BEFORE Newton had taken an open part in the fluxionary controversy, and before the publication even of the Commercium Epistolicum, Leibnitz had begun to challenge the soundness of the Newtonian philosophy, and to excite against it the prejudices of continental philosophers. In his Théodicée, published in 1710,[1] he attacks the theory of gravity, and accuses Newton of introducing occult qualities and miracles into philosophy; and, in a controversy which he had in 1711 with Hartsoeker,[2] who maintained that all things arose from certain atoms floating in a perfect fluid without cohesion, he took occasion to renew his attack upon the English philosophy. In this dispute <283> with the Dutch physician, the name of Newton is not mentioned by Leibnitz, but he was so obviously the person whose opinions were assailed, that he addressed a very able reply to the editor, in which neither his own name nor any of his writings are referred to. "In your weekly paper,"[3] he says, "dated May 5, 1712, I meet with two letters, one written by Mr. Leibnitz to Mr. Hartsoeker, the other by Mr. Hartsoeker to Mr. Leibnitz, in answer to the former. And in the letter of Mr. Leibnitz, meeting with some things reflecting upon the English, I hope you will do them the justice to publish this vindication as you have printed the reflection." He then proceeds to shew that the theory of gravity is "proved by mathematical demonstration, grounded upon experiments and the phenomena of nature; and that to understand the motions of the planets under the influence of gravity, without knowing the cause of gravity, is as good a progress in philosophy as to understand the frame of a clock, and the dependence of the wheels upon one another, without knowing the cause of the gravity of the weight which moves the machine, is in the philosophy of clockwork; or the understanding the frame of the bones and muscles, and their connexion in the body of an animal, and how the bones are moved by the contracting or dilating of the muscles, without knowing how the muscles are contracted and dilated by the power of the mind, is in the philosophy of animal motion."[4]

The pertinacity with which Leibnitz reiterated his attacks upon the doctrine of gravity, has no parallel in <284> the history of science, and it is difficult to believe that the love of truth was the only motive by which he was actuated. We have already seen[5] how he indulged in the same criticisms in the postscript of his letter to the Abbé Conti in November 1715, and we shall now find him in the climax of his hostility to Newton, when in the very same month he endeavoured to misrepresent and malign his philosophy, in his correspondence with the Princess of Wales. He had no doubt learned from her Royal Highness the regard which she entertained for Newton, and the pleasure and instruction which she derived from his conversation; and, under such circumstances, it might have been expected that a man of high principle would have kept in subordination his feelings as a rival, without abjuring his opinions as a philosopher. He might have taught the Princess his doctrine of pre-established harmony as incompatible with Newton's opinions respecting certain irregularities in the planetary system, or he might have whispered into the royal ear that gravity was an occult quality, and a miracle; but when he represented the Newtonian philosophy and the opinions of Locke as subversive of natural, and inferentially of revealed religion, he yielded to an ignoble impulse, and did violence to the dignity of philosophy.

In a letter which Leibnitz addressed to the Princess in the month of November 1715, the following charges were made against the English: —

"1. Natural religion itself seems to decay [in England[6]] very much. Many will have human souls to be material; others make God himself a corporeal being.


"2. Mr. Locke and his followers are uncertain at least whether the soul be not material and naturally perishable.

" 3. Sir Isaac Newton says that space is an organ, which God makes use of to perceive things by; — it will follow that they do not depend altogether upon Him, nor were produced by Him.

" 4. Sir Isaac Newton and his followers have also a very odd opinion concerning the Work of God. According to their doctrine, God Almighty wants to wind up his watch from time to time, otherwise it would cease to move. He had not, it seems, sufficient foresight to make it a perpetual motion. Nay, the machine of God's making is so imperfect according to these gentlemen, that he is obliged to clean it now and then by an extraordinary concourse, and even to mend it as a clockmaker mends his work; who must consequently be so much the more unskilful a workman, as he is oftener obliged to mend his work, and to set it right. According to my opinion the same force and vigour remains always in the world, and only passes from one part of matter to another, agreeably to the laws of nature and the beautiful pre-established order. And I hold that when God works miracles, he does not do it in order to supply the wants of nature, but those of grace. Whoever thinks otherwise, must needs have a very mean notion of the wisdom and power of God."

These views of Leibnitz having become the subject of conversation at court, where Newton and Locke were in high esteem, the king, who never seems to have had much affection for his countryman, expressed a wish that Sir Isaac Newton would draw up a reply in defence of his philosophy, as well as of his claim to be the original inventor of Fluxions. It was accordingly arranged that Newton should <286> undertake the mathematical part of the controversy, while Dr. Clarke was intrusted with the defence of the English philosophy. The Princess of Wales, therefore, communicated to the Dr. the preceding extracts from Leibnitz's letter, and Dr. Clarke's reply was transmitted to Leibnitz through her Royal Highness. Leibnitz replied to this communication; and after Dr. Clarke had returned his fifth answer to the fifth paper of Leibnitz, the death of the latter on the 14th November 1716, put an end to the controversy.[7]

While this dispute was going on, Leibnitz sent an account of it to John Bernoulli, in a letter dated June 7, 1716. After abusing Brook Taylor's Method of Increments in language which the editor has struck out, he tells his correspondent that he is engaged in a philosophical dispute with Newton, or rather with his defender Clarke, — that he had written to the Princess of Wales, who took an interest in such subjects, — "that philosophy or rather natural religion, was degenerating among the English," — that the Princess had transmitted extracts of his letter to Clarke, — that her Royal Highness had sent him his answer, and that he had replied four times to the communications of his opponent. He tells him that space is now the idol of Englishmen; and "that whatever is inexplicable from the nature of things, such as the Newtonian general attraction of matter, and other things of the same kind, is either miraculous or absurd." He expects that the contest, from which everything offensive is excluded, will be continued, and he concludes the para <287> graph with the following singular sentiment, the conclusion of which may be inferred from its being struck out by the editor:[8]

"Hujusmodi enim collationes mihi ludus jocusque sunt,[9] quia in philosophia,

Omnia precepi atque animo mecum ante peregi."[10]

* * * * *

It is very obvious from the notes on Dr. Clarke's replies to Leibnitz, that he had received assistance on several astronomical points from Newton himself.[11] Sir Isaac's attention indeed, had been called to the subject, by the postscript to Conti's letter, and in his reply to it, on the <288> 26th February 1716, he devotes a page to a defence of his views and a criticism upon those of his rival. Satisfied no doubt with the ample discussion which the subject was undergoing between Clarke and Leibnitz, he takes no notice of this portion of Leibnitz's rejoinder[12] in his celebrated "Remarks,"[13] which were written in May 1716. On a subsequent occasion, when M. Des Maizeaux requested from him some new observations on the subject, he declined to renew the discussion, and assigned the following reason for his silence: —

"You know," he says, "that when Mr. L'Abbé Conti had received a letter from Mr. Leibnitz with a large postscript against me, full of accusations foreign to the question, and the postscript was showed to the King, and I was pressed for an answer, to be also shewed to his Majesty,[14] and the same was afterwards sent to Mr. Leibnitz;[15] he sent it with his answer to Paris, declining to make good his charge, and pretending that I was the aggressor, and saying that he sent those letters to Paris that he might have neutral and intelligent witnesses of what passed between us. I looked upon this as an indirect practice, and forbore writing an answer in the form of a letter to be sent to him, and only wrote some observations[16] on his letter to satisfy my friends here that it was easy to have answered him had I thought fit to let him go on with his <289> politicks. As soon as I heard that he was dead, I caused the letters and observations to be printed, lest they should at any time come abroad imperfectly in France. You are now upon a design of reprinting them with some other letters written at the same time, whose originals have been left in your hands for that purpose by Mr. L'Abbé Conti, for making that controversy complete, and I see no necessity of adding anything more to what has been said, especially now Mr. Leibnitz is dead."[17]

After the death of Leibnitz, the fluxionary controversy was almost in abeyance. The attention of mathematicians, however, was again called to the subject by the Eloge of Leibnitz, from the pen of Fontenelle, which was published in the Memoirs of the Academy of Sciences for 1716, and by another Eloge which appeared in the Acta Eruditorum for 1717. The friends of Newton were not pleased with the observations of Fontenelle, and Mr. Chamberlayne, who had previously interfered between the rival analysts, did not scruple to complain of them in his "Lives of the French Philosophers." Fontenelle received this criticism with his usual urbanity, and wrote the following note to Mr. Chamberlayne: — "You complain of me, but after so civil a manner, that I think myself obliged to return you an answer. I confess to you sincerely that till we had seen the Commercium Epistolicum, it was commonly believed here that Leibnitz was the first inventor of the Differential Calculus, or at least the first publisher <290> of it, though it was as well known that Sir Isaac Newton was master of the secret at the same time; but as he did not challenge it, we could not be undeceived, and what I said concerning it was upon the credit of the common belief, which I did not find contradicted. But since it is so now, I promise you I will change my language whenever there is an opportunity, for I do assure you that it has been my study all my lifetime, to keep myself free from any partiality, whether national or personal, nothing being my concern but truth."[18]

When Newton himself perused the Eloge of Leibnitz, which was sent to him by Varignon, he did not scruple to express his dissatisfaction with it. In thanking Varignon for his "kind present of the Elogia of the Academicians," he says, "in that of Mr. Leibnitz Mr. Fontenelle has been very candid. There are some mistakes in matter of fact, but not by design. I reckon that Mr. Fontenelle was not sufficiently informed." He then proceeds to point out the mistakes to which he refers, criticising at the same time the Elogium of Leibnitz in the Acta Eruditorum, and repeating many of the leading facts which we have already given in the history of the controversy.[19] As no notice is taken of these criticisms in the letters of Varignon, it is probable that they were never sent to him, and this is the more likely, as I have found three copies of a more elaborate paper entitled Historical Annotations on the Elogium of Mr. Leibnitz, which, in so far as I have been able to ascertain, has not been published.[20]

But though the leaders in this controversy had ceased <291> to take a public or active part in it, yet some of them looked back with uneasiness to the part which they had played. John Bernoulli, who had been dragged into it by the importunities of Leibnitz, and whose character had been compromised by the disclosure of secrets which ought to have been concealed, was anxious for a reconciliation with Newton; and the Abbé Varignon, to whom he had communicated his desire, succeeded in the task. We have already[21] given a brief account of the correspondence which took place on this occasion, in so far as it forms a part of the fluxionary controversy. There are, however, other points of interest in these letters which throw some light on the personal character of their authors, and we have therefore given the most interesting of them in the Appendix.[22] The letters of Varignon relate chiefly to the French translation of Newton's Optics, by M. Coste, the publication of which had been delayed by the improper conduct of the bookseller who undertook it; while those of Newton, which we possess only in scrolls, are occupied with details respecting his controversy with Leibnitz, and his nominal reconciliation with Bernoulli. That Newton never forgave Bernoulli is very distinctly shown in the following paragraph of a letter to Varignon:[23]^ —

"Demoivre told me that Bernoulli wished to have my picture; but he has not yet acknowledged publicly that I possessed the method of fluxions and moments in 1672, as is confessed in the Eloge on Leibnitz, published in the History of your Academy. He has not yet acknowledged that I gave, in the first proposition of the Book of Quadratures, published in 1693 by Wallis, and in 1686 in Lem. 2, book ii. of the Principia, synthetically demonstrated, the true rule for differentiating differences; and <292> that I had in the year 1672 the rule for determining the curvature of curves. He has not yet acknowledged that, in the year 1669, when I wrote the Analysis by series, I had a method of accurately squaring curve lines when it could be done, and which is explained in my letter to Oldenburg, dated 24th October 1676, and in the Fifth Prop. of the Book of Quadratures; and also that Tables of Curvatures, which could be compared with the Conic Sections, were composed by me at that time. If these things were admitted, it would put an end to all disputes, and I could not then easily refuse him my picture."

In replying to this letter, Varignon says,[24] "I sent to Bernoulli, on the 21st October, the portions of your letter relating to his complaints, with the addition that you prohibited me from publishing them; but I took no notice of the conditions which you considered necessary before you granted him your picture, lest they should have annoyed him. In order, however, that you might still appear friendly to him, I informed him that three copies of your Optics, now in the press, were destined for himself, his son, and his nephew; and, indeed, in his last letter from Basle of the 22d November, he desires me to present to you, in his name and theirs, their best thanks for the many gifts you intend for them. But the answer which he has made to the parts which I transcribed from your last letter, I dare not communicate to you. I have deemed it better to transcribe it for Demoivre, who will tell it to you, that you may say to him what perhaps you would not wish to write."

From the high character of Varignon, both as a mathematician and an individual, Newton and his rivals were equally anxious to obtain his judgment in their favour. <293> Leibnitz had expressed to Bernoulli his great anxiety that Varignon would do nothing in France that would be injurious to his cause;[25] and Bernoulli, in his reply,[26] sends him an extract from a letter of Varignon's, in which, while he concedes to Newton an early knowledge of the doctrine of infinitesimals, he gives to Leibnitz the discovery of the differential calculus. Varignon has nowhere given an opposite opinion in his letters to Newton, though he could scarcely have avoided it had any favourable impression been made upon his mind by the information communicated to him, and by his subsequent perusal of the second edition of the Commercium Epistolicum, and the Recensio. Previous to the publication of this edition, Newton sent him a copy of the second, and, requested his opinion of it in the following letter.[27]

"To the celebrated M. Abbé Varignon,

Prof. of Mathematics in the College Mazarin.

"REVEREND SIR, — I send you a copy of the Commercium Epistolicum, reprinted here along with the account of it turned into Latin, and the Judgment of the 'Primary Mathematician.' All these were printed long before the death of Leibnitz, but this Commercium has not yet been offered for sale in the booksellers' shops. A preface to the reader is prefixed, and an annotation of which two parts are new, but taken from ancient writings. I earnestly entreat you to read these two, and if you find anything said which ought not to be said, or anything which ought to be said otherwise, and mention it to me, <294> I will take care that it shall be corrected, if necessary, before the book is published. The object of the book is, not that disputes may be revived, but that questions may be rejected which have nothing to do with the subject, and that what has been said respecting the first inventor of the method, either of fluxions, or moments, or differences, may be handed down to posterity, and quietly referred to their judgment. I am getting well slowly, and hope that I shall soon enjoy my usual health. — Farewell,            IS. NEWTON."

In replying to this letter, the Abbé wisely avoids the question at issue between his friends, and contents himself with making the following observations on the Commercium: — "I lately requested M. Demoivre to mention to you that I had some hesitation about two places in the first preface to the reader, which you begged me to consider, along with the notes on the anonymous epistle, dated 7th June 1713, in which I see nothing calculated to give offence. But it is otherwise in the above-mentioned preface, for, in page 5, there are two things which I think may be offensive." These two criticisms, which we have given in a note, though very trivial, were attended to in the edition of 1725.[28] This letter, which <295> announced to Newton that the French translation of his Optics was completed on the last day of July 1722, was the last which he received from Yarignon, who died a few months afterwards, on the 23d December 1722.[29]

In a preceding chapter we have mentioned the short correspondence which took place between Newton and John Bernoulli, and have quoted those portions of it which bear upon the Fluxionary controversy.[30] It commenced on the part of Bernoulli with a letter of thanks[31] for the copy of Newton's Optics, which he had received through Varignon, and for the copy of the Latin edition which was promised him, with apologies for the delay that has taken place in writing him, which he hopes he will not impute to any insensibility to his divine and unrivalled genius. He appeals to his correspondence with Montmort and Demoivre for a proof of his admiration of his talents and his affection for his character, and he cannot understand how it has happened that — after the torch had been lighted of that deadly war, which, to the disgrace of mathematical science, has raged for three years between the geometers of Britain and Germany — he, neither a Briton nor a German, but a Swiss, who belonged to no party, and would have done any thing <296> rather than voluntarily intermeddle with the disputes of others, should have fallen, as was reported, in his esteem. If such should be the case, which he cannot believe, he must ascribe it to a combination of sycophants who seek to advance their own reputation and that of their friends, by destroying the good name of others, and proscribing all who are not English, the innocent and the guilty, unless they are willing to applaud them in every thing. He believes, therefore, that many falsehoods have been told which have sunk him in his esteem, and, in defence of himself, he appeals to his writings, and declares that in these as well as in his letters, his conversations, his orations, and his lectures, he has always extolled him and his inventions with the highest praise. Nor can he doubt that such sincere appreciation of his talents will be more agreeable to posterity "than that immoderate ardour (not of praising you, for you cannot be too much praised) of arrogating to you what you do not claim, and leaving nothing to foreigners." This extravagant praise, which could not but be offensive to Newton, is followed by the solemn denial, (the substance of which we have already quoted,[32]) that he was the author of the celebrated letter in the Charta Volans, which he understood Newton had, on the authority of Leibnitz, ascribed to him in Raphson's Fluxions. He makes the best apology he can for Leibnitz's disregard of his feelings in ascribing the letter to him, and he concludes with an ardent expression of his gratitude to Newton for his splendid presents, and for his admission into the Royal Society, begging that he will regard him as "a most zealous worshipper of his immortal merits."

In Newton's reply to this letter,[33] he assures Bernoulli, <297> as we have already seen,[34] that as soon as he learned that he was not the author of the obnoxious letter, he wished to cultivate his friendship. He thanks him for his kind reception of his Optics, and will endeavour to repay his politeness by mutual friendship. He explains how he suspected him to be the writer of the letter of the 7th June, but hopes, as he is not the author of it, that this will do him no injury. He assures him that the addition to Cor. 1, Prop. xiii. Book I. of the Principia was made at the suggestion of Cotes, and was printed in 1709, before the commencement of these disputes, and he concludes with the promise that he will exert himself to put an end to the controversy between his friends and him.

To this letter Bernoulli replied on the 21st December 1719. After referring to the obnoxious letter in the manner we have elsewhere mentioned,[35] and to the publication of some of Leibnitz's letters, he wishes Newton's countrymen would consider if the controversy was to be carried on by the testimony of mathematicians, whether or not it would be better that other letters should be produced than those of Leibnitz, who cannot be regarded as a proper witness in his own cause. "I have letters," he adds, "from some learned men from countries which have taken no part in this national contest, and which, if I were to make public, I doubt if such of your countrymen as rate me with so much warmth, proceeding even to gross insults, would have much reason to boast. I have, among other authentic documents, a letter from M. Montmort, a very learned mathematician, lately dead, who, as you know, was, while he lived, attached to no party, being a Frenchman. I have, I say, a copy of a certain letter sent to me by him, which he addressed on the 18th December 1718, to the <298> celebrated Brook Taylor,[36] and which even of itself might put an end to the greatest part of the controversy, but not according to the views of Taylor and his foreign disciples. I willingly abstain, however, from publishing these letters, provided your countrymen will cease to provoke our patience, which I wish for the sake of peace." Bernoulli then expresses his satisfaction with Newton's statement respecting the corollary in the Principia. He explains that he had only spoken against the form of Newton's assertion in the first edition of the work, and he claims to be the first who gave the analysis of the inverse truth, without supposing the direct one to be already known. He then mentions a report brought by a friend of his from England, that he had been expelled from the Royal Society,[37] and he begs that Newton will let him know whether he was expelled by a decision of the Society, or by the single authority of the Secretary, whom at that time he suspects to be Brook Taylor.

The answer of Sir Isaac to this letter has not been found, but there can be no doubt that he explained to Bernoulli, as I find he did to another foreign member of the Royal Society, who made a similar complaint, that <299> the omission of his name from the list of the Fellows was merely an error of the person who copied it. No farther correspondence seems to have taken place between Newton and Bernoulli till 1723, when the latter acknowledged the receipt of three splendidly bound copies of the French edition of the Optics, for himself, his son, and his nephew. In this letter Bernoulli characterizes Newton's theory of light and colours as a discovery which will be more admired by posterity than it was then. He tells him that Hartsoeker had claimed for himself the discovery of the different refrangibility of light, and attacked his theory of the planetary system; and he expresses his surprise that no Englishman was at hand to defend their illustrious countryman against a "fellow so rude and barbarous." After giving an account of Hartsoeker's attack upon himself founded upon a letter of Newton's, and requesting his assistance in protecting him against the charge,[38] he concludes with thanking him in the name of the celebrated Scheuchzer for the kindness he had shewn to his son when in London, and giving him the privilege of conversing with the greatest of philosophers and mathematicians.[39]

It does not appear that Newton returned any answer to this letter, or that he carried on any correspondence with the other distinguished members of the Bernoulli family. Nicolas, the nephew of John, to whom, as we have seen, Newton presented copies of several of his <300> works, had pointed out a mistake in the 10th Prop. of the 2d Book of the Principia[40] He went to London in the summer of 1712, where he met with the kindest reception from Newton and Halley, a circumstance which he speaks of with much gratitude in a letter in which he thanks Newton for a copy of the second edition of the Principia.[41] In the fluxionary controversy he was attacked by Keill, as one of Newton's enemies, but it appears that he denied the imputation in an explanatory letter to Newton, to which he received no answer.[42]

In the latter part of Newton's life his correspondence was very limited, and with the exception of a few letters from Dr. Robert Smith of Cambridge, Fontenelle,[43] Dr. Derham,[44] and others, his other letters possess very little interest. We are informed by Conduitt that he destroyed many of his papers before his death, and it is probable that some of them were letters which he deemed of no importance.


Essais de Théodicée sur la Bonté de Dieu, la Liberté de l'Homme, et l'Origine du Mal.


Journal de Trevoux, May 1712.


Memoirs of Literature, No. XVIII. p. 137. See Cotes' letter to Newton in Edleston's Correspondence, &c., p. 153.


The scroll of this letter, which occupies two folio pages, has no date. It does not appear in the Memoirs of Literature for which it was written.


Vol. I. p. 60.


The words in England are not in the original paragraph, but they were added either by the Princess or Dr. Clarke, and, as we shall presently see, were meant to be understood by Leibnitz himself.


All these papers, which passed through the hands of the Princess, were published at Amsterdam in 1720, under the title of Recueil de Diverses Pièces sur la Philosophie, la Religion Naturelle, l'Histoire, les Mathématiques, &c., par Messrs. LEIBNIZ, CLARKE, NEWTON, &c. They wEre published also in French and English in 1738 in Dr. Clarke's Works, vol. iv. pp. 580-710.


We hope that those who possess the originals of the Commercium Epistolicum of Leibnitz and Bernoulli, will supply the numerous elisions which the editor had not the courage to insert, as they would throw much light on the temper with which the Fluxionary controversy was carried on by these eminent mathematicians. No such eliminations have been made in the letters of Newton or his friends.


It has been supposed by many persons that the Théodicée of Leibnitz, which was written for the information of the Queen of Prussia, with the view of counteracting the sceptical opinions of Bayle, did not express his own sentiments, and that Leibnitz really believed the doctrines which he impugned. Professor Pfaff of Tübingen, whose opinion of the Théodicée Leibnitz had requested, thus replied to him: "It seems to me that you have invented that theological system only in jest, while at the bottom you receive the doctrines of Bayle; but it is necessary that some one give the dangerous principles of Bayle a serious and thorough refutation." To this letter Leibnitz answered, "You are right, venerable sir, in what you say respecting the Theodicea. You have hit the nail on the head; and I wonder that no one before has taken this view of my intentions, for it is not the business of philosophers always to treat of subjects seriously; they who, as you correctly observe, so tax the powers of their mind in the invention of hypotheses. You who are a theologian, will pursue the theological course in the refutation of errors." This letter was, of course, understood in its natural meaning; but the biographer of Leibnitz, Dr. Gurhauer, maintains it to be an ironical answer to the presumptuous Professor! We do not venture to say, though he has himself said it, that Leibnitz's real opinions were not expressed in his Théodicée, and in his letter to the Princess of Wales, but we call the attention of the reader to the ludus et jocus, with which our metaphysical gladiator carried on his contest with Dr. Clarke, and pointed out the decay of natural religion in England.


Comm. Epistol. Leibnitii et Bernoullii, tom. ii. pp. 381, 382.


I have found, among Sir Isaac's papers, many folio pages of manuscript containing the same views as those given by Dr. Clarke.


Letter to Conti, April 14, 1716.


Raphson's Fluxions, p. 111.


"By the contrivance of some of the court of Hanover I was prevailed with to write an answer to the postscript of a letter written by Mr. Leibnitz to Mr. L'Abbé Conti, that both might be shewed to the King. I did it with reluctancy; and by the letters which Mr. Leibnitz thereupon wrote to several at court, I found that he was at the bottom of the design. It is now about forty years since I left off all correspondence by letters about mathematics and philosophy, and therefore I say nothing farther to you about these matters." — Scroll of a letter to the Abbé Varignon in 1718.


This was Newton's letter to Conti of the 26th February 1716.


Published in Raphson's Fluxions, p. 111.


In this scroll, of which there is a duplicate, another page is added, giving the usual history of his discovery of fluxions. In the duplicate, apparently the first written, there is added after the word dead, "For I have always industriously avoided disputes. If anything more were to be added, it should be what follows the following declaration." The pen is drawn through this last sentence, and the declaration is not mentioned. This paper was probably drawn up for the use of M. Des Maizeaux, in writing his preface to his Recueil, &c., which contains a clear account of the Fluxionary dispute. The Preface is dated October 27, 1719.


This extract from Fontenelle's letter, dated February 5, 1717, is in Mrs. Barton's handwriting, and seems to have been sent by Chamberlayne to Newton.


This scroll occupies nearly two closely written folio pages, and one part of it is almost obliterated with alterations.


These annotations occupy about ten closely written folio pages.


Pages 71-75.



[23] Sept. 26, 1721, o. s.


Dated December 9, 1721.


Spero dominum Varignonium curaturum, te presertim hortatore, ne quid in Gallia fiat de quo queri possim. Aug. 19, 1713, Com. Epist. Leib. et Bern. tom. ii. p. 321.


September 9, 1713.


Varignon had lost his copy of the first edition, from having lent it to a friend. The date of Newton's letter must have been in June or July 1722.


"1o. Lin. 12, 13. Legitur Jam velo sublato, ut militem in hac rixa pro se inducere: Mallem simpliciter Jam in hac rixa pro se inducere, ne quis sub illo velo prius la{illeg}itantem putet Dum. Bernoullium, cui Leibnitius epistolam predictam ascripsit. Adde quod ut Militem vilior est denominatio quam ut eundem Dum. Bernoullium non offendat.

"2o. Ibidem, Lin. 29. Legitur de Do Des Maizeaux et in lucem edidit: Mallem et me non consulto in lucem edidit ut nimirum hæc loquendi ratio concilietur cum Epistola quam ad Dum. Bernoullium, tua cum venia nuper scripsi.

"Hæc sunt quæ te lubente notavi in prædicti libri Præfatione prima ad Lectorem. At in notis ad Epistolam sine nomine datam die 7 Junii 1713, nibil mihi visum est quod sic paci noxium esse possit, ut Jam dixi." This letter is dated Paris, 4 Aug. 1722.


Pierre Varignon was born at Caen in 1654. In 1687 he published his Projet d'une Nouvelle Méchanique, in consequence of which he was elected a Member of the Academy of Sciences, and appointed Professor of Mathematics in the College Mazarin. Though of a robust constitution, his habits of severe study made such an impression upon it, that, in 1705, his life was for six months in great danger, and during the three following years, he was in a state of constant languor and fever, during the attacks of which, as he told Fontenelle, he believed that he was in the middle of a forest, where he saw the leaves of all the trees covered with algebraic calculations. After teaching his class at the College Mazarin, on the 22d December 1722, he was seized with an illness which carried him off on the following night. Newton contributed the plate for the portrait of Varignon to the edition of his Méchanique, re-published in 1725, as a present to the friends of Varignon.


Pages 71, 72.


Dated July 5, 1714. See APPENDIX, No. XXII.


Page 55, note.


I have found the scroll of this letter, but without a date. See APPENDIX, No. XXII.


See p. 72.


See p. 72, 73.


I have found among Newton's papers a copy of this very interesting letter. Montmort was the particular friend of Brook Taylor, and was much attached to Newton, to whom he sent in 1716 a present of fifty bottles of champagne. That Montmort was, as Bernoulli says, an impartial judge in this matter, can hardly be doubted, and as his letter expresses the opinion of continental mathematicians on the Fluxionary controversy, in a manner at once precise and intelligible, I consider it a duty to give it a place in the Appendix. In consequence of Bernoulli's reference to it in his correspondence with Newton, it has acquired a historical interest. See APPENDIX, No. XXIII., where I have prefixed to it Brook Taylor's letter to Sir Isaac, dated 22d April, 1716, in which Montmort's regard for Newton is specially mentioned.


This friend had seen in the list of Fellows for 1718 the name of Bernoulli; but in a work entitled Magnæ Britanniæ Notitia, by John Chamberlayne, the friend of Newton, published in 1718, p. 144, he saw a catalogue of the Fellows containing the name of his nephew, but not his own.


See p. 74.


John Bernoulli was born at Basle on the 7th August 1667, and died there on the 1st of January 1748, in the 81st year of his age. He was one of the most distinguished mathematicians of the last century. He was Professor of Mathematics at Basle, and one of the eight Associates of the Academy of Sciences. Two of his sons, Daniel and Nicolas, to the last of whom Newton sent copies of his Optics, were eminent mathematicians. His works were published in 1742 at Lausanne and Geneva, in 4 vols. 4to.


Page 263 of the 1st edit. and p. 232 of the 2d edit. In his letter to the Abbé Varignon, in the autumn of 1719, Newton mentions that N. Bernoulli had pointed out this mistake, and adds, "constructionem propositionis correxi, et correctam ei ostendi, et imprimi curavi non subdole, sed eo cognoscente." — Macclesfield Correspondence, vol. ii. p. 437. John Bernoulli had previously shewn in 1710, that Newton's result was erroneous when the curve was a circle, and he resumed the subject in the Leipsic Acts for February and March 1703. "It is remarkable," says Mr. Edleston, "that both of these mathematicians mistook the source of the error. They imagined that Newton had taken the coefficients of the successive powers of h in the expansion of xxpn for the successive fluxions of xx." — See Comm. Epist. Leib. et Bern. tom. ii. p. 229; Bernoulli Opera, tom. i. pp. 489, 509; and Edleston's Correspondence, &c., pp. 142, 145, 156, 170.


Dated Padua, May 31, 1717.


I find this fact stated in a letter to Newton from the Scotch mathematician James Stirling, who met with Nicolas Bernoulli when he was at Venice in 1719. The postscript to the letter containing a message from Bernoulli to Newton is interesting. I have given it in APPENDIX, No. XXIV.





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