Catalogue Entry: OTHE00076

Chapter XV

Author: David Brewster

Source: Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton, vol. 2 (Edinburgh: 1855).

[Normalized Text] [Diplomatic Text]


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.


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.


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.


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


Acta Eruditorum, 1700, p. 203.


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.


Acta Eruditorum, 1701, p. 134.


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.


A Supplement to the Remarks, p 6.


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 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.


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 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."


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


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


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.


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


Vanæ et injustæ vociferationes.


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.


"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.


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."


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.


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


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


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

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


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


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.


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 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."


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, Il commit l'indiscrétion de le trahir. — Mém. Acad. Berlin, 1799, 1800. Hist. p. 41.


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.


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


Ibid. Ibid., pp. 320. 321.


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


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.


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


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


\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 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.


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.


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.


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.


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


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.


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


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


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.


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.


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.


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


In an unpublished letter, dated May 23, 1718.


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.

[59] See p. 55.


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.


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


Dated Basle, Feb. 6, 1723.


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


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


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.


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.


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.


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


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.




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.


Analysis Fluxionum, p. 2, § 5.


Professor De Morgan, ut supra.


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.


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


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.


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.


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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