the correctness of this opinion I have found ample evidence in the manuscripts at Hurtsbourne Park;[67] and it is due to historical truth to state, that Newton supplied all the materials for the Commercium Epistolicum, and that, though Keill was its editor, and the committee of the Royal Society the authors of the Report, Newton was virtually responsible for its contents.

The share which Newton took in the fluxionary controversy either directly or through Dr. Keill, who did nothing without his approbation, and the mass of papers which he has left behind him on the subject, shew the great anxiety which he felt not only to be considered the first inventor of the calculus, but the only inventor who had a right to the reputation which it gave. He firmly believed, not only that Leibnitz might have derived the differential calculus from the papers actually communicated to him, but that he did derive it from that source, or from his ideas either oral or written, which were in circulation at the time of his visit to London.[68] That these <76> were the views of Newton, and, we may add, of all his friends in England, is evident from the new form given to the celebrated scholium in the third edition of the Principia, which appeared in 1725, under the editorship of Pemberton. The reference to Leibnitz and his method was wholly omitted, and replaced by a quotation from a letter to Collins in December 1672, containing, or supposed to contain, the Germ of Fluxions. This step was perhaps unwise. The statement in the two first editions granted nothing to Leibnitz, and even if it had, the truth which it embodied was not cancelled by its omission from the third; but viewing the matter as Newton did, we think he was justified in omitting the scholium. He had stated it, as he himself has said, as a mere historical fact, that Leibnitz had sent him a method which was similar to his own; and when he found that the German mathematician had regarded this simple statement as a recognition of his independent discovery of the calculus, he was not only entitled but constrained to cancel a passage which had been so erroneously interpreted, and so improperly used.

Some time after the death of Leibnitz, Newton drew up a History of the Method of Fluxions, the Preface to which has been found among his papers. I am disposed to think that this Preface was intended as an Introduction to the new edition of the Commercium Epistolicum and Recensio, which was published in 1725, and that it had not been thought advisable to enter into any fresh discussions on the subject. In the first paragraph of the Preface, Sir Isaac remarks, that as only a few copies of the Commer <77> cium had been published and sent to those only who could judge in such matters, that work and the Recensio should be again printed, in order that a true history of the calculus, drawn from ancient documents, might descend to posterity without any disputes, and "put an end to a controversy which was no longer necessary after the charge of plagiarism had been repelled." He then proceeds to enumerate by their dates seventeen letters from Leibnitz to Oldenburg, written between the 3d February 1673 and the 12th July 1677; and, after establishing his claim to the invention of the new calculus, he concludes with these words: "These things being premised, the Recensio of the Commercium Epistolicum should be read, and the Commercium itself consulted, if any doubt be entertained respecting the facts."

The following is an exact copy of the title-page of the manuscript :[69]

HISTORIA METHODI ANALYSEOS

QUAM NEWTONUS METHODUM FLUXIONUM

LEIBNITIUS METHODUM DIFFERENTIALE

VOCAVIT

IN COMMERCIO EPISTOLICO COLLINII ET ALIORUM

ET RECENSIONE COMMERCII

CONTENTA

QUORUM PRIUS EX ANTIQUIS LITERIS JUSSU REGLE S0CIETATIS

COLLECTUM FUIT ET EDITUM

ANNO 1712

ALTERA IN ACTIS PHILOSOPHICIS EJUSDEM SOCIETATIS

ANNO 1715

ANNO ET ALIQUOT MENSIBUS ANTE OBITUM LEIBNITII)

LUCEM VIDIT.

<78>

In studying this controversy, after the lapse of nearly a century and a half, when personal feelings have been extinguished, and national jealousies allayed, it is not difficult, we think, to form a correct estimate of the claims of the two rival analysts, and of the spirit and temper with which they were maintained. The following are the results at which we have arrived: —

1. That Newton was the first inventor of the Method of Fluxions; that the method was incomplete in its notation; and that the fundamental principle of it was not published to the world till 1687, twenty years after he had invented it.

2. That Leibnitz communicated to Newton, in 1677, his Differential Calculus, with a complete system of notation, and that he published it in 1684, three years before the publication of Newton's Method.

The admission of these two facts ought to satisfy the most ardent friends of the rival inventors; but in apportioning to each the laurels which they merit, new considerations have been introduced into the controversy. Conscious of his priority, Newton persisted in maintaining that the only question was, who was the first inventor, and that "second inventors have little or no honour, and no rights."[70] Upon this principle, which we cannot admit, <79> the whole merit of the new calculus must be given to Newton, and he undoubtedly claimed it. But at variance with this, there is another principle maintained in modern times, and by distinguished men, which transfers all the merit of an invention or discovery to the person who first gives it to the world. Upon this principle the merit of the new calculus must be adjudged to Leibnitz. These two extreme principles have not in the present case been adopted by the mathematical world. No writer has urged the second against the claims of Newton, or the first against those of Leibnitz. Priority of invention may be established otherwise than by publication; and the merit of a second inventor, when really such, is intellectually as great as the first. [71] There is a merit, however, of a peculiar kind which must ever attach to the first inventor who freely gives his invention to the public. While society concedes to him a high niche in the temple of fame, it cherishes also a feeling of gratitude for the gift it has received. To a second inventor society owes no obligation.

Hitherto we have taken it for granted that Newton and Leibnitz had borrowed nothing from each other; and, in stating the result of our inquiry, we have supposed this to be true. A very different opinion, however, has been maintained during the controversy. The unquestioned priority of Newton's discoveries has preserved him from the charge of having borrowed any thing from Leibnitz, excepting his ideas of notation; but a variety of circumstances, which it is necessary to mention, have given a certain degree of plausibility to the opinion that Leibnitz may have derived assistance, even of the highest <80> kind, from the previous labours of his rival. At an early period Newton had communicated to his friends, orally and in writing, the elements, or the germ of his method of fluxions, but certainly his discoveries in series. His manuscripts were copied, and, to a considerable extent, circulated in England. The letters and extracts, actually communicated to Leibnitz, may, or may not, have contained the information which Newton and his friends considered as sufficient to convey to him a knowledge of the method of fluxions; but the fact that he was twice in England in 1673 and 1676, and was in communication with the mathematicians who then adorned the metropolis of England, justified the idea that either orally, or from the circulated manuscripts[72] of Newton casually seen, or actually communicated to him, he might have derived that information.[73]

Had Leibnitz been an ordinary man, these views might have had much weight; but his powerful intellect, his knowledge of the subject, and the great improvements which he made in the new calculus, place it beyond a doubt that he was capable of inventing the differential method without any extraneous aid. His Theoria Motus Abstracti, dedicated to the Academy of Sciences in Paris in 1671, before he visited England, contains, according to Dr. William Hales,[74] "no obscure seeds of his diff'erential method;" and shows, in the opinion of Professor De Morgan, "that in 1671 it was working in Leibnitz's mind, that in the doctrine of infinitely small quantities lay the <81> true foundation of that approach to the differential calculus which Cavalieri presented."[75] Another argument in favour of Leibnitz is deduced by Professor De Morgan from seven MSS. of his, bearing the dates of November 11, 21, 22, 1675; and June 26, July, and November 1676, one bearing no date, and recently published by M. Gerhardt from the originals in the Royal Library at Hanover.[76] These MSS., of which Professor De Morgan has given a specimen, are, as he says, "study exercises in the use of both the differential and integral calculus,"[77] and, if genuine, and correct in their dates, possess a historical interest.

In adjudicating on a great question like the present, surrounded as it has been with national sympathies, we are compelled to look into the character of the parties at our bar. We cannot commend the conduct of Newton in concealing from Leibnitz, in transposed letters, the discoveries which he had made, nor can we justify his personal retreat from the battle-field, and his return under the vizor of an accomplished champion.[78] His representatives, however, were men of station and character, who gave their names, and staked their reputation in the contest; while Leibnitz and his disciples wielded the anonymous shafts of the slanderer, denied what they had written, and were publicly exposed through the very rents which they had left in their masks.

Instead of striving to prove that he was the inventor <82> of the new calculus, Leibnitz evaded the discussion by attacking the philosophy of Newton, which he did not understand, and challenging the English to the solution of mathematical problems. Nor were these problems his own. He obtained them, as we have seen, under the pledge of secrecy, from a friend whose name he did not scruple to betray; and, when the controversy was at its crisis, he tried to substitute authority for argument, by imploring the most distinguished mathematician on the Continent to declare that he was the first and the sole inventor of the new calculus. Bernoulli rashly yielded to the urgency of his patron, but, in the anonymous testimonial which he gave, Leibnitz inserted a parenthetic eulogy on the writer, which had the effect of removing his mask, and exposing him to the ridicule and laughter of the scientific world. Nor is it difficult to discover, or uncharitable to expose, the motive for the interpolation. It was intended to prove that the "eminent mathematician" was John Bernoulli, and, lest the proof should not be thought sufficient, Leibnitz publicly declared, while Bernoulli as publicly denied, that he was the author. Thus, to a certain extent, baffled in his schemes, Leibnitz, as we formerly stated, implored Bernoulli, when an opportunity should present itself, to make an early and public declaration that the method of fluxions was posterior to his calculus — that is, that Newton was a plagiarist. An opportunity soon occurred for the perpetration of this fresh act of injustice. Bernoulli unscrupulously prepared the document,[79] and, when it came into the hands of Leibnitz, <83> he imparted to it new elements of bitterness, — interpolating passages in praise of himself and Bernoulli, — altering other passages, so as to give to himself a discovery which belonged to his friend, — and, finally, leaving the words meam formulam to prove, as it did prove, to the world, that the testimony in the letter was the testimony of John Bernoulli. We have found nothing in the records of science so dishonest as this. As a portion of scientific history, closely connected with the fluxionary controversy, we have submitted it to the reader; but we have not allowed it to influence the decision which we have ventured to pronounce.

In charging Newton with plagiarism, and in persuading others to repeat and enforce the charge, we may find some apology in the excited feelings of Leibnitz, and in the insinuations which were occasionally thrown out against the originality of his discovery; but for other parts of his conduct, we seek in vain for an excuse. When he assailed the philosophy of Newton in his letters to the Abbé Conti, he exhibited only the petty feelings of a rival; but when he dared to calumniate that great and good man in his correspondence with the Princess of Wales, by whom Newton was respected and loved, — when he ventured to denounce his philosophy as physically false and dangerous to religion, — and when he founded these accusations on passages in the Principia and Optics, glowing with all the fervour of genuine piety, he cast a blot upon his name which all his talents as a philosopher will never be able to efface.[80]

[1]

Nicolas Facio de Duillier, an eminent mathematician, was born at Basle on the 16th February 1664. In 1684 and 1685 he became acquainted with Count Fenil, a Piedmontese, who, having incurred the displeasure of the Duke of Savoy, took refuge in France, where he became captain of a troop of horse. Having quarrelled one day with the commanding officer of his regiment, when drawn upon parade, the Count shot him dead, and, being well mounted, escaped from his pursuers. He fled to Alsace, where he took refuge in the house of Mr. Facio's maternal grandfather but, in order to assist him more effectually, he was sent to the house of Facio's father, who lived at Duillier. When walking alone with young Facio, the Count told him that he had offered to M. De Louvois to seize the Prince of Orange, and deliver him into the hands of the King; and he showed him the letter of M. Louvois, offering him the King's pardon, approving of the plan, and enclosing an order for money. The Prince of Orange was in the habit of taking a drive on the sands at Scheveling, <38> a village three miles from the Hague, and the Count proposed, with the aid of ten or twelve men, to land in a light ship with Dutch colours, and carry off the Prince to Dunkirk. The scheme was ripe for execution in 1686; but Facio, aware of the Count's design to take the life of his son, felt it his duty to thwart him in the commission of the two crimes which he had in view. He had become acquainted with Dr. Burnet at Geneva, and knowing that he was going to Holland to visit the Prince of Orange, he acquainted the Doctor with the Count's scheme, and agreed to accompany him to Holland with the view of explaining it to the Prince. The scheme was accordingly communicated to the Prince and Princess, and, though seconded by the latter, Monsieur Fagel and others had great difficulty in inducing the Prince to have the protection of a guard when he went abroad. In return for the services of Facio, it was resolved, on the strength of testimonials from Huygens, to create for him a professorship of mathematics for instructing the nobility and gentry of Holland, with a salary of 1200 florins, and a pension from the Prince.

Some delay having taken place in completing this arrangement, Facio got leave to pay a visit to England, where he arrived in 1687; but having been taken ill at Oxford, elected a Fellow of the Royal Society in 1687, and treated with much kindness by the English mathematicians, he remained till the accession of William III. When he visited Switzerland in 1699, 1700, and 1701, he learned that Count Fenil had received from the French Court a situation at Pignerol, a fortified city not far from Turin; and that in consequence of having conspired to surrender the place to the Duke of Savoy, he was condemned to be beheaded. In 1732 Facio endeavoured, but we believe unsuccessfully, to obtain, through the influence of Mr. Conduitt, some reward for having saved the life of the Prince of Orange. He assisted Conduitt in making out the design, and writing the inscription for Newton's Monument in Westminster Abbey.

In 1704, when Facio taught mathematics in Spitalfields, he unfortunately became secretary to the Camisards, or fanatical prophets from the Cevennes, who pretended to raise the dead, and perform other miracles. Lord Shaftesbury attacked them in his Letter on Enthusiasm; and having been unjustly suspected of some political scheme, Facio and other two prophets were seized by the police in 1707, and condemned to the pillory. On the 2d of December 1707, Facio stood on the pillory at Charing Cross with the following inscription on his hat: "Nicolas Facio convicted for abetting Klias Moner in his wicked and counterfeit prophecies, and causing them to be printed and published to terrify the Queen's people." It is stated by Spence (Observations, Anecdotes, &c., 1820, p. 159,) on the authority of Lockier, Dean of Peterborough, "that Sir Isaac Newton had a strong inclination to go and hear the French prophets, and was restrained from it with difficulty by some of his friends, who feared he might be infected by them as Facio had been." Facio spent the rest of his life at Worcester, where he died in 1753, nearly ninety years of age. See Phil. Trans. 1713, and Gentleman's Magazine, 1737, 1738.

[2]

Dr. Guhrauer, in his biography of Leibnitz, published in 1842, has most unjustly stated that Newton prompted this attack of Facio. We have carefully inspected all the manuscripts of Newton, and cannot discover the slightest evidence in support of a charge which deserves the severest reprobation.

[3]

These letters do not appear in the Correspondence of Huygens with Leibnitz and the other distinguished men of the seventeenth century, lately published by Professor Uylenbroek. There ere no letters dated between 1680 and 1690; but it appears from a letter to Leibnitz from Huygens, dated 18th November 1690, that he was acquainted with the calculus of Facio above referred to, and that it had been the subject of correspondence between these two celebrated mathematicians. Huygens tells Leibnitz that he had some share in the rule of Facio, and that it was Facio who first pointed out the mistake of Tschirnhaus. He adds that his method was a very beautiful one; and Uylenbroek, in a note on the subject, pointing at what Huygens had done in the matter, speaks of it as a fine invention. In a subsequent letter, dated 26th April l690, Leibnitz passes a high compliment to Facio. "As Facio has much penetration," he says, "I expect from him fine things when he comes to details; and having profited by your instruction and that of Newton, he will not fail to produce works which gain him distinction. I wish I were as fortunate as he is in being able to consult two such oracles." See Christiani Huygenii, aliorumque seculi xvii. virorum celebrium, Exercit. Math. et Philos., Fascic. i. p. 41, and Fascic. ii. pp. 56, 175. Hagæ Comitum, 1833.

[4]

Investigalio Geometrica, &c., p. 18. Lond. 1699.

[5]

Acta Eruditorum, 1700, p. 203.

[6]

We have already proved that Newton did not attach this meaning to his scholium; and in replying to this passage in the Recensio Commercii Epistolici, he himself distinctly denies having "acknowledged that Leibnitz invented his method by his own genius, unassisted by the letters of Newton."— Newtoni Opera, tom. iv. p. 489.

[7]

Acta Eruditorum, 1701, p. 134.

[8]

Guhrauer, the biographer of Leibnitz, proves that he was the author of the review, and affirms that Leibnitz constantly denied any knowledge of the authorship. See Essays from the Edinburgh Review, by Henry Rogers, pp. 226, 227.

[9]

A Supplement to the Remarks, p 6.

[10]

January, p. 34.

[11]

This was the name given by Leibnitz to the integral calculus, or the inverse method of fluxions.

[12]

The words within brackets are added by Newton, and bring out very distinctly the meaning of Leibnitz. In his letter to the Abbé Conti, dated 9th April 1716, Leibnitz virtually admits the authorship of the review, endeavours to give a different meaning to the words semperque adhibuit, and maintained that Newton allowed himself to be deceived by a man who poisoned his words, and sought a quarrel by the malignant interpretation of them. Newton was himself the interpreter. See Raphson's History of Fluxions, p. 103.

[13]

For September and October, p. 185.

[14]

This account was probably given to the Society in consequence of the following unpublished letter from Keill to Newton, written two days before the meeting, that is on the 3d April 1711. "I have now sent you the Acta Lipsice, (1705), where there is an account given of your book, (on Quadratures), and I desire you will read from page 34, &c. (namely, the passage which we have given from Newton's MS. in pages 39, 40). I hold not the volume (1710, p. 78) in which Wolfius has answered my letter, but I have sent you his letter transcribed from thence, and also a copy of my letter to him. I wish you would take the pains to read that part of their supplements, wherein they give an account of Dr. Friend's book, and from them you may gather how unfairly they deal with you; but really these things are trifles, not worth your while, since you can spend your time to much better purpose than minding anything such men can say. However, if you would look upon them so far as to let me hold your sentiments on that matter, you will much oblige, your most humble servant,            JO. KEILL."

[15]

Weld's History of the Royal Society, vol. i. p. 410

[16]

"Indicia perspicacissimi ingenii viro satis obtia, unde Leibnitius principia illius calculi hausit aut haurire potuit."

[17]

These sentiments, which we had formerly expressed, and which we again repeat, have been singularly misrepresented by Dr. Guhrauer in his Life of Leibnitz. A distinguished writer, Mr. Henry Rogers, in giving an account of this work, has defended us better than we could have done ourselves. "Dr. Guhrauer," he remarks, "is not a little indignant with Sir David Brewster for the supposed injustice which, in his Life of Newton, he has done to Leibnitz, and to which he frequently refers with much bitterness. Never was a complaint more unreasonable. Our distinguished countryman does not question Leibnitz's claim to be regarded as a true inventor of the calculus; he merely asserts the undoubted priority of Newton's discovery. He expressly affirms that there is no reason to believe Leibnitz a plagiarist; but that if there were any necessity for believing either to be so, it must be Leibnitz, and not Newton, who is open to the charge. Guhrauer angrily replies, not simply by saying (which is true) that there is no sufficient evidence of Leibnitz's <46> having stolen Newton's invention, but by denying the essential identity of the two methods, and by affirming that they are so different as to be considered 'unlike things,' than which nothing can, in our judgment, be more uncandid.

[18]

Homo doctus, sed novus, et parum peritus rerum anteactarum cognitor.

[19]

Vanæ et injustæ vociferationes.

[20]

The additions thus made at different times to the original committee, were first pointed out by Professor De Morgan, and were unknown to all preceding writers. The discovery was a very important one, as it had been asserted by Newton that the committee was a numerous one, consisting of persons of different nations, which was certainly not the character of the original committee. As Professor De Morgan has been led, after an anxious examination of the subject, "to differ from the general opinion in England as to the manner in which Leibnitz was treated," his defence of Newton's veracity was a graceful contribution, and cannot fail to give weight to his other opinions. — See his paper in the Philosophical Transactions, vol. xlvi. pp. 107-109.

[21]

"There may have been," says Professor De Morgan, "and I often suspect there was, something of truth in the surmise of Leibnitz, who thought that the near prospect of the Hanoverian succession created some dislike against the subject <49> and servant of the obnoxious Elector on the minds of the Jacobite portion of English science." "Amicus Anglus ad me scribit," says Leibnitz, "videri [eos qui parum Domui Hanoveranæ favent] aliquibus non tam et Mathematicos et Societatis Regiæ Socios in Socium, sed ut Toryos in Whigium quosdam egesse." — Philosophical Transactions, 1846, p. 108. Newton himself was a Whig, and a friend of the House of Hanover.

[22]

This work was not published for sale, and as the few copies of it which were printed were distributed as presents, it became so scarce that Raphson tells us, "it was not to be met with among the booksellers."

[23]

Newton states that a copy of the Commercium was sent to Leibnitz by the Resident of the Elector of Hanover, above a year before this, and several copies to Leipsic, one of which was for him.            MS.

[24]

Letters to the Count de Bothmar in Des Maizeaux's Recueil de Diverses Pièces, &c. tom. ii. p. 44.

[25]

See Acta Eruditorum, 1713, Feb., p. 77, and Mart., p. 155.

[26]

Commerc. Phil. et Math. G. G. Leibnitii et J. Bernoulli, tom. ii. pp. 308, 311.

[27] For May and June, pp. 208-217.

[28]

Remarques sur le Different enfre M. de Leibnitz et M. Newton, November and December, 1713, pp. 445-453.

[29]

This letter, in the Latin edition of it in the Charta Volans, referred, as we have stated, to Bernoulli, in the sentence quemadmodum ab eminente quodam mathematico dudum notatus est. The reference was continued in the French edition; but in another edition of the Charta Volans, which Leibnitz published two years afterwards in the Nouvelles Littéraires, December 28, 1715, p. 414, he omitted the above passage, as if to fix the authorship on Bernoulli; and in a letter to Madame Kilmansegg, dated April 18, 1716, he inserted a copy of the obnoxious letter, without the passage referred to, and without any hesitation ascribed it to Bernoulli.

[30]

There are several copies of this paper among Newton's manuscripts.

[31]

This paper, occupying forty-two pages, was drawn up with great care with the assistance of Sir Isaac, four of whose letters to Keill on the subject, dated April 2, 20, May 11, 15, 1714, have been published by Mr. Edleston. I have now before me the originals of six letters from Keill to Newton, dated May 2, 17, 19, 21, and June 29, 1714. In Newton's letter of April 2, he says that Keill "need not set his name to it." In Keill's reply of the 2d May, sending a part of his answer, he says, that "he never saw a bad cause defended with so much face and impudence before." He is to take Leibnitz "to task for filching of series," and he is "for putting his name to it;" for he adds, "I have said nothing but what is fully made out, and they have, on the contrary, thrown all the dirt and scandal they could without proving anything they have said, and therefore they thought it best to conceal their names. I believe Wolfius is the author of the Latin letter, for it is exactly agreeable to his caution and honesty, who is inferior to nobody but Mr. Leibnitz in prevarication. Dr. Halley and I do often drink your health. He and I are both of opinion that there should be fifty copies of the Commercium sent over to Johnson, (the publisher of the Journal Littéraire, to whom they were subsequently sent), and that there should be advertisements in the foreign Gazettes, that the original letters of the Commercium are in such a man's hands, to be viewed by gentlemen that are to travel in England, and particularly the letter with Gregory's quadrature of the circle." In his letters of the 25th and 29th June, he sends "the whole of his answer to Bernoulli and the Leipsic rogues, for you and Dr. Halley to change or take away what you please."

[32]

Leibnitz had not at this time written the letter to Bothmar or Madame Kilmansegg, declaring that Bernoulli was the author of it.

[33]

"Fallunt haud dubie qui me tibi detulerunt tanquam auctorem quarundam ex Schedis istis volantibus, in quibus forsan non satis honorifica tui fit mentio. Sed obsecro te, vir inclyte, atque per omnia humanitatis sacra obtestor ut tibi certo persuadeas, quicquid hoc modo sine nomine in lucem prodierit, id mihi falso imputari. . . . . Absit autem ut credam Leibnitium, virum sane optimum me nominando fucum vobis facere voluisse. Credibile namque potius est ipsum vel sua vel aliorum conjectura fuisse deceptum. . . . . Non tamen omni culpa vacabit quod tam temere et imprudenter aliquid proscripserit cujus nullam habebat notitiam."

[34]

The late John Bernoulli, speaking of the conduct of Leibnitz to his grandfather, says, Il commit l'indiscrétion de le trahir. — Mém. Acad. Berlin, 1799, 1800. Hist. p. 41.

[35]

The passage is curious, and it is obvious that the editor has omitted a part of the letter unfit for the public eye. "Satis apparet Newtonum id egisse suis blanditiis, ut benevolentiam tuam captaret; conscium sibi quam non recto stent talo quæ molitus est. Ego tamen etsi nolim, ut in mei gratiam tibi negotium facessas, expecto tamen ab equitate tua et candore, ut profitearis apud amicos quam primum, et publice data occasione, calculum Newtoni nostro posteriorem tibi videri." . . . . . . . — Commercium Phil. et Math. G. G. Leibnitii et J. Bernoullii, tom. ii. pp. 313, 314.

[36]

Ibid. Ibid., tom. ii. p. 314.

[37]

Ibid. Ibid., pp. 320. 321.

[38]

See Des Maizeaux, tom. ii. p. 116.

[39]

Mr. Weld, in his History of the Royal Society, vol. i. p. 415, and Phil. Mag. July 1847, p. 35, states that Professor De Morgan and I have committed a curious and grave mistake in adopting this opinion of Leibnitz; and that it was at the request of some of our most eminent philosophers that he corrected the mistake by publishing the resolution of the Society, as, if our views of the resolution were adopted, "a strong case would be made out against Newton." The Society never adopted the Report, in the sense of adopting, as a body, the opinion of their committee. They simply agreed to receive it, and ordered it to be printed. His autem die Aprilis 24, 1712, acceptis, Societas Regia Collectionem, &c &c, imprimi jussit. The cause of Newton was not affected by the adoption of the Report as their decision, and the resolution to re-consider it can mean nothing more than to express their willingness, which Newton himself often did, to receive any new information from Leibnitz or his friends, <59> and even to publish it in the Transactions. That Newton himself was of the opinion which we have been maintaining, is proved by a passage in his Remarks on Leibnitz's letter to Conti, where he says, in the month of May 1716, "If they (the Royal Society) have not yet given judgment against him, it is because the committee did not act as a jury, nor the Royal Society as a formal court of justice." . . . "And it is sufficient that the Society ordered their Report, with the papers upon which it is grounded, to be published." — Raphson's Fluxions, p. 112.

[40]

Published in Raphson's History of Fluxions, pp. 119, 121, and in the Additamenta Com. Epist., Newtoni Opera, tom. iv. pp. 614, 615.

[41]

It is published in Raphson's History of Fluxions, p. 97.

[42]

\These facts are stated in a yery interesting letter from Conti to Brook Taylor, dated May 21, 1721. It was published in the Memoirs of Brook Taylor, p. 121, and is of such importance that we have given it in APPENDIX, No. III.

[43]

This is the Recensio Commercii Epistolici, or an abstract or review of it. It occupies forty-one quarto pages, and has a preface Ad Lectorem. It was written by Sir Isaac Newton, a fact which Professor De Morgan had deduced from a variety of evidence. It was first published in the Phil. Trans. 1715, and was reprinted in Newtoni Opera, tom. iv. p. 445, and in the Journal Littéraire, torn. vii. pp. 113, 345. See Phil. Mag. June 1852.

[44]

A few days after this letter was written, April 13, Leibnitz wrote to Bernoulli that the "English dispute was renewed, and that Newton, when he saw that Keill was reckoned unworthy of an answer, had descended into the arena." He tells him "that Newton knows that the letter (of June 7, 1713) was his, and that he had described it 'as written by a mathematician, or a pretended mathematician,' as if he were ignorant of your merits, calling the whole Chart (the Charta Volans) defamatory, as if it were more calumnious than the additions to the Commercium Epistolicum." In replying to this letter, on the 20th May 1716, Bernoulli considers it fortunate that Newton has descended into the arena to fight in his own name, and without a mask. He expresses much confidence in his candour, and hopes that the historical truth will now be elicited. The most curious part of the letter, however, is the following passage: "I wonder how Newton could know that I was the author of that letter which you inserted in the Charta published against Newton, since no mortal knew that I wrote it except yourself to whom it was written, and I, by whom it was written." He then refers to Leibnitz's interpretation of the phrase pretended mathematician, as if it accused him of ignorance, and he shows very satisfactorily that it bore another meaning, (the real meaning of Newton as avowed in his remarks on Leibnitz's letter), in no way derogatory from his mathematical knowledge. In Leibnitz's next letter of the 7th June, he makes no reference to Bernoulli's expression of wonder, and has not the honesty to tell him that he had himself communicated the secret to Count Bothma,. and published it. See the Commercium Epistolicum Phil. et. Math. Leibnitii et Bernoullii, tom. ii. pp. 375, 377, 378.

[45]

Some time after this M. Remond de Montmort seems to have remonstrated with John Bernoulli, on the subject of defying the English analysts to the solution of problems. We do not know where this letter is to be seen, but we have found among Newton's papers Bernoulli's reply to it written after the death of Leibnitz, and dated 8th April 1717. In this reply, which he requested Remond to send to Newton, he protests that he had neither the inclination nor the leisure to enter into disputes with the English, or to defy them. It was Leibnitz, he says, who asked him for some problem which could be proposed to the English, and particularly to Keill, and of such a nature that it required a knowledge of their methods to solve. Leibnitz asked him to keep this a secret, in order that it might some day be of use to them against those who wished to defy them. "I imagined," he says, "a problem which seemed to have the qualities he desired, and I sent him two solutions that he might propose it to the English under his own name. I had reason, therefore, to be astonished when I saw that he had given me up as the author, and proposed the problem in spite of me, and even as if it had been done at my instigation. Have the goodness then to disabuse Mr. Newton of his opinion on this matter, and assure him from me that I never had the intention of trying the English by these sort of defiances, and I desire nothing so much as to live in friendship with him, and to find an opportunity of showing him how much I esteem his rare merit. I never speak of him, indeed, without much praise. It is, however, greatly to be desired that he would take the trouble of inspiring his friend Mr. Keill with sentiments of kindness and equity towards foreigners, and leave such in possession of what really belongs to them. For to desire to exclude us from every pretension would be a crying injustice." —See APPENDIX, No. IV.

[46]

It was entitled Epistola pro Eminente Mathematico, Do. Joanne Bernoullio contra quendam ex Anglia antagonistam scripta, and was published in the Acta Eruditorum for July 1716, pp. 296-315.

[47]

Mém. de Berlin, 1802, Hist., pp. 60-65.

[48]

Mem. Acad. Berlin, 1799, 1800, p. 47. The interpolation here referred to as an act of Leibnitz, is one of singular dishonesty. Bernoulli, in his letter to Wolf, <68> states that he first taught the exponential calculus; but in place of this statement, they make Bernoulli say that he was only the first who taught it publicly, and then they add what he never said, "Far be it for me to deny that it was first made known by Leibnitz," — thus making Bernoulli himself surrender his discovery to his rival. — Mém. Acad. Berlin, 1802, pp. 57, 58.

[49]

De Trajectoriis, &c. &c., in the Acta Eruditorum, 1718, pp. 261, 262.

[50]

Mém. Acad. Berlin, 1799, 1800, pp. 41, 42.

[51]

In a letter to Newton, dated May 17, 1717, Keill thus speaks of it: — "A friend of mine brought me the Acta the other day, and I was amazed at the impudence of Bernoulli. I believe there was never such a piece for falsehood, malice, envy, and ill-nature, published by a mathematician before. It is certainly wrote by himself, for though be speaks of Bernoulli always in the third person, yet towards the latter end of his paper, he forgot himself, and says that nobody but the antagonist can persuade himself that my formula was taken from Newton's." In a letter from Newton to Keill, May 2, 1718, he says that the meam solutionem "lays the letter upon Bernoulli." — See Edleston's Correspondence, Lett, xciii. p. 186.

[52]

We have found among Newton's papers a fair copy of this answer in French in the form of a letter to Bernoulli; and also Newton's annotations in separate folio sheets. It is doubtless another copy of the same piece, which Mr. Edleston found among the Lucasian papers, and which he justly supposes to be the libellum editum aut non editum to which Bernoulli refers in the Acta Eruditorum for May <70> 1719, p. 218, containing some vulgar and impertinent abuse of Keill as his antagonista Scotus — homo quidem natione Scotus, qui apud suos inclaruit moribus, ita apud exteros jam passim notus odio plusquam vatiniano quo flagrat, &c. — See Edleston's Correspondence, &c., p. 178; see also Newton's letter to Keill in p. 185, and note, p. 186, of the same Correspondence.

[53]

The death of Leibnitz was notified to Newton by the Abbé Conti, who was then at Hanover, in a letter dated November 1716. "M. Leibnitz," he says, "est mort, et la dispute est finie." After mentioning the manuscripts of Leibnitz, which he hopes the King will show him, he adds, "Je remarquerai s'il y a quelque chose touchant votre dispute, mais peut-etre qu'on cachera ce qui ne fait point d'honneur à la mémoire de M. Leibnitz."

[54]

These remarks, without a date, but written on the receipt of Leibnitz's letter of the 9th April, were first printed in Raphson's Fluxions, p. 111. They were afterwards translated into French, and published in Des Maizeaux's Recueil. I have found in the Portsmouth Papers the French proof, containing, in Newton's own hand, numerous corrections and several small additions to the Remarks, one of which mentions the month of May 1716, as the date when they were written.

[55]

This letter, dated May 2, 1718, has been published by Mr. Edleston, in his Correspondence, &c. in pp. 185, 186.

[56]

In an unpublished letter, dated May 23, 1718.

[57]

Newton had, in 1717, sent to Nicolas Bernoulli a copy of the second edition of the Principia. Bernoulli's letter of thanks, dated Pavia, 31st May 1717, has been preserved.

[58]

We quote from the Latin scroll, which has no date, and of which there are two copies among the Portsmouth Papers.

[59] See p. 55.

[60]

This letter, of which an imperfect scroll has been published in the Macclesfield Correspondence, vol. ii. p. 436, as a letter from Newton to ——, is supposed by Mr. Edleston to have been addressed to Montmart. The copy which I have found is a fuller and more perfect scroll than the one published by Mr. Rigaud. — See Edleston's Correspondence, &c. p. 187, note.

[61]

Letter of Varignon to Newton, Dec. 13, 1722, and the scroll of Newton's answer.

[62]

This work was translated by M. Coste and corrected by the Abbé Varignon, whose correspondence with Newton relates principally to certain difficulties which arose with the publisher, and to Newton's reconciliation to Bernoulli.

[63]

"Des Maizeaux, Recueil de Diverses Pièces, &c. tom. ii. p. 125, line 32."

[64]

Dated Basle, Feb. 6, 1723.

[65]

This review is the Recensio, &c., mentioned in page 63, note.

[66]

Phil. Mag. June 1852, vol. iii. p. 440.

[67]

I find among these MSS. scrolls of almost the whole of the Recensio, and five or six copies in his own hand of the Ad Lectorem.

[68]

In reference to this subject, I find two remarkable letters addressed to Newton <76> in 1720, by Dr. James Wilson, mentioning to him that he possessed several of his manuscripts, and had seen others which had been in general circulation. "Among the papers," he says, "I likewise observed there were some which deduced even the first principles of geometry from the fluxion of points." These letters seem to me of such importance, that I have given them in the APPENDIX, No. V.

[69]

In the first copy of this manuscript the word Prefatio is not inserted after the title Historia, &c. In the second it is inserted, and the title erased; and in the third the title is omitted, and the word Prefatio alone inserted. Newton seems <78> to have had much difficulty in fixing upon a title. Upon a separate folio which I have found, occupying a page and a half, there are no fewer than twelve forms of it. The first is Introductio ad Recensionem Libri, &c., but all the rest are Historia Methodi, &c., with eleven variations. In the second, third, and fourth, it is Historia Methodi Analyseos, &c. In the fifth and sixth the names of both the mathematicians are omitted. In the seventh it is Historia Methodi Differentialis, with both names omitted. In the eighth the change is remarkable. The title is Historia Methodi Analyseos per Fluxiones et Momenta a D. Newtoni inventæ, a D. Leibnitio Differentialis nominatæ, ex literis antiquis deducta. In the ninth, tenth, and eleventh, it is Hist. Meth. Fluxionum, &c.; and in the twelfth Differentialis is placed above Fluxionum.

[70]

"Secundis Inventoribus, etiam revera talibus, vel exiguus vel nullus honor, tituli vel juris nihil est." — Recensio, Newtoni Opera, tom. iv. p. 487.

[71]

We cannot here discuss this important subject. Such of our readers as take an interest in it, are referred to the North British Review, vol. vii. p. 233, &c., where it is treated in reference to the rival claims of Adams and Leverrier.

[72]

See APPENDIX, No. V.

[73]

We have made no reference to the singular opinion of Raphson and of Dr. James Wilson, that Leibnitz may have deciphered the anagram in which Newton concealed his method. See APPENDIX, No. V. — P.S. to letter of January 21, 1720-1. See also Professor De Morgan's paper in the Companion to the Almanac for 1852, p. 10.

[74]

Analysis Fluxionum, p. 2, § 5.

[75]

Professor De Morgan, ut supra.

[76]

Die Entdeckung der Differentialrechnung durch Leibnitz. Von der C. G. Gerhardt, 4to. Halle, 1848. See Professor De Morgan, Companion to the Almanac for 1852 pp. 17,18.

[77]

Ibid., p. 17. See p. 30, note.

[78]

Dr. Keill, Newton's principal champion, and who so nobly fought his battles, has been ungenerously treated by some of the historians of science. With his private letters to Newton before us, we have formed a high opinion both of his talents and character. Everything he did was open and manly, and he did nothing without the instruction and approbation of Newton and his friends.

[79]

His celebrated letter of the 9th April 1716, already described. See p. 64, and APPENDIX, No. IV. An instructive account of an instance of bad faith towards Leibnitz, on the part of Bernoulli, is given by his own grandson in the Mém. Acad. Berlin, 1802, pp. 51-66.

[80]

This anecdote is given in still stronger language by M. Biot in his Life of Newton, Biog. Univers., tom. xxxi. p. 178.

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Professor Rob Iliffe
Director, AHRC Newton Papers Project

Scott Mandelbrote,
Fellow & Perne librarian, Peterhouse, Cambridge

Faculty of History, George Street, Oxford, OX1 2RL - newtonproject@history.ox.ac.uk

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