Historical Annotations on the Elogium of Leibniz Isaac Newton c. 10,667 words The Newton Project Oxford 2020 Newton Project, University of Oxford

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 c. 1700-1727, in English with Latin and French, c. 10,667 words, 10 ff. 10 ff.

in English with Latin and French

 MS Add. 3968, ff. 372r-381v, Cambridge University Library, Cambridge, UK UKCambridgeCambridge University Library Portsmouth Collection MS Add. 3968, ff. 372r-381v c. 1700-1727 England English Latin French Isaac Newton Unknown Cataloguer (1) Unknown Cataloguer (2) Unknown Cataloguer (6) ScienceMathematics Transcription by Marie Soulier Transcription by Michelle Pfeffer Transcription continued by Robert Ralley Transcription completed by Robert Ralley. Code audited by Michael Hawkins.
372 Part of Hist Annotations in Elog of Leibnitz a 1717?

Pag 44. l. 1. What Mr Newton calls fluxions & marks sometimes with prickt letters & sometimes wthwith other marks Mr Leibnitz doth not call fluxions differences, nor hath any name or mark for them. What Mr Newton calls moments & marks sometimes with prickt letters sometimes with & particles other marks, Mr Leibnitz calls differentces & marks by prefixing the letter d Mr Leibnitz calls differences; AndBut & fluxions are motions of increase quantities of another kind. They are motions motions or velocities of increasieng They are no & not small of quantities & not parts of the increasing quantities.

Ib. l. 3, 4, 5. When the Marquess de l'Hospital represented that the Characters of Mr Leibnitz were more convenient then those of Mr Newton, he had seen only the marks used by Mr Newton in the second Lemma of the second Book of his Principles & therefore meant those Characters & not prickt letters. Of Of his marks by prickt letters &c he knew nothi The marks by prickt letters & the letter o are the most useful & the best adapted to true reasoning. But They that have been used to the characters of Mr Leibnitz will be apt to think them the best.

Ib. lin. penult. Before this, Dr Wallis in the Preface to the two first Volumes of his Works published A.C. 1695 wrote that Mr Newton in his two Letters of 1676 explained to Mr Leibnitz the Method found found by him ten years before or above, that is in the year 16656 or 1665 before. And an anonymous the Editors of the Acta Eruditorum in giving an account of those two Books replied falsly that Mr Newton had both publickly & privately allowed the invention of the Method to Mr Leibnitz. And even before this when Mr Leibnitz first published the elements of the differential method & made no mention of his corresp any thing he had re correspondence he had wthwith Mr Newton six years before by means of Mr Oldenbeg: Mr Newton added the wrote the Scholium to described the Elements of the Method in yethe second Lemma of the second book of his Principles not to give away the e & wrote the Scholium to that Lemma, not to give away the Lemma as Mr Leibnits has pretended, but to assert it to himself.

P. 48. lin. 15. Mr Newton was first accused of Plagiary in the Acta Eruditorum for Ianuary 16 1705 pag 34 & 35 & the accusation was justified by Mr Leibnitz himself in his Letter of 29 Decem. 1711 to Dr Sloan And when yethe Committee of the R S And for obviating this accusation the Committe insinuated that there was more colour to suspect Mr Leibnitz nec lex est justior ulla.

P. 49. l. 20. Mr Leibnitz has affirmed that he found the differentiall method in the year 1676, & therefore could not undertake to prove that he by a new Commercium that he found it before. And if he did not find it before, he was not the first inventor. And second Inventors have no right. The first Inventor has the sole right till another Inventor arises: & then to take away the right of wchwhich he was once justly possessed & share it with others would be injustice. All

p. 47. lin. 65, 6 A copy of This Letter was writ to Mr Collins in 1672 & a copy of it sent to Mr Leibnitz in 1676 Iune 1676 pag 34 & 35

p. 51. lin. 21. Mr Leibnitz went from London to Paris in March 1673 & continued to write Letters to Mr Oldenburg till Iune 8th fo about Arithmetical Matters till Iune 8th following. Then he intermitted his correspondence for a year & in the mean time applied himself to learn the higher Geometry by means of Mr Huygens whose Horologium oscillatorium came abroad that year in April. And by reading this first this & then some the other books I here mentioned, he got light into the method wchwhich gave him the Theoremes here mentioned like those of Barrow & Gregory. And now he had his Method by the Differentiæ generatrices in Arithmetic, & that by the Triangulum characteristicum in Geometry. But he had not yet the Differential method in Algebra, for he tells us in one of of his Letters that he found that in the year 1676.

Pag. 53 l. 6. He did not see Mr Newtons papers before the year 1676. Vpon the death of Mr Collins Gregory he desired that a collection of Gregory correspondence might be made & sent to Paris. It was sent Iune 26 1676 & therin was, 1 Mr Gregories Letter to Mr Collins dated 15 Feb. 16721 conteining Gregories Series for squaring the circle, published afterwards by Mr Leibnitz without ackcnowledgeing what he had received from London. 2 A letter of Mr Gregories Letter of 5 Sept 1670, in wchwhich Gregory mentions that from by the help of Dr Barrows method of Tangents he had found a general method of Tangents without calculus, vizt a method like that of Slusius. 3 Mr Newtons Letter of 10 Decem 1672 in wchwhich Mr Newton described his general method of Analysis & said that the method of Grego Tangents of Gregory & Slusius was but a Corollary or branch thereof. And at the same time Mr Newtons Letter of 13 Iune 1676 was also sent in the end of wchwhich he writes that Analysis by the method of series & anot some other methods becomes very (meaning the methods of fluxions & arbitrary series, becomes very universal. And in October following Mr Leibnitz coming to London saw Mr Newtons Letter of 24 October wherein Mr Newton further describes the Method of fluxions, & mentions also his m his Compendium of the Method of series communicated by Dr Barrow to Mr Collins presently in the ye upon the publishing of Mercators Logarithmotechnia, A.C. 1669, that is the Analysis per series numero terminorum infinitas. And having the year before written to Mr Oldenberg to procure Mr Newtons method of series & from Mr Collins & now meeting with this further notice of it: he could scarce miss of seeing it. For he app went to ap consulted Mr Collins at that very time to see what he could meet with of the correspondence of Mr Gregory & Mr Newton with Collins concercerningconcerning these series. And if he there saw this Analysis he had a sufficient plane description of the method of fluxions at the end of it.

P. 53. l. 22. Mr Newton inserted the inserted having occasion to use the Elements of the method of mo of Moments into yethe second Lemma of thise second Book of his Principles, & added a Scholium to the Lemma justify his doing so. And last And this he did without under in a manner without g or offend And when a Letter of Mr Leibnitz written neare then end of t in Autumn 16715 had been handed about some time among persons of note in London & Mr Newton was pressed to answer it, he returned an answer dated Feb 26 1616 & Mr Leibnitz sent these Letters with his Answer to

P. 48. l. 6 A Letter writ by Mr Leibnitz in Autumn 16 1715 being handed about some time among persons of note in London, Mr Newton was at length pressed prevailed with to answer it, which wchwhich he did by an Letter dated Feb 26 16716. Mr Leibnitz wrote answered it that Letter by another dated 9 Apr. 1716. But [considering that he because he began this Letter Answer with a pretence that MIr N had challenged him & that he would now enter the lists & give him satis] & instead of sending this Letter todirectly to London he sent it with the two former Letters to Paris, And ✝ ✝ The third came from thence to London from whence & it came thence to to London: Mr Newton returned no answer, but only shewed privately to some of his friends Mr Newton returned no answered him no further to this, but only drew up shewed some of his friends in private what answer might have been answered: & afte upon the death of Mr Leibnitz, becaus the three first Letters had been dispersed, published them, with what the answer what was drwndrawn up, but not sent.

P. 53 l 22 Mr Newton published the elements of the method in the 2d Schol of the 2d bo

1 What Mr Leibnitz calls Differences Mr Newton calls not Flu not fluxions but Moments & small particles. Fluxions are quantities of another kind & Mr Leibnitz hath no marks nor name for them. They are motions or velocities of increase & not partiscles of the increasing quantity.

2 to think them best: but that Mr Newtons are more universal & better adapted to just reasoning may appear by this instance. Let x, y, z be fluents x., y., z. their fluxions & x.×o, y.×o z.×o their moments: & let any equation expressing the relation of the fluents, as b⁢b⁢x−c⁢x⁢y+z⁢z=0 being given let it be required to find the relation of their fluxions. Put find in this equal Let x flow uniformly & it fluxion x. be 1 & its moment will be o & after one moment of x the fluents will become x+o, y+y.⁢o, z+z.⁢o, wchwhich being substituted for the former flu & the equation will become b⁢b⁢x+b⁢b⁢o−c⁢x⁢y−c⁢o⁢y−c⁢x⁢y.⁢o−c⁢y.⁢o⁢o+z⁢z+2⁢z⁢z.⁢o+z.⁢z.⁢o⁢o=0. And striking out b⁢b⁢x−c⁢x⁢y+z⁢z=0, there will remains b⁢b⁢o−c⁢o⁢y−c⁢x⁢y.⁢o−c⁢y.⁢o⁢o+2⁢z⁢z.⁢o+z.⁢z.⁢o⁢o=0. dDivide the whole by o & the Quotient will be b⁢b−c⁢y−c⁢x⁢y.−2⁢c⁢y.⁢o+2⁢z⁢z.+z.⁢z.⁢o=0. Let the moment o become infinitely little & the æqua terms −2⁢c⁢y.⁢o+z.⁢z.⁢o will become infi vanish, & the remaining equation will give the b⁢b−c⁢y−c⁢x⁢y.+2⁢z⁢z.=0 will give the relation of the fluxions to wchwhich the moments are proportional. Here the whole operation is exact & as evident as any thing in mathematicks & all the quantities are finite (as they ought to be in Geometry) toUntil the operation is finished & then o is made to decrease in infinitum & vanish And if o be at any time during the operation supposed indefinitely or infinitely little yet it is the only infinietlyinfinitely small quantity in the whole operation wchwhich is infin supposed infinitely little & it is always supposed to be a constant given quantity: whereas in the notation of Mr Leibnitz & the Artist is at liberty to take o for a quantity finite or infinitely small as he shall find it best for dispatch his purpose whether he has a mind to be exact or to make dispatch by approximation. But in the differential notation of Mr Leibnitz, there are more infinitely small quantititises then one. always two or more infinitely small quantities & more of them then one & all of them & one or more of them are always inconstant & but one, & the calculations are generally grounded upon approximations. The errors indeed are infinitely small, but Geometry admits of no errors. In these calculations a right line may be considered as touching a Curve in more points then one, but Ge & an chord infinitely short may be considered as coincident with its Arch: but Geometry admits of no such Propositions.

Mr Leibnitz might become acquainted wthwith Mr L Huguens in 1672 but when he was in London the first time wchwhich was in Ian. & Feb. 1673 he knew nothing of the higher Geometry. The Horologium oscillatorium of Mr Huguens was published in April 1673 The Letter writ to Collins in 1672 Mr Leibnitz did not see till 1676. Pag. 53. lin. 6. A copy of Mr Newtons Letter of 10 Decem. 1672 was not sent to Mr Leibnitz in Iune the end o Iune 26 1676. And Mr Leibnitz was not accused by the Committee of the R. S. of understanding all that he had seen, but only that in what he saw had seen, the Method of Fluxions was sufficiently described to any intelligent person. And Mr Tschurnhause & Mr Iames Bernoulli thought it almost described in Dr Barrows works alone. The words of Bernoulli in the Acta Erud. for Ian. 1691 pag. 14 are these Qui calculum Barrovianum — intellexerit alterum a Dn Leibnitio inventum ignorare vix poterit; utpote qui in priori illo fundatus est & nisi forte in differentialium notatione & operationis aliquo compendio ab eo non differt. The Marquess de l'Hospital in the Preface to his works Book said that Dr Barrows calculus stuck at fractions & surds & that where Dr Barrow left off Mr Leibnitz went on. He had not yet seen Mr Newtons Letters of 10 Decem. 1672 & 24 Octob 1672 in wchwhich Mr Newton wrote that his general method did not stuick not at surds. But Mr Leibnitz had seen them before he found the differential method in the year 1676. before he found the Differential Method, & thereby knew that Mr Newton was before him in this particular. He might learn from Gregories Letter of Sept 5 1670 that Gregory had improved Barrow's Method of Tangents so as to draw Tangents without calculation, & from Newton's of 10 Decem 1672 that this Method was the same with that of Slusius & that both Methods wasere a branch or Corollary or Branch of Newtons general Method & by consequentsce that Newton's general Met Barrows Method was a step to that of Gregory & Slusius & both of them were steps to Newtons general method, & this might make him write in the beginning of his Letter of 21 Iune 16977 Clarissimi Slusij Methodum Tangentium nondum esse absolutam Celeberrimo Newtono assentior; & then set down an specimen example of Dr Barrows method of Tangents with the notation altered, & conclude the calculation with these words Quod coincidit cum Regula Slusiana, ostenditque eam statim occurrere hanc Methodum intelligenti. And a little after: Methodo autem Slusiana omnes ordine irrationales tollendas esse nemo notn videt. Arbitror quæ373 Arbitror quæ celare voluit Newtonus de Tangentibus ducendis, ab his non abludere Quod addit, ex hoc eodem fundamento Quadraturas quoque reddi faciliores me in hac sententia hac confirmat; nimirum semper figuræ illæ sunt quadrabiles quæ sunt ad æquationem differentialem. Now Mr Newton L. having seen all this in Mr Newton's Letters & Papers abovementioned before he understood the method & understanding all this out of them so soon as he understood the Method, the Committee of the R. S. may be excused for saying that in what Mr Leibnitz had seen the Method was sufficiently described to any intelligent person. Pag 44 T lin 10, 11. The Editors of the Acta Erudit. would print nothing in other characters. Pag 45. l 8, 9. The ing assuming of right by second Inventors upon a supposition after it appears that he was not yethe first is plagiary notwithstanding theat the second Inventor may have invented apart without knowing what the first had done before. Pag 49 lin 9, 10. This writing without affow denyed in effect that Mr Newton understood the first Proposition in his own Book of Quadratures, or that the Elements of the Differential Method are conteined in the second Lemma of the second Book of Principles, or that the sentence Data æquatoneæquatione fluentes quotcunque quantitates involvente invenire fluxiones et vice versa, denotes the method of fluxions, or that the series for squaring of Curves wchwhich breaks off & becomes finite when the Curve may be squared by a finite equation, & wh whas found by thaet Method of fluxions altho Mr Newton said in his Letter of 24 Octob. 1676 that it was found by that method & in his book of Quadratures shewed how it was found by that Method, & there is no other method yet known by wchwhich it can be found. He denied these things not in express words but by denying that there was any p. 54. l. 7, 8. The Editors of the Acta Leipsica never would print any thing with other characters then those of Mr Leibnitz, wchwhich against Mr Leibnitz or wthwith other characters then the Differential. When Mr Fatio sent them a Paper against Mr Leibnitz they would not print it. Whe When In giving an Account of Dr Wa the two first Volumes of Dr Wallis's works they would not let the reader know what objection the that the DrDoctor ascribed the ascribed the DrDoctor ascribed the Differential method to Mr Newton as being found by him in the year 1666 or before, the oldest Inventor but shuffled of the Objection by suls pretending feigning that Newton had always both publickly & privately acknowledged Mr Leibnitz the inventor. N In giving an Account of Mr Newtons book of Quadratures instead of giving an account of Mr Newto the characters used by Mr Newton used in that Book they gave an account of the characters used by Mr Leibnitz. When Dr Keil sent them a paper with writ in Mr Newtons characters they would not print it in those characters. Pag. 53. lin 22. When In the year 1684 Mr Leibnitz published the elements of his calculus Method without making any mention of his the correspondence between him & Mr Newton eight years before as in candour he ought to have done. For he knew by that correspondence that Mr Newton had then & five ye such another Method, as is plain by his Letter of 12 Iuly 1677 & that he had it & wrote of it in the year 1671 or before & therefore was the oldest Inventor, as is plain by Mr Newton's Letters of 13 Iune & 24 October 1676. Mr Newton therefore inser in the year 1686 inserted set down the Elements of this method as his own in the second Scholium Lemma of the second book of his Principles & [in a Scholium added to that Lemma he told the Reader that he did not give away that Lemma to Mr Leibnitz as Mr Leibnitz has pretended but asserted his right to it as] added a Scholium to that Lemma not to give away that Lemma to Mr Leibnitz as has been pretended but to assert his own right to it as first inventor. And yet Mr Leibnitz co And yet Mr Leibnitz continued to claim it upon a pretence that he found it apart, tho he knew that he was not the first inventor.
374 Historical Annotations on the Elogium of Mr Leibnitz. 1 Pag. 44. lin. 1. Fluxions are not differences. They are quantities of another kind, & Mr Leibnitz hath no marks nor name for them. They are motions or velocities of increase & not parts of the increasing quantity. What Mr Leibnitz calls Differences Mr Newton calls Moments & particles& designes them by fluxions multiplied by the moment o. 2 Ib. lin. 3, 4, 5. When the Marquess de l'Hospital represented that the characters of Mr Leibnitz were more convenient then those of Mr Newton, he had seen only the characters used by Mr Newton in the second Lemma of the second book of his Principles & therefore meant no other. 3 Ib. lin. 22. Mr Fatio was not the first. Dr Wallis, so soon as he heard that the method of Mr Newton was spreading in Holland by the name of the Differential Method of Mr Leibnitz, wrote in the Preface to the first volume of his works, published in April 1695, that Mr Newton in his two Letters of Iune 13th & Octob. 24, 1676, had explained to Mr Leibnitz the method of fluxions or differences found by him ten years before or above; that is, in the year 1666 or before. 8 Pag 545. lin. 63. A letter writ by Mr Leibnitz in autumn 1715 being handed about among persons of note in London, Mr Newton was pressed to return an answer, & at length did so by a Letter dated Feb. 26, 1716, & Mr Leibnitz replied Apr 9th 1716, but sent his Reply to Paris (with Copies of the two former Letters) to be communicated to his friends there before it came to London. For which reason Mr Newton wrote to him no more, but only shewed privately to a few of his friends what might have been writ in answer. 4 Ib. Pag. 48. lin. 15. Mr Newton was accused of Plagiary in the Acta Eruditorum for Ianuary 1705 pag. 34 & 35, & the accusation was justified by Mr Leibnitz himself in his Letter to Dr Sloane dated 29 Ian. 1711. And for obviating this accusation the Commercium Epistolicum insinuated that the contrary was more to be suspected, Mr Leibnitz having seen severall of Mr Newton's Papers Letters in the year 1676, it not appearing that he had the Method before he saw them. 5 Pag 49. lin. 20. Mr Leibnitz pretended that the Committee of the R. Society had in the Commercium Epistolicum omitted many things wchwhich ought to have been published, & upon that account pretence proposed to print a new Commercium impartially, & in autumn 1714 desired that the original Letters in the custody of the R. Society might be sent to him for that purpose. Mr Newton replied before the R. Society that the Commercium was printed out of Originals which had been constantly in their Archives & those of Mr Collins, & had been also examined by those who knew the hands, & that they ought still to be kept safe for justifying what had been printed out of them. He added further that he did not print the Commercium himself, nor so much as produce any Letters or Papers which he had then in his own custody, because he would not make himself a witness in his own cause. And to prove the truth of what he said he produced two Letters written to himself the one by Mr Leibnitz March 7th 1693, the other by Dr Wallis Apr. 10th 1695. These Letters were examined before the R. Society by them who knew the hands & then they were read & laid up in the Archives of the R. Society as authentic. At the same time it was allowed that if Mr Leibnitz had any Letters in his custody which he thought material to be published, & pleased to send them to any friend in London whom he could trust with them that they might be publickly examined by those thawho knew the hands, & attested copies be taken of them: they might then be published either in the Phil. Transactions or by Mr Leibnitz himself. But nothing has been sent. On the contrary Mr Leibnitz having been since pressed to return a direct Answer to the Commercium, replied in his Letter of April 9th 1716. Pour repondre done de point en point a l'Ouvrage publié contre moi, il falloit une autre Ouvrage aussi grand pour la moins que celuy là, il falloit entrer dans une grand detail de quantité de Minuties passéses il y a 30 ou 40 ans dont je ne me souvenois gueres; il me falloit chercher mes velilles Lettesres dont plusieurs se sont perdues, outre que le plus souvent; je n'ay pas gardé les Minutes des miennes; et les autres sont ensevelies dans une grand tas de Papiers, qui je ne pouvois dedebrouiller qu' avec du Temps & de la patience. Mais je n'en avois gueres le loisir, etant chargé presentmant d'Occupations d'une toute autre nature. And the author of the Elogium of Mr Leibnitz published in the Acta Eruditorum for Iuly 1717 pag. 335, writes: Quo tamen perspicerent intelligentes quid de tota illa controversia sentiendum sit, Commercio Epistolico Anglorum aliud quoddam idemque amplius opponere decreverat, & paucis ante obitum diebus Cl. Wolfio significavit se Anglos famam ipsius lacessentes reipsa refutaturum: quamprimum enim a laboribus historicis vacaturus sit, daturum se aliquid in Analysi prorsus inexpectatum & cum inventis quæ hactenus in publicum prostant, sive Newtoni, sive aliorum nil quicquam affine habens. Here Mr Leibnitz wrote only that he would refute the English (he doth not say with a new Commercium, as the Author of the Elogium seems to understand, but) with a new surprizing invention in Analysis of another kind. And this he wrote a few days before his death, & we were to stay for the performance till his Historical labours should be at an end. Pag 51. lin. 22. Mr Leibnitz might become acquainted with Mr Hugens in the year 1672; but when he was in London the first time wchwhich was in Ianuary & February 1673, & while he kept a correspondence wthwith Mr Oldenburg about Arithmetical matters which was till Iune following, he knew nothing of the higher Geometry The Horologium oscillatorium of Mr Huguens was published in April 1673, & in studying the higher Geometry he read first this book & then the works of Paschal & Gregory of St Vincent & then fell upon his Triangulum characteristicum & his many Theorems, & went on to his Method founded on his Analytical Tables of Tangents & his Combinatory Art & this was the top of his skill when he wrote his Letter of 27 August 17 1676. For in that Letter he said of one part of this Letter Method Nihil est quod norim in tota Analysi momenti majoris. And of another part: Cujus vim ac potestatem nescio an quisquam hactenus sit consecutus. Ea verò nihil differt ab Analysi illa suprema ad cujus intima Cartesius non pervenit. Est enim ad eam constituendam opus Alphabeto cogitationum humanarum. In the same Letter he used the common Algebra where the Differential Calculus would have been proper had he then known it, & said that iInverse Problemes of Tangents could not be reduced to Equations. In October following he was again in England where he met with Barrows works & Newton's Letter of 24 Octob. 1676, & saw the correspondence of Gregory & Newton in the hands of Collins, having seen Newton's Letters of 10 Decem 1672 & 13 Iune 1676 three mon & Gregories of 5 Sept. 1670 & 15 Feb 1671 three months before. And it doth not appear that he found the Differential method before he saw all this. See his Letter of 9 April 16716. Pag. 53. lin. 6. The Letter was writ to Mr Collins in 1672 & seen by Mr Leibnitz in 1676. 375 NB. Mr Leibnitz in his Letter of Iune 21. 1677 acknowledged a similitude between the Methods & NB Mr Leibnitz observed & acknowledged this similitude of the Methods long before the publishing of the two books here mentioned, namely in his Letter of 13 Iune 16797. Here he acknowledges it again; but contends He acknowlegdged it also in his letter to me date And he Andlso in thise Paper in which he published the elentselements of the Differential method A.C. 1684 he allowed a methodus similis. Also in his Letter to me dated 717 March 1693 & printed above he allowed the same thing & e that by the Principia Philosophiæ mathematiaca I had shewed that I had such a method, & here he exprest himself in such a manner as with some deference to me, as if he also had endeavoured to do the like. And now after the publication of the edition of the two first Volumes of the Works of Dr Wallis he repeats the acknowledgment allowing that the Methods are so far the same that he calls them both by the common name of the infinitesimal method And theBut as the Analysis of Vieta & Cartes were called by the common name of Analysis speciosa & yet differed by some improvements wchwhich Cartes had made to the method of Vieta, so the the Diferential method h my infinitesimal Analysis & his might differ in some improvements which he had made to mine & which were not yet come to the knowledge of Dr Wallis. And three of those improvements he names, 1 the reduction of transcendent quantities to Equations. 2 The reduction of such Curves to Equations as Cartes called Mechanical. 3 The invention of Exponential Equations. [And thus the general infinitesimal method common to us boboth, & here allowed to be mine & the improvements made to it by Mr Leibnitz are his.] While Mr Leibnits contended from d that my method & his differed in somethings its plain that he did not yet begain to claim the whole [Nor did Dr Wallis claim for me the improvements wchwhich Mr Leibnitz had made to the Method. [The DrDoctor told him published that I had invented the Method in the year 1666 or before & Mr Leibn. in all the Letters which afterwards past between them, the did not deny it. [The DrDoctor told him published that in the year 1676 I had by Letters explained this method to Mr Leibnitz th & he answers that he had the first light into the method from the consideration of the summs & differences in Numbers: the Summs differences answering to tangents & the summs to Quadratures] I nor pretends that he had it before the year 1676. And second inventors have nor right]. Mr Leibnitz claimed the improvements & Dr Wallis claimed the rest for me as the oldest inventor by many years, & was not complained of for this by Mr Leibnitz. De te autem queri, saith Mr Leibnitz nunquam mihi in mentem venit quem facile apparet nostro [our improvements] in Actis Lipsientibus praodita, [our improvemts] non satis vidisse. — for saying that I invented the method in the year 1666 or before & explained it in my Letters ten years after in my Letters. The Mr Leibnitz did not deny that I complain of the DrDoctor for saying that invented yethe method in the year 1666 or before & explained it ten years after in my letters, but And so the question wchwhich then remained between them was about these improvements & particularly whether the symbols ∫a⁢ab+x, ∫dx2⁢x−x⁢x & such like by wchwhich he designed transcendent quantit & introduced them into equations or mine for the same purpose a⁢ab+x. dx2⁢x−x⁢x & the like, or &c were the oldest, or whether the summatory method or the inverse method of fl fluxions was the oldest. For my part I said in my Letter of 24 Octob 1676 that in the year 1671 I wrote a Tract in the year 16 five years before, that concerning the method of series & another method together, & that other e said there that the other method proceeded without sticking at surds & was founded in this Propositions: Data Æquatione fluentes quotcunque quantitates involvente invenire fluxiones & vice versa, that is in the direct & inverse methods of fluxions improperly called by Mr Leibnitz the methods differential & summatory methods. And I said further that this method extended to Problems about maxima &minima, & to tangensts directly & inversely, & to Quadratures, & some others & gave me the series there set down for squaring of Curves & some others of like nature. And in my Letter of 10 Decem. 1672 I (a copy of wchwhich was sent to Mr Leibnitz & came to his hands) I mentioned some others sorts of Problemes & particularyparticularly the working in mechanical curves & the finding the curvatures of Curves & the tangents of the Mechanical Curvs and in my letter of 13 Iune 1676 I said that my AnalysAnalysis (composed of the method of Series & another methods, (described afterward in my Letter ( vizt the methods methods of fluxions & arbitrary series] extended to almost all sorts of Problems exp except perhaps some numeral ones like those of Diophantus. And Mr Leibnitz in his Letter of 27 Aug. 1676, replied that he did not beleive that my method could be so general, nor extend to inverse Problems of Tangents & many others tho he had reduced one inverse probleme of Tangents (that proposed by Beaune) to a quadrature. And if all this & the method of extracting fluents out of In my Letter of 24 Octo. 1676 equations involving the fluxions & that of arbitrary series set down in my Letter of 24 Octob 1676 as known to me some years before, be not sufficient to secure these thing security: it no many must hereafter communicate any thing in writing till he has before he has secured it to himself by printing; This & so there's an end of correspondence in writing about sciences. And the next step is to make void all Indentures Bonds & other writings in law which are not in print: or at least to give the preference to those which are in print. – Copies of the two Letters of Mr Leibnitz here desired & of some others 377 Pag. 44. l. 1. Fluxions are not differences. They are quantities of another kind, & Mr Leibnitz hath no marks nor name for them. They are motions or velocities of increase & not parts of the increasing quantity. Ib. l. 3, 4, 5. When the Marquess de l'Hospital represented that the characters of Mr Leibnitz were more convenient then those of Mr Newton, he had seen only the characters used by Mr Newton in the second Lemma of the second book of his Principles & therefore meant no other. Ib. l. 22. Mr Fatio was not the first. Dr Wallis in the Preface to yethe first volume of his works dated published in April 1695 wrote that Mr Newton in his two Letters of Iune 13 & Octob 264 1676 sent to Mr Oldenburg to be communicated to Mr Leibnitz, had explained to Mr Leibnitz the method of fluxions ca found by him ten years before or above, that is, in the year 1666 or before. And Mr Newton in the year 1686 inserted the Elements of this Method into the second Lemma of the second Book of his P Pag. 48. lin. 15. Mr Newton was accused of Plagiary in the Acta Eruditorum for Ianuary 1705 pag 34 & 35 & the accusation was ratified justified by Mr Leibnitz himself in his Letter f to Dr Sloan dated 29 Decem 1711. And for obviating this accusation the Committee Commercium Epistolicum insinuated that there was in the year 1676 the contrary was more to be suspected several of Mr Mr Newton's papers relating to this matter were having been seen by Mr Leibnitz. w relating to this matter in the year 1676. Pag 49. l. 20. The whole correspondence of Mr Leibnitz & Mr Oldenburg from the begining of the year 1673 to the death of Mr Oldenburg is in the hands of the R. S. & they Pag 48. l. 6. A lLetter writ by Mr Leibnitz in Autumn 1715 being handed about among persons of note in London, Mr Newton was at length prevailed with to answer it This Answer was dated His Letter was dated Feb. 26. 1716, & Mr Leibnitz wrote an Answered to Mr Newton the letter it 9 Apr. 1716, but sent it his Answer to Paris (wthwith copies of the two former Letters) to be communicated to his friends at Paris there before it came to London, & began it with a pretence that Mr Newton's Letter was a challenge & as if Mr Newton had been the Aggressor. For wchwhich reasons Mr Newton wrote to him no more, but yet drew up in writing what might hav be said in answer & shewed it privately to a few of only shewed privately to a few of his friends what might have been said in Answer some Observations upon the last letter what might have been writ in answer And because the three Letters had been communicated in France, Mr Newton upon both France & England published them upon the death of Mr Leibnitz published them with together wthwith the said Observations. Pag 49. lin. 20. All the Letters of Mr Leibnitz to Mr Oldenburg are from the beginning of the year 1673 to the death of Mr Oldenburg are in the hands of the R. S & so are copies of all Mr Oldenburgs & M Letters to Mr Leibnitz from Decem 8 1674 to yethe end of the year 1696. Mr Leibnitz complained that And a Commercium of a later date can signify little. Mr Leibnitz complained that the Committee of the R. S. had extracted out of themse old Letters every thing that made against him & omitted every thing that made for him but foreigners who have since viewed the Letters have found it otherwise. And when lately wnwhen Mr Leibnitz pretended to gaive two instances of things omitted in them hath be he was found mistaken in them both. And in Autumn 16 1714 Mr Leibnitz desiring that the original Letters in their custody of yethe R. S. might be sent to him in order to his printing a new Commercium, the was answered, that if he had any thing in his custody wchwhich he thought material to be printed, & pleased to send the original MS to any of his friends in London; they would order it to be printed in the P. Transactions after the hand had been examined. But MSS not examined by unconcerned persons who knew the hands they would not regard. P. 51. lin. 22. M The Horologium oscillatorium of Mr Huguens was published in April 1673. Af Mr Leibnitz began presently after to study the higher Geometry Then he fell upon the triangulum characteristicum wchwhich might help him to many new Theorems like those of Gregory & Barrow. Then he fell upon his Analysis & his many new Theorems, & his a & went on to his method Method by analytical Tables of Tangents & the Combinatory Art, & this was the top of his skill when he wrote his Letter of 27 Aug. 1676. For in that Letter he saith of these things one part of this method: Nihil est quod norim in tota Analysi momenti majoris. And of anotherther part: Cujus vim ac potestatem nescio an quisquam hactenus sit consecutus. Ea vero nihil differt ab Analysi illa suprema ad Cujus intima Cartesius non pervenit. Est enim ad eam constituendam opus Alphabeto cogitationum humanarum. ✝ ✝ And there are other indications in the Letter by wchwhich it may be gathered that the differential method was not yet known to him. He seems to have learnt it in the Autumn or winter following. ✝ And soon After this, he fell upon the differential method Analysis. wchwhich was of a nature above tA The method therefore by differential equations he was not yet acquainted with, for he adds sunt Quod dicere b as may be gathered also from his words wchwhich follow in the same Letter: Quod dicere videmini plerasque difficultates ad Series infinitas reduci, id mihi non videtur. Sunt enim multa usque adeo mira et implexa ut neque ab æquationibus non pendeant. Qualia sunt (ex multis alijs) Problemata methodi tangentium inversæ. Mr Leibnitz in his Letter of 9 Apr 16 1716 reprehen said that he judged that by the words certa Analysi solvi in his Letter of 27 Aug. 1676 that he must have had them some light into the Differential calculus. And at that time. But wWhether the certa Analysis were the Differential method or the Analysis illa suprema ad cujus intima Cartesius non pervenit may be doubted: but how ever nothing more can be affirmed then that Mr Leibnitz according to the best of his knowledge & memory bega got some light into the Me Differential method in the year 1676. Pag. 53. l. 6. A copy of Mr Newtons Letter dated 10 Decem 1672 did not come to thise hands of Mr Leibnitz before Iuly 1676 was not sent to him before Iune 26 1676. Pag. 49. lin. 20. All the Letters of Mr Leibnitz to Mr Lds Oldenburg from the beginning of the year 1683 are in the east to the dearthdeath of Mr Oldenburg are in the custody of the R. Society In autumn 1714 Mr Leibnitz wrote a Letter to London signifying that he intended to print a new Commercium & desiriing desiring that the Original Letters in the custody of the R. Society might be sent to him infor that order to his printing an impartial Commercium purpose. The Letter being read before the R. Society Mr Newton replied that when their Committee of the R. S printed the Commercium out of their archives & those of Mr Collins he did not ent so much as produce the Letters in his own custody because he would not make himself a witness in his own cause. And to satisfy them of the truth of this he produced two Letters written to himself the one writ to him by Mr Leibnitz himself the oth March 7th 1693 the other by Dr Wallis Apr. 10th 1695. The Letters were examined before the R. S by those that knew the hands & then read & of Mr Leibnitz pretended that the Committee of the R. Soc. had omitted many things wchwhich ought to have been published, & upon that pretence proposed to publish a new Commercium. And in his Letters of Novem. 16 17165 & Apr. 9 1716 he to pr to make good his complaint he instanced in two things that they had omitted but was mistaken in them both. The Original Letters have been seen by forreigners & nothing material has been found omitted. Pag 49. lin. 20. Mr Leibnitz pretended that the Committee of the R. S. had in their Commercium Epist omitted many things wchwhich ought to have been published & upon that pretence proposed to print a new Commercium impartially: And in autumn 1714 wrote to London t desired that the original Letters in the custody of the R. Society might be sent to him for that purpose. His Letter being read before the R. Society; Mr Newton replied that their Commit Commercium was printed out of Originals wchwhich had been kept remained from the beginning in the Archives of the R. S. & those of Mr Collins, from the beginning & that he did not thi the hands being examined by those that knew them & were still to be kept for justifying w also had been printed out of them & that he himself did not intermeddle with those Originals nor so much as produce the letters & Papers in his own custody because he would not make himself a witness in his own cause. And to prove the truth of this he produced two shewed them two old Letters written to himself the one by Mr Leibnitz March 7th 1693 the other by Dr Wallis Apr. 10th 1695. These Letters were examined – – – – as authentic unattested papers. And now if Mr Leibnitz has left any orig For making good his accusation of the Committee as if they had pu ommitted what made against Mr Newton, he lately charged them with two such omissions but was mistaken in them both. The Original letters have been seen by forreigners & nothing material has been found omitted. – and that for further before printing they had been also been examined by those who knew the hands; & that they ought still to be kept by those knew the hand by the R. Society for justifying what had been printed out of them. He added further that he did not intermeddle with those Originals nor so much as produce what papers he had in his own custody because he would not 379 Historical Annotations on the Elogium of Mr Leibnitz. 1 Pag. 44. lin. 1. Fluxions are not differences. They are quantities of another kind, & Mr Leibnitz hath no marks nor name for them. They are motions or velocities of increase & not parts of the increasing quantity. What Mr Leibnitz calls Differences Mr Newton calls particles & Moments & parts. 2 Ib. l. 3, 4, 5. When the Marquess de l'Hospital represented that the characters of Mr Leibnitz were more convenient then those of Mr Newton, he had seen only the characters used by Mr Newton in the second Lemma of the second book of his Principles & therefore meant no other. 3 Ib. l. 22. Mr Fatio was not the first. Dr Wallis, so soon as he heard that the method of Mr Newton was spreading in Holland by the name of the differential method of Mr Leibnitz, wrote in the Preface to the first volume of his works published in April 1695, that Mr Newton in his two Letters of Iune 13 & Octob. 24 1676, sent to had explained to Mr Leibnitz the method of fluxions or differences found by him ten years before or above; that is, in the year 1666 or before. 5 Pag. 48. lin. 15. Mr Newton was accused of Plagiary in the Acta Eruditorum for Ianuary 1705 pag. 34 & 35. & the accusation was justified by Mr Leibnitz himself in his Letter to Dr Sloan dated 29 Ian 1711. And for obviating this accusation the Commercium Epistolicum insinuated that the contrary was more to be suspected, Mr Leibnitz having seen several of Mr Mr Newtons Papers in the year 1676. 4 Pag. 48. lin 6. A Letter writ by Mr Leibnitz in autumn 1715 being handed about among persons of note in London, Mr Newton was pressed to return an answer, & did so by a Letter dated Feb. 26. 1716 & Mr Leibnitz answered him replied Apr. 9th 1716, but sent his Answer Reply to Paris (with Copies of the two former Letters) to be communicated to his friends there before it came to London. For wchwhich reason Mr Newton wrote to him no more, but only shewed privately to a few of his friends what might have been writ in answer. 6 Pag. 49. lin. 20. Mr Leibnitz pretended that the Committee of the R. Society had in the Commercium Epistolicum omitted many things wchwhich ought to have been published, & upon that pretence proposed to print a new Commercium impartially, & in autumn 1714 desired that the original Letters in the custody of the R. Society might be sent to him for that purpose. Mr Newton replied before the R. Society that the Commercium was printed out of Originals which had been constantly in their Archives of the R. Society & those of Mr Collins & had been also examined by those who knew the hands, & that they ought still to be kept by the R. Society for justifying what had been printed out of them. He added further that he did not print the Commercium himself nor so much as produce the papers wchwhich he had then in his own custody, because he would not make himself a witness in his own cause. And to prove the truth of what he said he shewed them produced two Letters written to himself the one by Mr Leibnitz March 7th 1693, the other by Dr Wallis Apr. 10 1695. These Letters were examined before the R. Society by them who knew the hands & then they were read & laid up in the Archives of the R. Society as authentic. At the same time it was allowed that if Mr Leibnitz had any Letters in his custody wchwhich he thought material to be published & pleased to sentd them to any friend in London whom he could trust with them that they might be publickly examined by those who knew the hands & attested copies be taken of them: they might then be published either in the Ph. Transactions or by Mr Leibnits himself. But nothing has been sent. On the contrary Mr Leibnitz having been since pressed to ‡ ‡ to return a direct Answer to yethe Commercium, replied in his Letter of April 9th 1716 Pour repondre done de point en point a l'Ouvrage publié contre moi, il falloit une autre Ouvrage aussi grand pour le moins que celuy là, il falloit entrer dans une grand detail de qualite de Minuties passees il y a 30 ou 40 ans dont Ie ne me souvenois gueres, il me falloit chercher mes vieilles Lettres, dont plusieurs sont perdues, outre que le plus souvent, je nay pas gardé les Minutes des Miens miennes, et les autres sont ensevelies dans une grand tas de Papiers, qui je ne pouvois de brouiller qui avec du Temps & de la patience. Mais je n'en avois gueres le loisir, etant chargé presentmant d'Occupations d'une toute autre nature. And in the author of thise Elogium of Mr Leibnitz published in the Acta Eruditorum for Iuly 1717 pag. 335 the Author of the Elogium writes: Quo tamen perspicerent intelligentes quid de tota illa controversia sentiendum sit, Commercio Epistolico Anglorum aliud quoddam suum idemque amplius opponere decreverat, & paucsis ante obitum diebus Cl. Wolfio significavit se Anglos famam ipsius lacessentes reipsa refutaturum: quam primum enim a laboribus historicis vacaturus sit, daturum se aliquid in Analysi prorsus inexpectatum & cum inventis quæ hactenus in publicum prostant, sive Newtoni, sive aliorum nil quicquam affine habens. He doth no We were to stay till his Historical labours were at an end, & then he would confute the English; he doth not say with a new Commercium, but with a new surprizing invention in Analysis of another kind then the differential method; & this he wrote a few days before his death. And perhaps he meant his Alphabetum cogitationum humanarum or something like it. Mr L The author of the Elogium tells us of an aliud quoddam [Commercium] idemque amplius, but Mr Leibnitz himself wrote only that so soon as historical labours were at an end he would refute the English (he doth not say with a new Commercium as the Author of the Elogium seems to understand but) with a new surprizing invention in Analysis of another kind; & this he wrote a few days before his death, & we were to stay for this till his historical labours were over should be at an end. Pag 51. lin. 22. He returned from London to Paris in Febr. 1673 & began to study the higher Geometry a few months after. The Horologium oscillatorium of Mr Huygens was published in in April 1673. Mr Leibnitz soon after read this Book & then some others [began presently after to study the higher Geometry] & then fell upon his Triangulum characteristicum & his many Theorems, & went on to his Method by Analytical Tables of Tangents, & by his Combinatory Art. And this was the top of his skill when he wrote his Letter of 27 Aug. 1676. For in that Letter he said of one part of this method: Nihil est quod norim in tota Analysi momenti majoris. And of another part: Cujus vim ac potestatem nescio an quisquam hactenus sit consecutus. Ea vero nihil differt ab Analysi illa suprema ad cujus intima Cartesius non pervenit. Est enim ad eam constituendam opus Alphabeto cogitationum humanarum. And soon after this, he fell upon the Differential Analysis. Pag. 53. l. 6. A copy of Mr Newton's Letter of dated 10 Decem. 1672 was not sent to him before Iune 26, 1676. Mr Leibnits [Might be acquainted wthwith Mr Hugens in 1672 but he] came to London in the beginning of the next year 1673 & returned to Paris in March following & kept a correspondence with Mr Oldenburg about Arithmetical questions till Iune 8 following, & hitherto he was unacquainted with the higher Geometry. The Horologium ascillatorium were of Mr Huygens was published in April 1673 & when he began to study the higher Geometry he read first this book & then the works of Paschal & Gregory of St Vincent & then fell upon his Triangulum characteristicum & his many Theorems, & went on to his method by Analytical Tables of Tables of Tangents & the combinatory Art. And this was the top of his skill when he wrote his Letter of 27 Aug. 1676. – – – humanarum. And In the same Letter he used the common Algebra where the Differential calculus would have been proper had he then known it, & said that inverse problems of Tangents & many others could not be reduced to equations. But soon soon not be It was therefor after the writing of this Letter that he fell upon the Differential calculus. In October following he was inagain in England where he might meett wthwith the Barrows works of Gregory & Dr Barrow &c learn Dr Barrows method of Tangents & & Mr Newton's Letter of 24 Octob 1676. [And Iames Bernoulli in the Acta Eruditorum for Ian 1691 pag 14 wrote, Vt verum fatear, qQui calculum Barrovium — intellexerit, alterum a Dn. L. inventum ignorare vix poterit; utpote qui in prior illao fundatus est & nisi forte in differentialium notatione & operationis aliquo compendio ab eo non differt. And the Marques de l'Hospital in his Preface that Dr Barrow's calculus taught not how to take away fractions & surds; Aand that where he & others left off Mr Leibnitz began. [And Mr Newton in his Letters of 10 Decem. 1672 & 24. Octob. 1676 that his method proceeded wit did not stop at fractions & surds. proceeded in equations involving surds.] But the Marquess had not seen Mr Newtons Letters of 10 Dec. 1672 & 24 Octob. 1676] & saw the correspondence of Gregory & Newton in the hands of Collins. 381 Criticism of Fontenell Cl to Varignon endof 1718 or beginning of 1719 SrSir I am much obliged to you for your large Letter in order principally to bring Mr Iohn Bernoulli & me to a better understanding. Mr Leibnitz has attributed to him the Letter of Iune 7th 1713 & in that Letter inserted into a flying Paper dated 29 Iuly following & ist that Letter he his cited by the title of he cites sti cites himself by the title of Eminens quidam Mathematicus en effect denies & took upon him to give as a judge al so twice between Mr Leibnitz & the Committee of the R. Society & in that sentence denied (in effect that that when I wrote the book of Quadratures, (wchwhich I can assure you was above 40 years ago, (except the Introduction & Conclusion)) I did not understand the first Proposition of the Book ✝ And I return you my hearty thanks for your kind present of the Elogia of the Academiciens. In that of Mr Leibnitz Mr Fontenelle has been very candit. There are some mistakes in matter of fact but not by designe. I reccon that Mr Fontenell was not sufficiently informed. He seems to follows the Marquess de l'Hospital in saying that the differential characters are the more convenient, but the Marquess whom I reccon a very candid person when he published his book of infinitely littles had seen no other characters of mine then those in the Book of Principles. In pag. 44 lin 22 he should have mentioned Dr Wallis before Mr Fatio if he had known what the DrDoctor wrote in the Preface to the two first Volumes of his works. Pag. 48 lin 15 he should have mentioned that I was first accused of Plagiary in the Acta Eruditorum for Ianuary 1705 pag. 34 & 35 & by Mr Leibnitz himself in his Letter to Dr Sloan dated 29 Ian. 1711, had he been advised of it. & For I this was in opposition to my saying in the Introduction to the book of Quadratures that I found the method of fluxions gradually in the years 1665 & 1666. Pag. 49, l. 20 they should have told have given him a wrong information from Germany. For in the Elogium of Mr Leibnitz printed in the Acta Eruditorum for Iuly 1717 page 335 were are told that a few days before his death he wrote to Mr Wolfius that he would refute the English after his historical labours were over. Pag. 51 lin. 22 Mr Leibnitz became acquainted wthwith Mr Hugens in 1672 came to London & returned to Paris in the beginning of 1673, kept a correspondence with Mr Oldenburg till Iune follow about Arithmetical questions till Iune following & hitherto knew nothing of the higher Geometry. The Horologium oscillatorium of Mr Hugens was published in April 1673 & he begun with this book. tohe But doth A And it doth not appear that he knew any thing of the Differential Method before his second coming to London at wchwhich time he met with my Letter of 24 Octob 1676 & Dr Barrows works & my Letter of 24 Octob 1676 & saw in the hands of Collins & the Letters & Papers sent to him by me & Gregory having received Pag. 53. lin. 6, the Letter here referred unto was writ by Collings in 1672 & see but not seen by Mr Leibnitz till 1676. [Pag. 53 l. 22 Mr Leibnitz is blamed here in point of candor for concealing what he knew of other mens inventions. He received Gregories series twice from England & by a copy of Gregories Letter dated 15 Feb 1671 knew that Gregory had invented it before that time the date of that Letter & yet printed it as his own in 1682 without making any mention that he ha G he had received it from London & that it was first invented by Gregory. He might have said that he invented it himself before he knew that Gregory had invented it, bef but he should not have concealed his having receiving it from London, & much less should he have concealed his knowledge that Gregory had invented it before him. And so when he printed the elements of the Differential Method he should not have concealed his knowledge of what he seen in my Leitters concerning such a method. For its very plane by his Letters of 21 Iune 1677 that he then understood that my method was of the same kind with his own. And much less should he have concealed his knowledg after I had in the second Lemma of the second Book of Principles set down the Elemtents of my method & in the Scholium upon that Lemma explained the sententce in inwchwhich I had couched that Lemm Memthod of wchwhich I said in my Letter of 24 Octob. 1676 where I said that I had explained it in a Tract written in the five years before. He knew therefore that I was the firs before him & should not have concealed his knowledge. H In his Letter of 7 March 1693 he acknowledged of his own that I had shewed by my Book of Principles that I had such a method when I wrote it & to deny this afterwards proceeded from the want of candor.] All th Dr Barrows works & Gregories Letters of 5 Sept 1670, & 15 Sept 1671 & mine of 10 Decem 1672 381 13 Iune 1676 & 24 Octob 1676 were all of them seen by him when he was the second time in England or within three months less thethen four months before & it doth not ap appear that he understood the Differential Method before he saw all these Papers. And the Committee of the R. Society have affirmed nothing more thaten that he saw them & that I was before it appears that he had s had the Method, & that in them the Method of fluxions it sufficiently described to any intelligent person. But if the friends of Mr Leibnitz beleive that he did not understand those Papers the Gentlemen of Mr Leibnitz has told us that Mr Iohn Benoulli was the author of the Letter dated 7 Iune 1713 & & inserted into the flying Paper of 29 Iuly following. In was written by Mr Iohn Bernoulli. And the author of that Letter Mr Benoulli to conceale himself, For he was citesd himself has told the world that he is not it was not written by I. B. Mr Bernoulli by the name of an Eminent Mathematician, & In that Letter he has to teollds the world that I d (in effect) that I did not understand the first Proposition of the Book of Quadratures & that in the Introduction to that Book I did not write of the Method of Fluxions because there are no prickt letters in it & therefore that in the years 1665 & 1666 (in wchwhich I said Ithat in that Introduction that I found thaet Method of fluxions gradually) I did not so much as dream of that Method it. And for p Mr Leibnitz hath subscribed to these opinions telling us that as these are the judgment of a primary candid & ai & impartial Mathematician, & for a further Demonstration thereof sent a hads challengeding to the English Mathematicians to solve a Problem of Mr Iohn Bernoulli. TWhen the Commer. Epist. came abroad Mr Leibnitz appealed from the judgment of the Committee of the R. Society to that of a primary & impartial Mathematician & the judgement of that Mathematician was inserted into the dated 7 Iunely 167713 was inserted into a flying paper dated 29 Iuly 1713 & which was dated 24 Iuly 1713 & was written by somebody who knew what passed at Paris above 36 years before between Mr Leibnitz & Mr Hugens 37 years before,. & dated 29 Iuly 1713. And the Mathematician distinguished himself denyed that he was Mr Iohn Bernoulli by citing cited Mr Iohn Bernoulli by the name of an Eminent Mathematician [& [thereby denyed that Mr Iohn Bernoulli was the author of that judgm Iudge to whom Mr Leibnitz appealed,] but Mr Leibnitz has since told us again & again that Mr Bernoulli was that Iudge the Mathematician. I This impartial Iudg in that Paper of 7 Iune 1613 has told the world (in effect) has given a IudmentIudgment which amounts to this our people look upon as if he had said that I did not understand the first Proposition of my book of Quadratures & that in the Introduction to that book & in the 2d Lemma of the 2d Book of Principles & the Scholium upon it I did not write of not Lette I said nothing of the Method of Fluxions because there are no prickt letters in them, & that in the years 1665 & 1666, in which I said in that Introduction that I found the Method of fluxions gradually, I did not so much as dream of it. nor knew any thing of the method till before the third Volume of Dr Barrow's works ca understood the Method till it was grown commonly known by others. And Mr Leibnitz hath subscribed to this judgment this judgment & dem these opinions & endeavoured to demonstrated propagate support it them, by telling the world they are that it is the judgment of an Eminent a primary & impartial Mathematician & that is the judgmtjudgment of Mr Iohn Mr Iohn Bernoulli himself, & by sending a challenging the English Mathematicians to solve a Problem of that great man. Th And now Mr Bernoulli writes And that he beleived that Mr me in my saying that I found hte Method by my self till Mr Bernulli gave a contrary judgment. And thus Mr Leibnitz has made Mr Iohn Bernulli the Principal in this controversy. There have been several defamato detracting papers printed in the Acta Eruditorum without the names of the authors, & such Papers are in England accounted unfair, uncandid & of ill repute & condemned by the name of Libells.