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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 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, 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.
Having been elected a Fellow of the Royal Society in 1687, he took an active part in its proceedings, and communicated papers to its 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.Transactions. In the year 1699 he published a tract entitled a "Geometrical Investigation
"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. 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.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 Investigalio Geometrica, &c., p. 18. Lond. 1699.
Strong as these expressions are, they cannot be regarded as charging Leibnitz with plagiarism. He is styled We have already proved that Newton did not attach this meaning to his scholium; and in replying to this passage in the 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,Acta Eruditorum, 1700, p. 203.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.Acta Eruditorum, but they refused to print it on the ground of their aversion to controversy.Acta Eruditorum, 1701, p. 134.
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 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.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,A Supplement to the Remarks, p 6.
"In the January, p. 34. This was the name given by Leibnitz to the integral calculus, or the inverse method of fluxions. 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 Acta Eruditorum for 1705,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.
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,
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, For September and October, p. 185. 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 Weld's "Indicia perspicacissimi ingenii viro satis obtia, unde Leibnitius principia illius calculi hausit aut haurire potuit."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 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 ;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, History of the Royal Society, vol. i. p. 410
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 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 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.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
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 Homo doctus, sed novus, et parum peritus rerum anteactarum cognitor. Vanæ et injustæ vociferationes.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;
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.
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. 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 "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 Philosophical Transactions, vol. xlvi. pp. 107-109.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.Philosophical Transactions, 1846, p. 108. Newton himself was a Whig, and a friend of the House of Hanover.
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
"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
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 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."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.
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 Newton states that a copy of the Letters to the Count de Bothmar in Des Maizeaux's malicious falsehoods, I did not think proper to send for it by post, but wrote to M. Bernoulli to give me his sentiments.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. that it appeared prohable that Sir Isaac Newton had formed his calculus after having seen mine."Recueil de Diverses Pièces, &c. tom. ii. p. 44.Charta Volans, dated July 29, 1713, and
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, See Acta Eruditorum, 1713, Feb., p. 77, and Mart., p. 155.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."Commerc. Phil. et Math. G. G. Leibnitii et J. Bernoulli, tom. ii. pp. 308, 311.as was long ago remarked by a certain eminent mathematician, which placed Bernoulli in the ridiculous position of praising himself.
Previous to the publication of the This letter, in the Latin edition of it in the Charta Volans, Dr. Keill sent to the Journal Littéraire for 1713,Remarques sur le Different enfre M. de Leibnitz et M. Newton, November and December, 1713, pp. 445-453.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.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.
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 There are several copies of this paper among Newton's manuscripts. 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 Leibnitz had not at this time written the letter to Bothmar or Madame Kilmansegg, declaring that Bernoulli was the author of it. "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." The late John Bernoulli, speaking of the conduct of Leibnitz to his grandfather, says, 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, Journal Littéraire for July and August 1714.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."Il commit l'indiscrétion de le trahir. — Mém. Acad. Berlin, 1799, 1800. Hist. p. 41.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."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.Ibid. Ibid., tom. ii. p. 314.Ibid. Ibid., pp. 320. 321.
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 See Des Maizeaux, tom. ii. p. 116.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,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 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." Mr. Weld, in his History of the Royal Society, vol. i. p. 415, and Published in Raphson's 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, 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.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.History of Fluxions, pp. 119, 121, and in the Additamenta Com. Epist., Newtoni Opera, tom. iv. pp. 614, 615.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, It is published in Raphson's History of Fluxions, p. 97.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
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. \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.
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 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
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 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.
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 A few days after this letter was written, April 13, Leibnitz wrote to Bernoulli that the "English dispute was renewed, and that Newton, 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.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.
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 It was entitled Epistola pro Eminente Mathematico, which has formed so curious 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,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.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,Mém. de Berlin, 1802, Hist., pp. 60-65.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."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, 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.
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 De Trajectoriis, &c. &c., in the Acta Eruditorum, 1718, pp. 261, 262.Pro Eminente Mathematico!Mém. Acad. Berlin, 1799, 1800, pp. 41, 42.
This celebrated letter, as might have been expected, excited the indignation of Newton and his friends. They had no difficulty in discovering its author; 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.
"Si pergis dicere quæ vis, audies quæ non vis." 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 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.
After the death of Leibnitz, which took place on the 14th November 1716, the controversy to a considerable 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." 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.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, 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, This letter, dated May 2, 1718, has been published by Mr. Edleston, in his In an unpublished letter, dated May 23, 1718.Correspondence, &c. in pp. 185, 186.
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, 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. We quote from the Latin scroll, which has no date, and of which there are two copies among the Portsmouth Papers.
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.
The letter of Newton, to which this was the reply, was enclosed in one to Varignon, This letter, of which an imperfect scroll has been published in the Macclesfield Letter of Varignon to Newton, Dec. 13, 1722, and the scroll of Newton's answer. 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. "Des Maizeaux, Dated Basle, Feb. 6, 1723.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.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,Recueil de Diverses Pièces, &c. tom. ii. p. 125, line 32."
In the year 1725, a new edition of the This review is the I find among these MSS. scrolls of almost the whole of the Commercium Epistolicum was published, with notes, a general review of it,Recensio, &c., mentioned in page 63, note.Phil. Mag. June 1852, vol. iii. p. 440.Recensio, and five or six copies in his own hand of the Ad Lectorem.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. In reference to this subject, I find two remarkable letters addressed to Newton
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 Commercium 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 : 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 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.
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 "Secundis Inventoribus, We cannot here discuss this important subject. Such of our readers as take an interest in it, are referred to the first inventor, and that "second inventors have little or no honour, and no rights."etiam revera talibus, vel exiguus vel nullus honor, tituli vel juris nihil est." — Recensio, Newtoni Opera, tom. iv. p. 487.North British Review, vol. vii. p. 233, &c., where it is treated in reference to the rival claims of Adams and Leverrier.
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 See APPENDIX, No. V. 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.
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 Professor De Morgan, Die Entdeckung der Differentialrechnung durch Leibnitz. Von der C. G. Gerhardt, 4to. Halle, 1848. See Professor De Morgan, Theoria Motus Abstracti, dedicated to the Academy of Sciences in Paris in 1671, before he visited England, contains, according to Dr. William Hales,Analysis Fluxionum, p. 2, § 5.ut supra.Companion to the Almanac for 1852 pp. 17,18.Ibid., p. 17. See p. 30, note.
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. 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.
Instead of striving to prove that he was the inventor 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.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 This anecdote is given in still stronger language by M. Biot in his 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.Life of Newton, Biog. Univers., tom. xxxi. p. 178.