and that Mr. Collins was very free in communicating to able Mathematicians what he had received from Mr. Newton and Mr. Gregory.

2. THAT when Mr. Leibnitz was the firft Time in London, he contended for another differential Method, properly fo called; and notwithstanding that he was Thewn by Dr. Pell, that it was Mouton's Method, perfifted in maintaining it to be his own Invention, by Reason that he had found it by himself, without knowing what Mouton had done before, and had much improved it. And we find no Mention of his having any other differential Method than Mouton's, before his Letter of the 21ft of June 1677, which was a Year after a Copy of Mr. Newton's Letter, of the 10th of December 1676, had been fent to Paris to be communicated to him; and above Four Years after Mr. Collins began to communicate that Letter to his Correfpondents, in which Letter the Method of Fluxions was fufficiently defcrib'd to any intelligent Perfon.

3. That by Mr. Newton's Letter of the 13th of June 1676, it appears, that he had the Method of Fluxions above five Years before the writing of that Letter. And by his Analysis per Equationes Numero terminorum infinitas, communicated by Dr. Barrow to Mr. Collins in July 1669, we find that he had invented the Method before that Time.

4. That the Differential Method is one and the fame with the Method of Fluxions, excepting the Name and Mode of Notation, Mr. Leibnitz calling those Quantities Differences, which Mr. Newton calls Moments or Fluxions; and marking them with the Letter d, a Mark not used by Mr. Newton. And therefore we take the proper Question to be, not who invented this or that Method. but who was the firft Inventor of the Method. And we believe that thofe, who have reputed Mr. Leibnitz the first Inventor, knew little or nothing of his Correfpondence with Mr. Collins and Mr. Oldenburgh long before; nor of Mr. Newton's having that Method above fifteen Years before Mr. Leibnitz began to publifh it, in the Acta Eruditorum of Leipfick.

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<6 FOR which Reafons we reckon Mr. Newton the first "Inventor; and are of Opinion, that Mr. Keill, in afferting the fame, has been no ways injurious to Mr. Leibnitz. And we fubmit to the Judgment of the Society, whether "the Extract and Papers now prefented to you, together with what is extant to the fame purpofe in Dr. Wallis's "Third Volume, may not deferve to be made publick.'

WHEN the Commercium Epiftolicum was first publifhed, Mr. Leibnitz being then at Vienna, that he might let it pafs without any Anfwer thereco, pretended for two Years that he had not leen it; but that he had appeal'd to the Judgment of an eminent Mathematician, who was very fkilful in thefe Matters, and not at all a Party-Man: And difpers'd abroad his Opinion, dated the 7th of June 1713, inclosed in a flying Paper dated the 29th of July, without the Name either of the Judge, or of the Printer, or of the City in which it was printed. And about the End of the Year 1715, in his Letters which he wrote to Mr. L' Abbe Conti, then at London, he (inftead of replying to the Commercium Epiftolicum as he ought to have done) flies off to New Queries concerning Occult Qualities, Univerfal Gravity, Miracles, the Organs and Senforium of the Deity, Space, Time, a Vacuum, Atoms, the Perfection of the World, and a Supra-Mundane Intelligence; and propofed a Problem taken out of the Acta Eruditorum to be folv'd by the English Mathematicians: All which Things have nothing to do with the Matter in Difpute.

Befides, he accufed the Committee appointed by the Royal Society, who had publifhed the Commercium from Antient Papers, as if they had been prejudic'd against him; and, in printing the old Letters, had omitted all thofe things which either made for him, or against Mr. > Newton. And to prove this, he wrote in his first Letter to the Abbe Conti, that in his Second Journey into England, Mr. Collins fhew'd him a Part of his Commercium, in which Mr. Newton acknowledg'd his Ignorance in many Things, and faid (amongst others) that he had found out nothing about the Dimenfions of Curvilinear Figures, excepting that of the Ciffoid: But that the Committee had fupprefs'd all this. Mr. Newton, in his Letter to the a forefaid Abbe Conti, dated the 26th of February, 17},

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anfwered;

anfwered, That this was not omitted by them, but was extant in his Letter fent to Mr. Oldenburgh the 24th of October 1676, and printed in the Commercium Epiftolicum, Page the 74th, Lines the 10th and 11th. Afterwards Mr. Leibnitz, in his next Letter to M. L'Abbe Conti, dated the 9th of April, 1719, confefs'd, that he was mistaken. But, fays he, I will give you another Example. NEWTON, in one of his Letters to Mr. Collins, owns, That he could not find the Magnitude of the Second Sections (or Second Segments) of Spheroids, and fuch like Bodies: But that the Committee had not published this Paffage, or this Letter. In the Obfervations that Mr. Newton made upon this Letter of Leibnitz, he anfwers, That if the Committee had omitted this, they had done it very justly, fince Cavillings of this Nature have no Relation to the Matter in Queftion: But that the Committee had indeed not omitted it. For Mr. Collins, in his Letter to Mr. Gregery of the 24th of December 1670, as alfo in his to Mr. Bertet 1671, (both printed in the Commercium, Pages the 24th and 26th) writes, That the Newtonian Method extended to the Second Segments of Solids, which are generated by Rotation. And Mr. Oldenburgh wrote the fame to Mr. Leibnitz himself, December the 8th, 1674, as may be seen in the Commercium, Page the 39th. Therefore Mr. Leibnitz is again miftaken. Furthermore, in the Philofophical Transactions for Jan. and Feb. 1718. Page the 925th, it is faid, that M. L'Abbe Conti spent feveral Hours in looking over the Old Letters and Letter-Books preferv'd in the Archives of the Royal Society, to fee if he could find any thing which would make either for Mr. Leibnitz, or a gainst Mr. Newton, and which was omitted in the Commercium Epiftolicum; but he could find nothing of this kind.

MOREOVER, Mr. Leibnitz, that he might difmifs the Commercium Epiftolicum without any Anfwer, in his first Letter to Mr. L'Abbe Conti fays, That they who had written against him (that is the Committee appointed by the koyal Society) and had attacked his Candor by hard and ill-grounded Interpretations, should not have the Pleasure of ferng bis Anfwer to the weak Arguments of those who made fo ill an Ufe of them. Indeed thofe Interpretations are of no Authority, except what they derive from the Letters

Letters themselves; but that they are ill-grounded Mr. Leibnitz has never yet been able to fhow.

BUT immediately upon this, Mr. Newton, who could fcarcely be perfuaded to anfwer him, in his first Letter to Mr. L'Abbe Conti dated the 25th of February 17 thus wrote: Mr. Leibnitz hitherto has refused to answer (viz. the Commercium Epiftolicum) well knowing it to be impoffible to confute Matters of Fact. He excufes his Silence in this Matter, pretending, he has not yet feen the Book ; and that he has no Leifure to examine it, but that he had defired an eminent Mathematician to take this Trouble upon him. He alfo ujes a new Pretence that he may not answer it, faying, That the English fball not have the Pleasure of feeing his Anfwers to their impotent Reasonings, and proposes new Philofophical Disputes, and Problems to be folved, both which have nothing to do with the Controversy. But Mr. Leibnitz in his next to Mr. L'Abbe Conti of the 9th of April 1716 continued to excuse himfelf from giving any Anfwer; For, (fays he) in order to anfwer particularly a Book publish'd against me, it will require another Work no less than that is; I must run over a vaft Body of Minutes of 30 or 40 Years past, and of which I remember very little. It will be neceffary to examine old Letters, a great Part of which are loft, befides that I have preferv'd but a small Part of my Remarks, and the rest are buried in an immenfe Heap of Papers, which I cannot without much Time and Patience examine. But I have no Leifure at all for thefe Things, being taken up with Affairs of another Nature. And, a little after he fays, They ought not to have mangled the Letters ; for there are but very few of my Papers, of which I have even the Minutes left. Thus having weighed all Things, and feeing fuch evident Marks of Malignity and Falfhood, I thought it unworthy of me to enter into a Difpute with a Set of Men who have behaved themselves fo very ill.

I FIND that in confuting them, it will be difficult to abstain from Reproaches and harfh Expreffions, fuch as their Actions deferve, and I do not defire to exhibit fuch. a Spectacle to the Publick, having a Mind to spend my Time better, which ought to be precious to me, and to defpife the Judgment of thofe who would pronounce Sentence against me upon fuch a Work; especially fines

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the Royal Society hath not feen fit to do it. Thus far Leibnitz. He runs off from the first Queftion into wrangling, and propofing new Questions.

But after his Death (which happen'd in November following) in his Elogy, which was printed in the Acta Eruditorum, for the Month of July 1717, his Friends wrote, That he had determined to oppofe fomething of his own to the Commercium Epiftolicum Collinii, et aliorum; and that he had fignified to the, Famous Wolfius, a few Days be fore his Death, that he would in very deed refute the Englife, who had difcredited him: And that, as foon as he had any Vacancy from his Hiftorical Labours, he would publish fome thing in Analyfis altogether unexpected, and which fhould have no Affinity to the Inventions hitherto exhibited to the Publick, whether of Mr. Newton, or of others.

This they fay. But from what has been faid already, it is plain that he had no other Commercium Epiftolicum to publifh. And as for his new Invention, which has no Affinity to thefe Things, this hath nothing to do in the Matter. Paffing by therefore thefe Dreams of fick Men, the whole Question ought to be referr'd to ancient Letters.

In the Beginning of Mr. Leibnitz's Second Letter to M. L'Abbe Conti he calls the firft Letter of Sir Ifaac Newton a fort of Challenge from him; and adds, I will not enter the Lifts against his Emiffaries, whether you confider the Accufer upon the Foundation of the Commercium Epiftolicum, or the Preface full of Acrimony, which ano ther of them has prefixed to the new Edition of his Principia: But when he shall voluntarily appear by himself, I am ready to give him Satisfaction. To this Mr. Newton anfwered, That Leibnitz had laid afide old Letters and Papers, and had run off to Questions about Philosophy, and other Matters; and that he had induc'd that Great Mathematician, to whom without any Name, as a Fudge, he had attributed that Letter of the 7th of June 1713, as a Second in the Quarrel, challenging the English Mathematicians to folve certain Problems: As if a Duel with himself, or a Battle with his Army of Scholars he boafts of, was a more proper Way to determine the Truth, than an Examination of ancient and authentick Writings; or as if Mathematicks hereafter were to be fil led with Heroick Actions, inftead of Reafonings and Demonftrations.

LET