Several drafts of letters of Newton to Des Maizeaux after the death of Leibniz Isaac Newton c. 24,628 words The Newton Project Oxford 2020 Newton Project, University of Oxford

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 c. 1716-1720, in English and Latin with a little French, c. 24,628 words, 29 ff. 29 ff.

in English and Latin with a little French

 MS Add. 3968, ff. 383r-411v, Cambridge University Library, Cambridge, UK UKCambridgeCambridge University Library Portsmouth Collection MS Add. 3968, ff. 383r-411v c. 1716-1720 England English Latin French Isaac Newton Unknown Hand (10) Unknown Cataloguer (1) Unknown Cataloguer (2) Unknown Cataloguer (3) Unknown Cataloguer (4) Unknown Cataloguer (5) 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.
119)383

SrSir

The author of the Letter written to Mr Leibnitz of 7 Iune 1713, when he wrote it, (who according to Mr Leibnitz was Mr Iohn Ber-] did then know by the first Proposition of the Book of Quadratures that Mr Newton understood second third & fourth differences & gave a true rule for finding them & by the Introduction to that Book that Mr Newton he practised the Method of fluxions as well without prickt letters as with 'em, & by continued to put the letter o for yethe fluxion moment of x without destroying the advantages of the let differential method calculus & therefore in that Let & that the Principia Philosophiæ were writ by composition the Method of Synthesis & could not have been written by that Method without a previous Analysis, & that the synthesis is best where the Analysis is not in writing by Synthesis there Analytical calculations ought to be avoyded the Analysis is to be concealed.

And as for

Mr Leibnitz has told us that the author of this Letter was Mr Iohn Bernoulli. And as for the Letter of 29 Iuly 1713 it was certainly writ by some body who remembred what Mr Leibnits did at Paris 39 above 39 years before, as may be gathered from this sentence. Modum quo Leibnitius, ad seriei Nicolai Mercatoris (primi to imitationem, invenit seriem suam, ipse statim, Hugenio B. Lutetiæ agenti communicavit, qui et per Epistolam laudavit.

SrSir

I have run my eye over the printed Letters & g had the wchwhich you have put into my hands, & & since you have the Originalls I think it is right to let them come abroad I have noted some observed some faults wchwhich may be put into yethe errata. Pag. 8 l 13 dele c'est a dire, commune ou superficielle. Pag. 16. l. 5. write A Londres Feb. 26, 171516 st. vet. Pag. 17. l. 13 write en Iuillet 1714. P. 19. l 20 desquelles. P. 46. l. 11 en 1677. P. 75 lin 15 write en Iuin 1713 P. 78 l. 9 write 24, 26.

In the Letter of Mr Leibnitz to Madam la Comtesse de Kilmanségger, pag. 51, 52 he writes gives an Account of his finding the series for the circle like that of Greg Mercator for the Ellipsis & then adds Cependant le mien fut assez – – – j'appris tard. If you consult the original Letters you will see that Mr Gregory found this series in the beginning of the year 1671 & pse sent it then to Mr Collins in a Letter dated 15 Feb 167071 & that Mr Collins inserted a copy of this Letter into the Collection of Gregories papers sent to Mr Leibnitz in Iulyne 1676. And Mr Oldendenburg sent the same series to Mr Leibnitz in a letter dated Apr. 15. 1675 & Mr Leibnitz in a letter dated 20 May 1675 acknowledged the receipt of Mr Oldenburgs Letter. And after all this Mr Oldenbur Leibnitz sent this Series to Mr Newton as his own in a letter dated 27 Aug 16676 & published it in Germany without A.C. 1682 without mentioning that he had received it from England & that Gregory was the first invented it before him. In the same Letter pag. 34, 35 Mr Leibnitz transcribes the second Le Scholium upon the Lemma of 2d Book of my Principles & then adds. Ainsi, Mr Newton ne me contesta point de avoir trouvé la chose de mon chef. [But he goes from the Question. The true Question is not, whether Mr Bernoull Leibnitz found it apart, but whether he was the first Inventor. I ne Neither I nor the Committee of the R. Society ever accused of not finding the method by himself but we say that have said that he was not the first inventor & in my Letters of 10 Dece the year 1676 received saw copies of my Letters of 10 Decem 1672, 13 Iune 1676 & 24 Octob 1676 that those Letters were sufficient to make him understand that I in the ye I had a met very general method of wchwhich & the method of Series together I wrote a Tract in the year 1671 & in sad Scholium I expl founded this method upon a sentence wchwhich in] And its very true that Mr Newton neither then nor at any time since contested the point whether Mr Leibnitz invented this series by himself or not. This was not the Question but whether Mr Leinitz was the first inventor. And in this Scholium Mr Newton grants that Mr Leibnitz had refers to his Letters of 13 Iune & 24 Octob 1676 by wchwhich it appears that he had the Method when he wrote those Letters & atnd least five years before or above, & to the Letters of the Letter of Mr Leibnitz of 21 Iune wh 1677 wchwhich is the first instance of Mr Leibnitz his having it. [He tells us that he found it (as he think in ] And he doth not now pretend to have In the year 1684 Mr Leibnitz published the elements of the Differential Method, & in the end of his paper added that this method extended to the solution of such Problemes as could not be resolved without either this or another method like it. BecAnd becaus he did not say whose was the other method not what he knew of it nor make any mention of his correspondence with Mr me eight years before by means of Mr Oldenburg about these matters, as he ought to have done; I supplied the defffect by writing the said Scholium. In the second Lemma of the second Book of Principles I demonstrated the said Elements of theis method synthetically because I had occasion to make use of them in the following Propositions, & I added the aforesaid Lemma Scholium not to give away the Lemma as Mr Leibnitz hath pretended but to assert it to my self satisfy the Reader that I had it before I kn
And that in the end of the year 1671 I invented the Method of extracting fluents out of Equations involving fluxions & at the request of Dr Wallis sent it to him in September 1692, & that in the year 1676 I wrote the book of Quadratures (exccept the Introduction & Conclusion) & when I had finished the 10th Proposition extracting most of it out of old papers And & when I had finished tenth Proposition wthwith its Corollaries & the composure thereof was fresh in memory I wrote the tenth upon the second Corollary upon the Letter about it it to Mr Collins my Letter of dated Octob. 8. 1676 wchwhich Mr Iones found amonge his papers & published. by Mr Iones② And that as I invented the Method of fluxions & the Theory of Colours in the years 1665 & 1666 & in the year 16721 was upon a designe of publishing them, but so for a reason mentioned in my Letter of 24 Octob 1676 I forbore publishing them till the year 16 1704. ① And that when I wrote in my Letter of 24 Octob. 1676 that the general TheremesTheoremes there mentioned for squaring of Curves were founded on the Method of fluxions, I had relation to the method of finding them described in the six first Propositions of the Book of Quadratures. ③ The Introduction to the Book of Quadratures [where the Method of fluxions is taught without the use of prickt letters is a demonstra] is a demonstration that I did not confine the Method of fluxions is not confined to prickt Letters the method of fluxions is taught without pricket Letters & the letter o is used without both in the Introduction & in the Book it self without destroying the advantages of the ✝ ✝ the differention Notation, & the Notation by pricks is shorter then that by the letter d, & the Notation by prikcks & the letter o together is more has more advantages then that by the letter d & the first Proposition of the Book is a demonstration that when I understood all the degrees of fluxions when I wrote it, & my saying in the Introduction that I found the Method gradually in the years 1665 & 1666, w which has occasioned all this squabble, is not so much as Dr Wallis affirmed long before nine years before long before in the Preface to the two first Volumes of his works without being then contradicted by any body. And that in the end of the year 1671 I invented the Method of extracting fluents out of Equations involving fluxions mentioned in my Letter of 24 Octob. 1676, & in the year 1676 I wrote the book fo Quadratures except the Introduction & Conclusion extracting most of it out of old Papers. &And when I wrote in my Letter of 24 Octob 1676 that the general Theoremes there mentioned for squaring of Curves were founded on the Method of fluxions, I had relation to teh method of finding them described in the six first Propositions of Qua the Book of Quadratures, And that And when I wrote to Mr Collins my Letters of 8 Octob. Novem. 1676 to Mr published by Mr Iones I had newly finished relation to the tenth Proposition of the Book of Quadratures & had those things with itits Corollaries wchwhich being then newly written were fresh in memory. as may be perceived by comparing the Letter with that Proposition & particularly with the second Corollaryies thereof with that Letter it self which was writ upon them. And that Iin the writieng the book of Principles I made very gre by the help of the book of Quadratures & in the year 1692 my two Letters of dated Aug 27 & Sep. 17 1692 I sent to Dr Wallis the method of fluxions described in my the first Proposition of the book of Quadratures & the method of extracting fluents out of equations involving fluxions mentioned in my Letter of Octob 24, 1676 both which methods thwere printed the next year in the second Volume of the Doctors works pag. 391, 392, 393, 394, 395. And the reaso And that About the same time that I invented the method of fluxions I invented also the Theory of Colours vizt in the beginning of the year 16766winter between the years 1665 & 1666, & in the year 1671 I was upon a design of publishing both: but soon after laid aside my designe for a reason mentioned in my Letter of 24 Octob. 1676 In & for the same reason forbore to publish them till the year 1704. And who 384 And that in yethe end of And that these papers, where I considered only first fluxions, were with composed without prickt letters, but where I considered second third & fourth fluxions (as for instance in extracting fluents out of Equations involving fluxions) I used prickt letters & that I in the year 1676 I wrote the book of Quadratures (except the Introduction & Conclusion,) & when I had fin extracting most of it out of old papers & without with relation to the tenth Proposition & its Corrollaries, (when I had newly finished them, & they very fresh in memory I wrote to Mr Collins my Letter of 8 Octob. Novem. 1676 published by Mr Iones ‡ ‡ And that the Tables at the end of that Proposition for squaring of some Curves & comparing others wthwith the Conic Sections were invented by the inverse method of fluxions before the year 1671 as may be understood by my Letter of 24 Octob 1676, [& most of their above four years before] And that in my Letter of 24 Octob. 1676, where I said that the Theorem general Theoremes there mentioned were for squaring of Curves were founded on the Method of fluxions described in copied from the first Proposition of the Book of Quadratures & the method of extracting fluents out of equations involving fluxions mentioned in my Letter of the Octob 24 1676, both wchwhich Methods were printed the next year viz A.C. 30 170693 in the second volume of the Doctors works. pag. 391, 392, 393, 394, 395. [All wchwhich may suffice to justify mey f saying in the Indtroduction to the Book of Quadratures that I found this method gradually in the years 1665 & 1666, wchwhich was not so much as was said & published by Dr Wallis nine years before in the Preface to yethe first Volume of his works without being then contradicted.] And that I usualusually put letters for fluxions where I considered only first fluxions but where I considered also second third & fourth fluxions (as for instance in extracting – – –) distinguished ymthem by letters with one two or more pricks. And that in the year 1676 – – – – 3094. 395. And that about the same time that Mr Leibnitz does not pretend to have found it before the year 1676 & in his Letter of 13 Iune 27 Aug. 1676 there are some things wchwhich satisfy me that he did not know it when he wrote that Letter 124385 & therefore was either Mr Iohn Bernoulli himself or copied the expression solutionem meam from one of his Letters Mr I. Bernoulli's letters. SrSir I have perused the printed sheets wchwhich you left in my hands & beleive that the Letter of M. Leibnitz to Mr Remond wchwhich is printed in the eighth place should have been printed in the second, the contents thereof relating to the Postscript of the Letter of Mr Leibnitz to Mr l'Abbé Conti wchwhich is printed in the first place. Also the Letter of Mr Leibnitz to Mr l'Abbé Conti wchwhich was writ in answer to mine & is dated 9 April 1716 should have come before the Letter of Mr Leibnitz to Madam Kilmanseg la Comtess de Kilmansegger dated 18 April 1716 None of the Letters being written to me I did not think it my self concerned to answer any of them till Mr l'Abbé Contej sollicited me to answer the Posctscript of his first Letter wchwhich is printed in the third place, th that my Answer as well as that Postscript might be shedwedn to the King. But when my Answer was sent to Mr Leibnits with a Letter of Mr l' Conti & he sent both open to Mr Remond at Paris with his Answer to them as he had done the Poscript before, & his Answer was sent from Mr Remond to Mr L'Abbé Contei & he gave Mr l'Abbe Conti notice that he took this Method that he might have neutral & intelligent witnesses of the dispute, & in his Letter Answer represented me I refused to answ write any m an Answer to be sent to him & only wrote some Annotations Remarks upon his Answer & shewed them privately to some friends here to satisfy them that it was easy to have returned an Answer had I thought fit to let him go on with his politicks. And as soon as I heard that he was dead I printed caused his first Postscript with m the Letters with to be printed with those Remarks least they should come out imperfectly abroad. At the same time that these Letters were sent to Mr Remond Mr Leibnitz wrote also to Madam la Comtesse de Kilmansegger & a large Poscript to the Baron Bothmar, [& there was also a paper published in the Acta Eruditorum for Iuly 1716 by an Anonymous author none of] wchwhich have been yet answered nor indeed need any answer. The Paper neither of about thisese matters. And theise Letter & Postscript wasere then shewed me, but I did they being not written to me I did not write any Answer to them; & much less do I think it proper for me now to meddle with them, Mr Leibnitz being dead. There was also at the same time a paper published in the Acta Eruditorum for [written by an Anonymous Author] against Dr Keill, & for a Panegeric upon Mr. I. Bernoulli & against a satyr agtagainst Dr Keill published in the Acta Eruditorum for Iuly 16716. But this Paper being a anonymous of railery against the Doctor & without the name of the Author & deserves no Answer. Such Papers are of an infamous reputation in England. The author has fathered thits pPaper upon Mr Iohn Bernoulli by calling a formula of his meam formulam meam pag. 314 lin 27 & yet thereby he has made it incredible that Mr I. Bernoulli should be the author by calling himself Eminentem Mathematicum excelsum ingenium & virum ad abstrusa et abdita detegenda natum. p. 296 l. 13] we There was also at the same time a Panegiric upon Mr I. Bernoulli & a Satyr upon Dr Keill publi written by an anomnymous author & published In the Acta eruditorum for Iuly 1716. The author haz fathered it upon Mr Iohn Bernoulli himself by calling a formula of his meam formulam pag. 34 lin. 27 & thereby has made Mr I. Bernoulli call himself eminentem Mathematicum, excelsum ingenium & virum ad abstrusa et abdita detegenda natum pag. 296 l. 13 & p. 298. l 32 & p. 301 lin 29. But its possible that the author may have copied the words meam formulam out of one of Mr I. Bernoullis Letters. Mr Nicolas Bernoulli was Bernoulli was in England in Autumn A.C. 16 1712 & It was at the sollicitation of Mr Leibnitz l'Abbé Conti that I wrote an Answer to the said Postscript of his Letter, he pressing me to it that the Postscript letter of Mr Leibnitz to Madam le Comtesse de Kilmansegger & theis Postscript of his Letter to M Baron Bothmar no answer has been given & I do not think it necessary to write one especially now Mr Leibnitz is dead. They contein only his narratives of the facts. He was in London in the beginning of the year 1673 & Mr Leibnitz went from London to Paris in Febr. or March 1673 carrying with him the Mercators Logarithmotechnia But he did not yet understand the hig & kept a correspondence with Mr Oldenburg till Iune following for he dyd not yet understand the higher Geometry He began to learn the higher Geometry in summer 1673. The Horolgogium oscillatorium of Mr Le Huygens came out that year in April & this was the first book wchwhich he read in studying that sort of Geometry Mr Huygens himself assisting him introducing him. He never pretended to have found the differential method before the year 1676. And when he wrote his Letter of 27 Aug. 1676 he placed the perfection of Analysis not in this Calculus as he did after he knew it, but in another method founded on Analytical Tables of Tangents & the Combinatory Art. Nihil est, saith he, quod norim in tota Analysi momenti majoris. And a little after. Ea verò non differt ab Analysi illa suprema SVPREMA ad cujus intima Cartesius non pervenit. Est enim ad eam constituendam opus Alphabeto cogitationum humanarum. He had then newly received my Letter of 13 Iune 1676 & accompanied with a collection of Gregories letters & papers made to at his request by Mr Collins. In that Collection was a letter of Mr Gregory signifying that he had improved Dr Barrows method of tangents so as to make it draw Tangents without any calculation & another a Letter a copy of one of my Letters dated 10 Decem 1672 in wchwhich I said that the Method of Tangents of Gregory & Slusius were a branch or corollary of my general method & that this method stuck not at surdes. And by by there Letters it was easy to understand that Dr Barrows method of TangtsTangents was capable of being improved so as to give the method of tangtstangents of Gregory & Slusius & that the method was capable of further improvement so as to give my general method. In October following he came to London in his way from Paris to Hanover & there met with Dr Barrow's Lectures & saw my Letter to of October 24 1716 & wherein he had notice of my Compendium of Series sent by Dr Barrow to Mr Collins in the year 1669 & saw also also in the hands of Mr Collins several of mine & Gregories Letters. He might soon after invent the differential Method by himself: but by what he had see for the next year in his Letter of for in his way home he w from London he was meditating how to improve the Method of Tangents of Slusius as appeares by his Letter to Mr Oldenburg fr dated from Amsterdam 1828 Novem. 1696. And the next year in a Letter to Mr Oldenburg dated 21 Iune he wrote Clariss sent his new method with this Introduction: Clarissimi Slusij tMethodum tangentium nondum esse absolutam Celeberrimo Newtono assentior: And & set And this meth he shewe abbreviated Dr Barrows method of Tangents & shewed how it might be improved so as to give the method of Tangents of Slusius & proceed in equations involving surds. And then added subaed: Arbitror, quæ celare voluit Newtonus de tangentibus ducendis ab his non abludere. Quod addit, ex eodem fundamento quadraturas quoque reddi faciliores, me in sententia hac confirmat. And seven years after when he published the Method as his own without making mention of his former correspondence with the English in these matters: wchwhich put me upon a necessity of writing the Scholium upon the second Lemma in the second Book of Principles, least I it should be thought to have that borrowed that Lemma from Mr Leibnitz. M In the end of the year 1669 & beginning of the year following Mr Collins sent Mr Iames 386 Mr Iames Bernoulli in the Acta eruditorum for Ianuary 1691 pag. 14, said – – – – – – & 24 Octob. 1676. In the end of the year 1669 & beginn Mr Collins sent notice to Mr Iames Gregory that I had a general Method of series, & Mr Gregory by this N notice & an example in one of my series, being put upon searching after this Method found it after a years study. But tho he found it by himself, yet because he knew that I had it before him he never claimed a right to it. I wrote the Book of Quadratures in the year 1676, except – – – – – published by Mr Iames. He that compares that Letter with those Propositions & particularly with the second Coll Corollary of the 10th Proposition will easily see that when I had composed those Propositions before I wrote that Letter. The Tables at the end – – – And in the same Letter wh by wchwhich those Theoremes could be invented. The Book of Quadratures was therefore composed before Mr Leibnitz understood the differental Method. At the request of Dr Wallis I sent to him – – – nor are necessary to the Method. The Marquess published the book of infinitement petits in the year 1696, & three years after the first Proposition of the book of Quadratures had been published by Dr Wallis. And therefore my Rule for finding second third & fourth di fluxions was published three years before the Rules for finding second third & fourth fdifferences came abroad. To the Reader Towards the end of the year 1715 Mr Leibnitz (I think about November) Mr Leibnitz writing to Mr l'Abbe Conti then at London about the systeme of Mr Nigrisoli, added a large Postscript relating about the invention of the Differential Method. And the Postscript was sent also to Mr Remond at Paris. The Letter Postscript not being written to me I did not think my self concerned to meddle with it. But Mr Leibnitz declining to having laid a de declining to answer Dr Keil or the Commercium Epistolicum or to meddle with any body but me: L Mr l'Abbé le Conti at length pressed me to write an Answer to the Postscript that then they might bothe be shewed to the King. And when his M And when Mr my Answer was shewed to the Kin sent to Mr Leibnitz hee wrote an Answer to it & sent it ope with his Answer open to Mr Remond at Paris & the Answer was sent by Mr Remond to en Mr l'Abbe conti. This tricking management compared with the beginning of his Answer made me sensible that Mr Leibnitz he was upon a design of setting aside the Committee of the R. Society & Dr Keill & stopping me all my friends in England & engaging me alone with all his posse.& the ancient Records published in the Commercium Epistolicum, & stripping me of my friends, & attaquing me alone with all his posse of disciples, & with what interest he & all his interest at St But Whereupon I refused to write an Answer in the form of a Letter to be sent to him & only wro yet to satisfy my friends that it was easy to have answer hitm had I thought fit to let him go on wthwith his plitiquespolitiques, I wrote an Answer in the form of Observations & shewed tithem privately to some of my friends. for And as soon as I heard that Mr Leibnitz was dead I caused the Letters & Observations to be printed least they should at any time hereafter come abroad imperfectly in France. There were some other Letters writ by Mr Leibnitz, Mr l'Abbé Conti, & Mr Remond; & by Mr l'Abbé Conti left in the hands of ** Mr de M. to be published together with what I had caused to be published before. And a few days since a spe specimen copy of the same was brought to me printed off except the last sheet. But they being put together in wrong order I have caused them to be reprinted in due order of time, together with a scandalus libel Paper published about the same time in the Acta LipiensiaLipsiensia by one a nameless author who called a solution of Mr Iohn Bernoulli solutionem meāam Mr Leibnitz began to learn the higher Geometry in summer 1673. The E Horologium Oscillatorium of Mr Huygens came out that year in April & this was the first book wchwhich he began to read of that sort of Geometry Mr Huygens himself introducing him. He has represented that he thinks he fell into the differential method in about the year 1676. He never pretended to have found it earlier. And when he wrote his Letter of 27 Aug. 1676 he placed the perfection of Analysis not in the differential calculus as he did afterwards but in a method founded on Analytical Tables of Tangents & the combinatory Art. Nihil est, saith he, quod norim in tota Analysi momenti majoris. And a little after: Ea vero non differt ab Analysi illa suprema SVPREMA ad cujus intinaintima Cartesius non pervenit. Est enim ad eam constituendam opus Alphabeto cogitationum humanarum. And in answer to what I had said about in my letter of 13 Iune 1676 concerning the universality of my method he replied: id mihi non videtur. In October following he came to London the second time & there met with Dr Barrows Lectures & saw my Letter of Octob. 24, 1676, & three months before received a copycopy of my Letter to Mr Colling of 10 Decem 1672 112387 ② to Des Maiseaux a Vou SrSir I have perused the printed sheets wchwhich you left in my hands & beg leave to take notice that when the Postscript of Mr Leibnitz's first Letter to Mr l'Abbé Conti (wchwhich I think was writ about November 16715 & sent to Mr Remond) at Paris) was shewed to me: it being not sent to me I did not think my self concerned to answ meddle with it, till at length I was pressed by Mr l'Abbé Conti to answer it that the Postscript wthwith my Answer might be shewed to the King. And when Mr Leibnitz sent it with his Answer to Mr Remond at Paris & his Answer was sent open from Paris to Mr l'Abbé Conti & I refused to write any thing furt any Answer thing more to be sent to him. For I perceived that as he was had formed formerly appealed from the ancien Commercium Epistolicum & the judgment of the Committee of the R. Society to N that upon it to the judgmtjudgment of Mr Iohn Bernoulli so he was now upon a designe of appealing to his friends at Paris his army of disciples & his interest at Court. However But yet I wrote a Paper of Remarks upon his Answer Letter & shewed it to some friends in private to let them see how easy it was to have answered his Letter had I thought fit to let him go on with his Politiques. And whe I heard that he was dead I printed the Letters with these Remarks least they should be published abroad imperfectly abroad. o And since you are reprinting them with some other Letters written at the same time, to make the collection more perfect & in some of those Letters he tells his own story at large; tho I will not write an Answer to those letters now he is dead; yet since he w since in his Letter of 4 March 1711 when I had not so much as see knew not how I ha what had been printed against me Six years before in the Acta Eruditorum nor was any way concerned in this controversy, he appealed from Dr Keill to me & against Dr Keill & would not let me rest contend with no body but me nor let me rest till I h set pen to paper: I think I may be allowed to tell the story my self, & leave you to & leave it to be compared with his Narrations. He went from London to Paris in Febr. 1673, carrying along with him Mercators Logarithmotechnia, & kept a correspondence with Mr Oldenburg till Iune following For he did not yet understand the higher Geometry. The Horologium Oscillatorium of Mr Huygens came out in April 1673 the same year in April & this was the first book which he read in studying the higher Geometry, Mr Huygens himself introducing him. & as to the Method of fluxions he never pretended to have found it before the year 1676. Mr Iames GregoriedGregory died in the end of the year 16675, & when the news came to Paris Mr Leibnitz desired that the Letters & Papers of Mr Gregory might be collected & sent a copy of them sent to Paris wchwhich was done in Iune following. He desired also that the demonstration of some of my series (meaning the method of finding them wchwhich I had sent to bors in the Analysis per Æquationes numero terminorum infinitas) might be procured from Mr Collins & sent to him, & promised to send back something of his own in recompence: whereupon at the request of Mr Oldenburg & Mr Collings, I wrote my Letter of 13 Iune 1676. At th And this Letter was sent to him at the same time wthwith the aforesaid collections of Gregories Letters In that Collection was a copy of a Letter of Mr Gregory dated dated 5 Sept 1670 signifying that he had improved Dr Barrows method of Tangents so as to draw tangents into a general method of drawing Tangents without any calculation. There was also sent him in the same Collection a copy of one of my Letters to Mr Collins dated 10 Decem. 1672, in wchwhich I said that the Method of Tangents of Gregory & Slusius were a branch or corollary of my general method of Analysis, & that this method stuck not at surds, & that I had interwoven this Method with the method of Series, meaning in a Tract wchwhich I wrote of them both in the year 1671. And by these Letters it was easy to understand that Dr Barrows method of Tangents was capable of being improved so as to give the method of Tangents of388 of Gregory & Slusius, & that this Method was capable of further improvement so as to give my general Method of Analysis. In my Letter of 13 Iune I said: Ex his videre est quantum fines prAnalyseos per hujusmodi series infinitas æquationes ampliantur: quippe quæ, earum beneficio, ad omnia pene dixerim problemata (si numeralia Diophanti et similia excipias) sese extendit; non tamen omnino universalis evadit nisi per ulteriores quasdam methodos eliciendi series infinitas — Sed quomodo in istis casibus procedendum sit, jam non vacat dicere ut neque alia quædam tradere quæ circa Reductionem infinitarum serienum in finitas, ubi rei narua tulerit, excogitavi. Nam parcius scribo quod hæ speculationes diu mihi fastidio estse cœperunt; adeo ut ab ijsdem jam per quinque fere annos abstinuerim. And to this Mr Leibnitz in his Letter of 27 Aug. 1676 replied: Quod dicere videmini plerasque difficulcates exceptis Problematibus Diophantæis) ad series infinitas reduci; id mihi non videtur. Sunt enim multa usque adeo mira et implexa ut neque ab æquationibus pendeant neque ex quadraturis. Qualia sunt (ex multis alijs) Problemata methodi tangentium inversæ. When he wrote this Letter he placed the perfection of Analysis, not in the differential Calculus as he did after he knew it; but in another method founded on Analytical Tables of Tangents & the Combinatory Art. Nihil est, saith he, quod norim in tota Analysi momenti majoris. And a little after: Ea vero non differt ab Analysi illa suprema SVPREMA ad cujus intima Cartesius non pervenit. Est enim ad eam constituendam opus Alphabeto cogitationum hujmanarum. And these things induce me to beleive that he wrote this Letter before he found the Differential Method. In October following he came from Paris to London, & there met with Dr Barrow's Lectures & saw my Letter of October 24, 1676, & therin had notice of my Compendium of Series sent by Dr Barrow to Mr Collins in the year 1669 under the title of Analysis per æquationes &c, & consulting Mr Collins for what he wanted, saw in his hands several of mine & Gregories Letters, especially those relating to series, & in his way home from London was meditating how to improve the method of Tangents of Slusius as appears by his Letter to Mr Oldenburg dated from Amsterdam 1828 Novem 1676. And the next year in a Letter to Mr Oldenburg dated 21 Iune he sent hither his new method with this Introduction Clarissimi Slusij methodum tangentium nondum esse absolutam celeberrimo Newtono assentior. And in describing this Method he abbreviated Dr Barrows method of Tangents & shewed how it might be improved so as to give the method of Slusius & to proceed in equations involving surds; & then subjoyned: Arbitror quæ celare voluit Newtonus de tangentibus ducendis ab his non abludere: Quod addit, ex eodem fundamento quadraturas reddi faciliores me in sententia hac confirmat. And after seven years he published the elements of the method as his own without mentioning the correspondence which he had had with the English formerly about these matters. He mentioned indeed a Methodus similis; but whose was that Method & what he knew of it he did not say, as he should have done. And this his silence put me upon a necessity of writing the Scholium upon the second Lemma of the second Book of Principles, least it should be thought that I borrowed that Lemma from Mr Leibnitz. Mr Iames Bernoulli in the Acta Eruditorum for December 1691 pag. 14, said that the Calculus of Mr Leibnitz was founded in that of Dr Barrow & differed not from it except in the notation of differentials & some compendium of operation. And the Marquess de l'Hospital in the Preface to his Analysis of infinite petits published A.C. 1696 represented that where Dr Barrow left off Mr Leibnitz proceeded, & that the451 the improvement wchwhich he made to Dr Barrows Analysis consisted in excluding fractions & surds: but he did not then know that Mr Leibnis had notice of this improvement from me by mty two Letters above mentioned, dated 10 Decem. 1672 & 24 Octob. 1676. After he had notice that such an improvement was to be made, he fo might find it proprio Marte, but by that notice knew that I had it before him. In the end of the year 1669 Mr Collins sent notice to Mr Iames Gregory that I had a general method of Series & Mr Gregory by this Notice & one of my Series being put upon searching after this method found it after a years study. But tho he found it proprio Marte yet he never because he knew that I had it before him, he never claimed a right to it. I wrote the Book of Quadratures in the year 1676, except the Introduction & Conclusion, extracting most of it out of old Papers; & when I had finished it, & the 7th 8th 9th & 10th Propositions with their Corollaries were fresh in memory, I wrote upon them to Mr Collins that Letter wchwhich was dated 8 Novem. 1676 & published by Mr Iones. T He that compares that Letter with those Propositions & particularly with the second Corollary of the tenth Proposition, will easily see that I had composed those Propositions before I wrote that Letter. The Tables at the end of the 10th Proposition for squaring some Curves & comparing others with the Conic Sections were invented by the inverse method of fluxions before the year 1671 as may be understood by my Letter of 24 Octob. 1676. [And in the same Letter where I mentioned represented that the general Series Theoremes there mentioned set down for squaring of Curves by a series werase invented by the method of fluxions, I meant the direct & inverse method set down described in the first six Propositions of the Book of Quadratures. For I know of no other Method by wchwhich thosate Theoremes & others there mentioned could be invented.] The Book of Quadratures was therefore composed before Mr Leibnitz understood the differential Method. At the request of Dr Wallis I sent to him in two Letters dated 27 Aug. & 17 Septem. 1692 the first Proposition of the Book of Quadratures copied almost verbatim from the Book, & also the method of Extracting fluents out of equations involving fluxions mentioned in my Letter of 24 Aug Octob. 1676 & copied from an older paper, & the DotorDoctor printed them both the same year (vizt A.C. 1692) in the second Volume of his works, pag. 391, 392, 393, 394, 395, 396, subjoyning an explication of the method of fluxions direct & inverse comprehended in thies sentence: Data æquatione fluentes quotcunque quantitates involvente, invenire fluxiones, & vice versa. This second volume came abroad in the year 1693, two years before the first Volume, & three years before the Marquess de l'Hospital published his Analysis des infinitement petits. And this is a demonstration that in those days I used prickt letters, & understood second third & fourth fluxions: long before the Rule for finding first second third & fourth differences came abroad. which was that is & gives a preceding y my Rule for finding them] & that my Rule for finding them was the first made publick that was made publick. not only the first that was invented but also the first that was made publick. When I considered only first fluxions I seldom used letters with pricks. But when I considered also second third & fourt fourth fluxions I distinguished them by letters with one two or more pricks & for fluents I put the fluxion either included within a square (as in the above mentioned Analysis) or with a square prefixed (as in some other papers) or with an oblique line upon it. And these notations by pricks & oblique lines are the shortest & best yet used, but were not known to the Marquess de l'Hospital when he recommended the differential notation, nor are necessary to the Method. 389 SrSir I have viewed the printed papers you left in my hands. The Remarks are only upon the Letter of Mr Leibnitz to M. l'Abbé Conti dated 9 Apr. 1716. The Letters to the Princess & the Comtesse of Kilmansegger, & the Postscript of a Letter to Baron Bothmar are without an Answer; & I do not see that they need any. None of his Letters were writ to me, & I had not answered any of them had not Mr l'Abbé Conti pressed me to write an answer to the Postscript of of his a Letter to him that both might be shewed to the King. But when I found that Mr Leibnitz sent his Answer to mine all the Letters open to Paris & it his answer came hither from thence I declined returning an Answer to it writing any more Letters & only drew up wrote the Remarks upon it that Answer to satisfy my friends here that what he writ was easy to have been answered, if it had come hither directly. The Commercium Epistolicum notwithstanding any thing which has hitherto been said against it, remains in full force, & while that remains unshaken there is no need of sayin writing any thing further about these matters. Mr Leibnitz objected against it that in printing the ancient Letters & papers many things had been omitted wchwhich made for him & against me: but in offering to prove this twice by two instances he failed ias with. often. He objected also that the Committee of the R. Society strained things against him by fals interpretations, & particularly that they had maliciously interpreted the words of the Acta Eruditorum for Ianuary 1705, by saying: Sensus verborum est quod Newtonus fluxiones pro differentijs Leibnitianis substituit: but he has misinterpreted the place himself. For the Editors of the Acta in this Paragraph, call Mr Leibnitz the INVENTOR, & thence deduce this conclusion Pro differentijs IGITVR Leibnitianis Newtonus adhibet, semperque [pro differentijs illis] adhibuit fluxiones — ijsque tum in suis Principijs Naturæ Mathematicis, tum in alijs postea editis [pro differentijs illis] eleganter est usus QVEMADMODVM ET Honoratus Fabrius in sua Synopsi Geometrica motuum progressus Cavallerianæ methodio substituit. This is the interpretation wchwhich the Committee put upon the place, & the words igitur & quemadmodum & enforce it; & therefore the objection vanishes, & the Commercium Epistolicum remains untouched It has been said alledged that Mr Leibnitz found the Method by himself. But this second inventors have no right. Whether Mr Leibnitz found the method by himself or not is not the Question. The Committee of the Royall Society did not enter into this Question, but on the contrary said: We take the proper Question to be, not who invented this or that Method, but who was the first inventor of the Method. And we beleive that those who have reputed Mr Leibnitz the first Inventor, knew little or nothing of his correspondence with Mr Collins & Mr Oldenbourg long before, nor of Mr Newton's having the Method above 15 years before Mr Leibnitz by began to publish it in the Acta Eruditorum of Leipsic. Here the Committee treat Mr Leibnitz as second inventor & complain of Mr Leibnitz him only for publishing the Method as his own without disco making any mention of the correspondence which he had with me & my friends about it long before he began to published it. By that correspondence he had notice in Iune or Iuly 1676 that I had a very general Method of Analysis, wchwhich remarked extended to the abstruser sorts of Problems & that this Analysis proceeded without stopping at Surds, & that it was an improvement of the Method of Tangents of Gregory & Slusius, & that the method of Tangents of Gregory was an improvement of the Method of Tangents of Barrow. He had notice also that my method gave Theoremes for squaring & that I had it when I wrote my Letter of 10 Decem 1672 & that I had interwoven this method with the method of infinite series before I wrote that Letter And in October 1676 he had further notice of these things & met with Dr Barrows Lectures in London & in his Letter of 21 Iune 1677 sent back an improvement of Dr Barrow's method method of Tangents so as to give the Method of Gregory & Slusius & to proceed without stopping at surds, & then added: 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. For he had notice also the year before he wrote this These last words relate to the notice which he had also, that my method produced series Theorems for squaring of curvilinear figures by converging series which in some cases break off, & become finite; & that it produced also m Theorems for comparing curvilinear figures with the Conic sections: but how it produced these Theorems he was not able to find out. He had notice also that my Analysis by the help of converging Equations was so general as to extend to almost all Problems except some numeral ones like those of Diophantus; but in his Letter of 13 Aug. 1676 he questioned its being so general & placed the perfection of Analysis in Analytical tables of tangents & the combinatory art & therefore was hitherto a stranger to the Differential Method Analysis.. He had notice also that I had this method when I wrote my Letter of 10 Decem 1672 & that I wrote a Tract upon it in 1670 the year 16701, & between that year & they neglected it till the year 1676. had neglected it the year 1671. And tho after all these notices he might find out the method propria marte, yet by publishing ithe method as his own eight yers after the correspondence by which he had all these notices, & doing it without mentioning that correspondence; phe put me upon a necessity of mentioning it in the Book of Principles, & gave just occasion to the Committee of the R. Society to do the like. And as Mr Leibnitz never found fault with me for what I did to mentioning it so the Committee of the R. Society are not to be blamed. for what they did. Mr Iames Bernoulli in the Acta Eruditorum for Decem. 16711691 & the Marquess de l'Hospital in the Introduction to his Analysis represented that the differential Method was an improvement of Dr Barrow's Method of Tangents, & the Marquess represented further that the improvement lay in shewing how to proceed without stopping at surds: but the Marquess did not then know that Mr Leibnitz had notice of this improvement of from me before he found it, & the Committee complained of him justly for concealing thits & all the other notices. It has been said that in the old Letters & Papers published in the Commercium Epistolicum there are no prickt letters. And indeed I seldome used prickt letters when I considered only first fluxions, as in the Introduction to the Book of Quadratures: but when I considered also second third & fourth fluxions, as in the body of the book, I distinguished them by the number of pricks. In the year 1692, at the request of Dr Wallis I sent to him the first Proposition of the Book of quadratures with its solution & examples in first & second fluxions, copied almost verbatim from the book, I sent him also the method of extracting fluents out of Equations involving fluxions, wchwhich to the best of my memory was composed in the year 1671: & the Doctor printed them both the same year in the second Volume of his works which came abroad the next year A.C. 1693. And thence it may be understood that the Book of Quadratures was then in manuscript. In my Letter of 24 Octob. 16756 I set down the first Proposition of this Book verbatim in an Ænigma, & said that it was the foundation of the method there concealed, & that it gave me general Theorems for squaring of figures by series which sometimes break of & become finite, & how it gave me such series is explained in the first six Propositions of this Book, & I know no other method of finding them. And therefore I had the Method at that time so far as it is conteined in those six Propositions. In the same Letter I copied also many Ordinates of curves from a Table in the end of the tenth Proposition & upon the 7th 8th 9th & 10th Propositions I wrote to Mr Collins my Letter of 8 Novem. 1676 printed by Mr Iones. And from all this it may be understood that the book was then in manuscript. And as the notation used in this Book is the oldest, so it is the best shortest & most expedite, but was not known to the Marquess de l'Hospital when he recommended the differential Notation. If it be asked why I did not publish ## If it be asked why I did not publish this book sooner, it was for the same reason that I did not publish the Theory of colours sooner, & I gave the reason in my Letter of 24 Octob. 1676. ⊡ ⊡ The first Proposition ⊡ The first Proposition of the Book of Quadratures is certainly the foundation of the method of fluxions. That Proposition was comprehended verbatim in the Ænigma by wchwhich in my Letter of Octob. 24 1676 I concealed the method foundation of the Method there spoken of, & therefore that Method there spoken of was the Method of fluxions. In that Letter I said that I had written a Tract on this Method & the Method of series together five years before, but did not finish it, nor meddle any more wthwith these things till the year 1676, being tired with them. And in my Letter of Iune 16 13, 1676 I wrote to the same purpose. And this is the Method which I described in my Letter of Decem 10th 1672. In my Analysis per ǽquationes numero terminorum infinitas, I said of the Method described in that Tract: Denique ad Analyticam merito pertinere censeatur cujus beneficio Curvarum areæ et longitudines &c (id modo fiat) exacte et Geometrice determinentur. Sed ista narrandi non est locus. This relates to Quadratures by Series wchwhich in some cases break off & become finite; as you may understand also by the Letter of Mr Collins to Mr Strode Iuly 26 1672. And therefore before Dr Barrow sent that Tract of Analysis to Mr Collins, that is, before Iuly 1699, I had the method of fluxions so far at the least as it is conteined in the first six Propositions of the Book of Quadraturs. The Committee of the R. S. said that I had this Method above 15 years before Mr Leibnitz began to publish it. And Mr Collins in a Letter to Mr Bertet The Committee of the Royal Society said that I had this Method above fifteen years before Mr Leibnitz began to publish it; ☉ ☉ ☉ ☉ & this is demonstrated certain by my having in those days series for squaring of figures which in some cases break off & become finite. And Mr. Collins in a letter to And Mr Collins in a Letter to Mr Bertet dated Feb. 21. 167071 said that about four years before that time I found a general Analysis for squaring all curvilinear spaces & doing what ever depends upon Quadratures. And in a Letter to Mr Strode dated 26 Iuly 1672 he said that by the Analysis per ǽquationes numero terminorum infinitas & other papers communicated before to Dr Barrow he it appeared that I had the Method & applyed it generally some years before the Doctor sent that Analysis to Mr Collins, that is some years before Iuly 1669. And in a Letter of Aug. 11 1676 to Mr David Gregory the brother of Mr Iames Gr. Mr Collins wrote that a few months after the Logarithmotechnia of Mr Mercator came abroade, [wchwhich was in Sept. 16688.] a copy of it being sent to Dr Barrow at Cambridge he wrote back that this doctrine of infinite series was invented by Mr Newton me about two years before the Publication of Mr Mercators Logarithmotechnia [that is about Sept. 16686] & generally applied to all Curves & then sent to him Mr Newtons my Manuscript.. And I see no reason why the testimony of Dr Barrow should be questioned in this matter grounded upon what I had communicated to him from time to time, before the Logarithmotechnia came abroad, should be questioned in this matter. Dr Wallis also who flourished in those days & was inquisitive & skilfull, & received copies of my Letters from Mr Oldenburgh in yethe year 1676; published the same thing in the Preface to the first Volume of his Works without being then contradicted, saying that in my Letters of Iune 13 & Octob 24 1676 I explained to Mr Leibnitz the Method found out invented by me ten years before that time or above. And the testimony of these three ancient knowing & intelligent credible witnesses may suffice to excuse me for saying in the Introduction to the book of Quadratures that I found the Method by degrees in the years 1665 & 1666. [I was then in the prime of my age for invention & most intent upon & mathematicks & philosophy & found out in those two years the methods of series & fluxions & the Theory of colours & began If Mr Leibnitz &c and Mr Collins, in his Letter to Mr Strode dated 26 Iuly 1672, said that by the Analysis per Æquationes numero terminorum infinitas & other papers communicated before to Dr Barrow it appeared that I had the Method & applied it generally some390 some years before the Doctor sent that Analysis to Mr Collins that is, some years before Iuly 1669. And I see no reason why the testimony of Dr Barrow should be disputed questioned in this matter. [And I hope this may suffice to excuse me for saying in the Introduction to the Book of Quadratures that I found the method by degrees in the years 1665 & 1666. For] Dr Wallis also who flourished in those days & was inquisitive & skilfull & received copies of my Letters from Mr Oldenburgh in the year 1676, affirmed published the same thing [nine years before me] in the Preface to the first Volume of his Works without being then contradicted or blamed for, saying that in my Letters from of Iune 13 & Octob. 24 1676 I explained to Mr Leibnitz the method found by me ten years before that time or above. And the testimony of these three ancient intelligent & credible ⨳ ⨳ And the testimony of these three ancient knowing & credible witnesses may suffice to excuse me for saying in the Introduction to the Book of Principles Quadratures that I found the method: by degrees in the years 1665 & 1666. If Mr Leibnitz could have made a good objection against the Commercium Epistolicum, he might have done it in a short Letter without writing another book as big. But this book being matter of fact & unanswerable he treated it with opprobious language & avoided answering it by several excuses, & endeavoured to lay it aside by appealing to the judgment of his friend Mr Bernoulli & by writing to his friends at Court, & by running the dispute into a squabble about a Vacuum, & Atoms, & universal gravity, & occult qualities, & Miracles, & the Sensorium of God, & the perfection of the world, & the definitions nature of time & space, & the solving of Problemes, & the Question whether he did not find the Differential Method proprio marte: all which are nothing to the purpose. Mr Iames Gregory after a years study found the method of converging Series proprio marte, but did not claim it because he had notice of it from England that there was such a general method before he searched for it, & by that notice knew that he was not the first inventor. Gregorius autem, said Mr Collins, Newtonum primum ejus inventorem anticipare haud integrum ducit. There is but one proper Question, & that is: Who was the first Inventor? Let it be proved that Mr Leibnitz had the Method not only before I Iune 1677 & but also before Iune the year 1677, & then that he had it before he had any notice of it from England, & then let it be further proved that he had it before the date of my Letter of Decem. 10th 1672, & by consequence some months before he began to learn the higher Geometry & before the year 1671 in wchwhich that in I wrote a tract upon it & before Iuly 1699 &c; & then by these steps if they can be proven made the Commercium Epistolicum will at length begin to be shaken. For the proof lies upon the friends of Mr Leib. In the mean time, as it was with difficulty that I was induced to write my Letter of Feb. 26 167 1716 in answer to Mr Leibnitz about these matters, so I do not think the Method of such consequence that I should write any more about it. But whatever is done, I do not think this business of such consequence that I should meddle with it any further. Mr Leibnitz pretended that I SrSir I have viewed the printed papers you left in my hands. The remarks are only upon the Letter of Mr Leibnitz of dated 9 Apr. 16716. The Letters to the Comtesse of Kilmansegger & the Postscript to Baron Bothmar are without an answer, nor do I see that they need any. None of the Letters were writ to me & I had not answered any of them had not Abbe Conti pressed me to write an answer to thaet Postscript of his Letter that the Answer both might be shewed to the King. And when Mr Leibnitz refsant sent his Answer to open to Paris to e & it came hither from thence & was full of railery & I declined returning an Answer & only drew up remarks to satisfy my to satisfy my friends privately that what he writ was easy to be answered if I had th he had sent his Letter hither directly. In his Letter to Mr the Countess of Kilmansegger he said that I formerly applauded his series for the circle, & that it was found afterwards that Gregory had found the very same same series, but it was late before he knew this: but the truth is that he knew this before he sent the Series to me & ought to have let me known as much. He had before that time received it twice (if not thrice) from England as appears by authentic papers published in the Commercium Epistolicum. page 41, 47, 25. [In his Letter of 27 Aug. 1676 wherein he sent it to me he said that he had communicated to his friends above three years before, that is some time before 2 August 1673. And yet he did begin to learn that the higher Geometry before that summer. He kept a correspondence with Mr Oldenburgh about numeral questions till Iune that year & then began to study the higher Geometry with reading the Horologium Oscillatoryium vel of Mr Huygens wchwhich came abroad that year in April that year.] In the same Letter he saith that in the L Scholium to the second Lemma of the second my Principles pag 253, 254 I did not dispute his having found the differential Method by himself. No more did I ever dispute Mr Iames Gregories finding having found the Method of converging series by himself. He had notice from England that there was such a method & spent a year in searching after it, & before he found it, but never laid claim to it because he knew that I had it before him. M M So Collins Epist ad Th. Strode: D. Gregorius autem D. Newtonum primum ejus Inventorem anticipare haud integrum ducit. Vide Commerc. Epist. pag. 29. Mr Iames Bernoulli & the Marquess de l'Hospital gave notice to represented that where Dr Ba Mr Leibnitz met with Dr Barrows Lectures at London in November October 1676, & the Mr Iames Bernulli & yethe Marquess de l'Hospital have represented that where the DrDoctor left off Mr Leibnitz proceeded, & the Marquess s has told us that the improvement made by Mr Leibnitz to the DrsDoctors methods lay in shewing how to proceed without avoid frac proceed wthwithout stopping at fractions & surds. But the Marquess did not then know that I Mr Leibnitz had notice of this from me by my Letter to Mr Collins of 10 Decem. 1672 (a copy of wchwhich Mr Leibnitz received at Paris in Iuly 1676,) & again by my Letter to Mr Oldenburg of 24 Octob 1676 wchwhich he saw at that time in London. [Nor did the Marquess know that I in these two Letters I had] When Mr Leibnits published the Elements of the Differential Method, instead of claiming them he should have told the world what notices correspondence he had had notices he had received from England about those matters those matters such a method before he found it. By By his concealing these notices he th what he knew of these notices he put me upon a necessity of making some mention of them in the Book of Principles, & particulary upon representing that I had writ to him first about this method, & that I did this eight years before he published it, & that I did this ten years before, that is in the year 1676 & that I then concealed it in setting down this sentence enigmatically Data æquatione fluentes quotcunque quantitates involvente invenire fluxiones et vice versa. Which sen the first part of wchwhich sentence being the first Proposition of the Book of Quadratures verbatim, may suffice to satisfy any man of candor that the Book of Quadratures was then in in Manuscript. Whether Mr Leibnitz found the method by himself or not was not the Question but whether he was the first inventor. In thise Letter Postscript of his Letter to the Count de Bothmar he cites a passage out of the Acta eruditorum for Ianuary 16 1705 & there pretends that the words semperque adhibuit came are maliciously interpreted by substituit. For, saith he, theose words seen to be put expresly to signify that Mr I used fluxions before the publishing of his calculisus. And so they might & yet be truly interpreted by substituit, unless they be put expresly to signify that I used fluxions for d the Leibnitian differences before he Mr Leibnitz invented the differential method. But saith he, between the words semper adhibuit & substituit there is this difference; the one signifies that Mr Newton always imployed his Method, the other that Pere Fabri formed his in imitation of another In the Introduction to the Book of Quadratures I said that I found the Method by degrees in the years 1665 & 1666: if he did grants that the words semperque adhibuit extend to all times ever since, he has absolved me from plagiary; & the Method is mine: but if he otherwise not, & it lay upon him to prove me guilty. For his complimtcompliment In the interpretation wchwhich that I found the method proprio marte does not excuse absolve me from the guilt. He that claims an meth invention In the interpretation wchwhich he would put upon the words passage he omits the force of the words igitur & quemadmodum as I said in my Remarks, & In the beginning of the Paragraph Mr Leibniz is called the Inventor, wchwhich & thence in drawn this conclusion. Pro differentijs IGITVR Leibnitianis Newtonus adhibet semperque [pro ijsdem differentijs] adhibuit fluxiones, quemadmodu — ijsque tum in suis Principijs Natura Mathematicis tum in alijs postea editis eleganter est [pro differentijs Leibnitianis] eleganter est usus; QVEMADMODVM et Honoratus Fabrius in sua Synopsi Geometrica, motuum progressus Cavallerianæ methodo substituit. This is certainly the true meaning of the words & therefore [in accusing the Committee of the R. Society of a malitius interpretation he Mr Leibnitz was certainly in the wrong] they amount to an accusation of plagiary & it lay upon Mr Leibnitz to prove histhe accusation. Mr Leibnitz accused the Committee of the R. Society of omitt partiality in omitting every thing wchwhich made for him or against me, & offered to prove this by two instances, but failed in both. He accused them also of inter attaquing his candor by forced interpretations & of & here called one of their interpretations a malicious one but has missiinterpreted the place himself. And therefore the Commercium Epistolicum remains unshaken. And untill this is answerd there will be no need of saying any thing more about this matter. The Committee did not enter into the Question whether392 whether Mr Leibnitz invented the Method proprio Marte or not. On the contrary they said that they did not taoketooke the Question to be not who invented this or that Method but who was the first inventor of the Method. [And for proving that Mr Leibnitz was not the first inventor they have appealed to my Letters of 13 Iune & 24 Octob. 1676 & 10 Decem 1672 & my Analysis per æquationes] And for proving that I was the first they appeadled to ancient letters & papers. Mr Bernoulli answered that in those Letters & Papers there were no prickt letters: wchwhich is as much as to say that the Introduction to the book of Quadratures & the Proposition Data æquatione fluentes quotcunque quantitates inv.involvente does not treat of the method of fluxions because there are no prick lletters in them. He said also that prict letters did not appear till the third Volume of Dr Wallis's works came abroad, wchwhich was in the year 166 1699 wchwhich & so he was mistaken in matter of fact. For the first Proposition of the Book of Quadratures with the solution & explicati examples in first & second fluxions came was published almost word for word six years before in the second Volume of the Doctors works. He said also that I did not understand second fluxions, & this is as much as to say that he & had not read the first Proposition of the Book of Quadratures. So then the Commercium Epistolicum remains unshaken. 106)Add 3968393 After 17167 Iuly to Des Maizeaux Not to Conti Natsine p. 111 SrSir I have viewed the printed papers you left in my hands. The Remarks are only upon the Letter of Mr Leibnitz to Mr. l'Abbé Conti dated 9 Apr. 1716. The Letters to the Comtesse of Kilmansegger, & the Postscript of a Letter to Baron Compt Bothmar are without an Answer, & I do not see that they need oaney. None of his Letters were writ to me, & I had not answered them any of them had not Mr l'Abbé Conti pressed me to write an Answer to the Postscript of a Letter to him that both might be shewed to the King. But I when I understood that Mr Leibnitz sent all the Letters open to Paris, & only wrote the Remarks his Answer came hither from thence, I declined writing any more Letters, & only wrote the Remarks upon that Answer to satisfy my friends here that what he writ was easy to have been answered if it had come hither directly. The Commercium Epistolicum, notwithstanding any thing which has hitherto been said against it, remains in full force, & while that remains unshaken there is no need of writing any further about these matters. Mr Leibnitz objected against it that in printing the ancient Letters & papers many things had been omitted wchwhich made for him & against me: but in offering twice to prove this by instances, he failed as often. He objected also that the Committee of the R. Society strained things against him by fals interpretations but he never proved this in any one instance He said indeed that they had maliciously interpreted the words of the Acta Eruditorum for Ianuary 1705, by saying: Sensus verborum est quod Newtonus fluxiones pro differentijs Leibnitianis substituit: but he has misrepresented the place himself. For the Editors of the Acta in this Paragraph call Mr Leibnitz the INVENTOR, & thence deduce this conclusion. Pro differentijs IGITVR Leibnitianis Newtonus adhibet semperque [pro ijsdem] adhibuit fluxiones — ijsque tum in suis Principijs Naturæ Mathematicis, tum in alijs postea editis [pro differentijs illis] eleganter est usus QVEMADMODVM ET Honoratus Fabrius in sua Synopsi Geometriaca motuum progressus Cavallerianæ methodo substituit. This is the interpretation wchwhich the Committee put upon the place, & the words igitur & quemadmodum et enforce it. It has been represented that in the Commercium Epistolicum Mr Leibnitz is complained of as having published my Method as his own; whereas he found the Method by himself. But second inventors have no right. Whether Mr Leibnitz found the Method by himself or not is not the Question. The Committee of the Royal Society did not enter into this Question, but on the contrary said: We take the proper Question to be, not who invented this or that Method but who was the first inventor of the method. And we beleive that those who have reputed Mr Leibnitz the first Inventor, knew little or nothing of his correspondence with Mr Collins & Mr Oldenbourg long before, nor of Mr Newton's having the Method above 15 years before Mr Leibnitz began to publish it in the Acta eruditorum of Leipsic. Here the Committee of the R. Society treat Mr Leibnitz as an second Inventor but not asnd complain of him only for publishing the Method as his own without making any mention of the correspondence wchwhich he had with me & my friends about it long before he published it, & by that concealement claiming the Method as first Inventor. By that correspondence he had notice in Iune or Iuly 1676 that I had a very general method of Analysis wchwhich extended to the abstruser sorts of394 of Problems in Geometry.✝ ✝ & that the Method of Tangents of Gregory & Slusius was but a branch or rather a Corollary thereof & that it proceeded without any troublesome calculation & without sticking at surds. & that I had it when I wrote my Letter of 10 Decem 1672, & that I had interwoven it with the Method of infinite series before I wrote that Letter, & that my Letter of 10 Decem. 1672 & being tyred with these speculations I had absteined from them five years when I wrote my Letter of 13 Iune 1676. & that my methods of The Art of Analysis by these methods became so general as to reach almost all sorts of Problems except perhaps some numeral ones like those of Diophantus. But all this was not yet sufficient to make him understand the differential method. For in his Answer dated 13 Aug. 1676, he wrote back. Quod dicere videmini plerasque difficultates (exceptis Problematibus Diophantæis) ad Series infinitas reduci; id mihi non videtur. Sunt enim multa usque adeo mira et implexa ut neque ab æquationibus pendeant neque ex quadraturis. Qualia sunt (ex multis alijs) Problemata methodi tangentium inversæ. And in the same Letter he placed the perfection of Analysis in Analytical Tables of Tangents & the combinatory art: saying of the one, Nihil est quod norim in tota Analysi momenti majoris; & of the other, Ea vero nihil differt ab Analysi illa suprema, ad cujus intima, quantum sentio judicare possum, Cartesius non pervenit. Est enim ad eam constituendam opus Alphabeto Cogitationum humanarum. Mr Iames Bernoulli in the Acta Eruditorum for December 1691 & the Marquess de l'Hospital in the Introduction to his Analysis represented that the Differential Method was an improvement of Dr Barrow's method of tangents, & the Marquess represented further that the improvement lay in shewing how to proceed without stopping at surds. But the Marquess did not then know that Mr Leibnitz had notice of this improvement from me before he found it, & the Committee complained of him justly for concealing this & all the foregoing notices. In October 1676 Mr Leibnitz came to London & there met with Dr Barrows Lectures & with my Letter to Mr Oldenburgh dated 24 Oct. 1676, in wchwhich the above mentioned notices were repeated & he was also told that the Tract in wchwhich I interwove the two Methods was written five years before, that is, in the year 1671. And that before the plague wchwhich raged in the year 1665 forced me from the Vniversity, I had found the method of converging Series (by including redactions by the binomial Rule & by division & extraction of roots both simple & affected,) so as to be able to deduce the areas of all figures & yethe lengths of all curve lines from their Abscissas & Ordinates & on the contrary to deduce the Abscissas & Ordinates & any other right lines from the areas & lengths of yethe Curves. And He was told also that when Mercators Logarithmotechnia came abroad, Dr Barrow sent Mr Collins a Compendium of these the Method of these Series, meaning the Analysis per æquationes numero terminorum infinitas. And at the same time he consulted Mr Collins to see what he could meet with in his hands of mine & Gregories Letters & Papers, & there saw a great part of our correspondence. And in his way from London to Hannover he was told that meditating how to improve the Method of Tangents of Slusius For in a Letter to Mr Oldenburgh from Amsterdam dated 1828 Novem. 1676 he wrote: Methodus Tangentium a Slusiūjo publicata nondum rei fastigium tenet. Potest aliquid amplius præstari in eo genere, quod maximi foret momenti usus ad omnis generis Problemata — Nimirum posset brevis quædam calculari circa Tangentes Tabula &c. He had not therefore yet found the right improvement, but at length he found it proprio Marte. For the next year in a Letter to Mr Oldenburgh dated 21 Iune 1677 he wrote: Clarissimi Slusij methodum tangentium nondum esse absolutam celeberrimo Newtono assentior. And then Et jam a multo tempore rem tangentium generalius tractavi395 tractavi, scilicet per differentias Ordinatarum. And then he set down Dr Barrows method of Tangents with a new notation & shewed how it might be improved so as to proceed without give the method of Tangents of Slusius, & to proceed without stopping at surds; & then added: Arbitror quæ celare voluit Newtonus de Tangentibus ducendis, ab his non abludere. Quod addit, ex hoc eodem fundamento Quadraturas quoque reddi faciliores, me in sententia hac confirmat. 109)2397 After Iuly 1717 2 SrSir the I have viewed the printed papers you left in my hands. The Remarks are only upon the Letter of Mr Leibnitz to Abbé Conti dated 9 Apr. 1716. The Letters to the Comtesse of Kilmansegger & the Postscript of a Letter to Baron Bothmar are without an Answer, & I do not see that they need any. MThey were not written to me & Mr Leibnitz is & therefore I desire to be excused from medling with them None of the his Letters were writ to me, & I had not answered any of them had not Mr l'Abbé Conti pressed me to write an answer to the Postscript of his Letter that both might be shewed to the King. But when Mr Leibnitz sent his Answer to mine open to Paris & it came hither from thence I declined writing returning an Answer to it & only drew up the Remarks to satisfy my friends that what he writ was easy to have been answered, if it had come hither directly. The Commercium Epistolicum notwithstanding any thing wchwhich has hitherto been written against me remains in full force, & while that remains unshaken there is no need of saying writing any thing further. The Commercium Epistolicum notwithstanding any thing which has hitherto been written remains in full force . Mr Leibnitz indeed objected against it that in printing the ancient Letters many things had been omitted wchwhich made for him & against me: but in & offerinedg to prove this by two instances, hebut failed in both He has objected also that the Lette Committee of yethe R. Society have strained things against him by false interpretations & particularly that they in the Passag they had maliciously interpreted the words of the Acta Eruditorum for Ianuary 1705, by saying: Sensus verborum est quod Newtonus fluxiones differentijs Leibnitianis SVSTITVIT. but he has misinterpreted the place himself For T The Editors of the Acta in this Paragraph call Mr Leibnitz the InventorINVENTOR & thence draw this conclusion Pro differentijs igitur IGITVR Leibnitianis Newtonus adhibet semperque [pro differentijs Leibnitianis illis] adhibuit fluxiones, . . . . . ijsque tum in suis Principijs Naturæ Mathematicis, tum in alijs postea editis [pro differentijs Leibnitianis] eleganter est usus QVEMADMODVM etET Honoratus Fabrius in sua Synopsi eleganter est usus Geometrica, motumum progressus Cavallerianæ methodo substituit. The words igitur & the words quemadmodum et (the force of wchwhich Mr Leibnitz omits) enforce the interpretation here set down, wchwhich is the interpretation put upon themis by the Committee Paragraph in the Commercium Epistolicum. Mr I. Bernoulli objected against that when the ancient Letters & Papers were first written I did not so much as dream of the me Analys method of fluxions because there are no prickt letters in them & these letters first appeard in the th: which is much as to say that when I wrote explained the method of fluxions in the Introduction to the Book of Quadratures I did not so much as dream of the Method of fluxions because there are no prickt letters in it, & when I was set down the first Proposition of the Book of Quadratures enigmatically in my Letter of 24 Octob. 1676 as a testimony that the method was founded in the first Proposition of this Book was then in Manuscript, I did not so much as dream of the Method of fluxions because there are no prickt letters in the Propos Ænigma. ③ Or that wh in my Letter of 24 Octob 1676 I did not copy from the Book of Quadratures then in Manuscript the Ordinates of curves wchwhich may be compared wthwith the Conic Sections because there are no prickt letters in that Letter. ② oOr that my Letter to Mr Collins dated 8 Novem. 1676, & published by Mr Iones hadd no relation to the 7th 8th 9th & 10th Propositions of the Book of Quadratures then in Manuscript because there are no prickt letters in that Letter. ① Or that my saying in my Letter of 24 Octob. 1676 that the series for squaring of Curves wchwhich in some cases breaks off & becoms finite finite was invented by the Method whose foundation was comprehended in the said Ænigma that is by the method founded in the first Proposition of the book of Quadratures, he was not invented by the method comprehended in the first six founded in the first Proposition & carried on in five next Propositions of the Book of Q. then in Manuscript because there are no prickt letters in that that Letter. Mr Iohn Bernou ④ Or that Mr the Marquess de l'Hospital was mistaken in saying that the Book of Principles is full of this Calculus, because there are no prickt letters in it. Or that Mr Leibnitz himself was mistaken when he wrote to me, 7 March 1693, Mirifice ampliaveras Geometriam Mirifice ampliaveras Geometriam tuis seribusseriebus, sed Edito Principiorum opere ostendisti patere tibi quæ etiam quæ Analysi receptæ non subsunt. Conatus sum Ego quoque notis commodis adhibitis quæ differentias et summas exhibent Geometriam illam quam transcendentem appello Analysi quodammodo subjicere. Mr Io. Bernoulli carried on his objectioedn further in these words: Prima vice hæc literæ punctatæ comparuerunt in tertio volumine Operum Wallisij, multis annis postquam Calculus differentialis jam ubique locorum invaluisset but he was mistaken in matter of fact. For the first , – – Et apparit Newtono rectam methodum differentiandi differentialia non innotuisse longo tempore posquam alijs fuisset familiaris. But he erred in matter of fact. For in the year 1692 at the request of Dr Wallis I copied sent him the first Proposition of the book of Quadraturs copi with its solutions extending to second third & fourth fluxions &c & examples copie in first & second fluxions, copied almost verbatim from the book of Quadratures then in Manuscript & the DrDoctor that year printed what I sent him in the second Volume of his works printed what I sent him, & the book came abroad the next year when the Differential method was but beginning to be in vogue & three years before the method of finding second third & fourth differences was published by the Marquess de l'Hospital. So then the crdi Commercium Epistolicum stands unshaken against all Objections wchwhich have hitertohitherto been made. Mr Leibnitz instead of answering it used his utmost endeavour to get away from it & to run the dispute into a squabble about a Vacuum & Atoms & universal gravity & Occult Qualities & miracles & the Sensorium of God & the absolute perfection of the world & solving of Probleme &c the definitions of time & space & the solving of Problemes & the Question whether he did not find the method proprio Marte: all wchwhich are notihing to the purpose. If he could have made a material objection against the book he might have made it in a short Letter without writing another Book as big: but for want of such an Objection, the run away from the Question endeavoured to lay the Commer Epist aside without answering it. Book remains untoucht. Whether Mr Leibnitz found the Method by himself or not was not the Question. The Committee of the R. Society did not Enter into this Question but on the contrary said: We take the proper Question to be not who invented this or that Method but who was the first Inventor of the Method. And we beleive that those who have reputed Mr Leibnitz the first Inventor knew little or nothing of his Correspondence with Mr Collins M& Mr Oldenberg long before nor of Mr Newton's having the Method above 15 years before Mr Leibnitz began to publish it in the Acta Eruditorum of Leipsic. It was the duty of Mr Leibnitz to in point of candor, when he published the Elements of the differential method, instead of making them his own to have given the wordld some account of his knowle former correspondence with Mr Collins & Mr Oldenburg in relation this matter. And the Committee complain of him for concealing this. By that correspondence he had notice Here the Committee complain of Mr Leibnitz for concealing his correspondence wthwith the English me & my friends about theise maethemods long before he began to published the Elements of thei Method it. By that correspondence he had notice that I had a very general Method of Analysis & that this Analysis proceeded398ded without stopping at surds & that it was an improvement of the method of tangents of Gregory & Slusius, & that the Method of Tangents of Gregory was an improvement of the Method of tangents of Barrow., & he knew that the method which he head in his Letter of 21 Iune 1677 he he sent back to me was an improvement of Dr Barrows method of tangents so as to give the method of Gregory & Slusius & to proceed without stopping at surds. He knew had notice also that my Method gave converging series wchwhich brake off & me Theorems for squaring of curvilinear figures by converging series wchwhich in some cases brake off off & became finite & one of those Theorems was sent to him; & that it gave me also Theorems for comparing curvilinear figures with the Conic Sections, & that my Analysis by the help of Converging æquations was so general as to extend to almost all Problems except some numeral ones like those of Diophantus, & that I had this Method when I wrote my Letter of 16 10 Decem. 1672, & had wrote a Tract of upon it in 1670. And the Committee of the R. Society blame complained of him for concealing all his knowledge of all this & making himself the first inventor when he published the Elements of the differential Method as his own by means of that concealment & putting upon the proof of what he ought to have acknowledged himself of his own accord in point of candor. And their complaint was just When Mr Leibnitz came to London the second time he met with Dr Barrows Lectures. And Mr Iames Bernoulli in the Acta Erud. for Dec. 1691 & the Marquess de l'Hospital in yethe Introduction to his Analysis have represented that the Differential Method was an improvement of Dr Barrows method of Tangents, & the Marquess has represented further that the improvemtimprovement lay in shewing how to proceed without stopping at surds: but the Marquess did not then know that Mr Leibnitz had notice be of this improvement from mee before he found the m it. & the Committe complained of him justly for concealing it. Mr Leibnitz in his Letter of 21 Iune 1677 acknowledged that hIe had this improvement from me gave him notice of The Marquess said also that Mr L. [in yethe Iournal des Scavans du 30 Aust 1694 Leibnitz had done me justice in acknowledging that I had found the method of fluxions proprio marte, but he would not have said so till if he had known that Mr Leibnitz had not acknowledged concealed the Notices wchwhich I g above mentioned correspondence if had b known tithem. notices wchwhich I gave him of improving my having notices this method before he found it. He agreed with Mr Leibnitz [He commended the differential notation, but he repeated what Mr Leibnitz had said before & had not seen the notation by prickt letters wchwhich is more expedite. He had only seen the Notation in the Scholium upon the second Le Book of Principles.] The Author of the Elogium of Mr Leibnitz published in the Acta Eruditorum for Iuly 1717 said: Commercio Epistolico Anglorum aliud quoddam suum, idemque almplius, [D. Leibnitius] opponere decreverat, et paucis ante obitum diebus Cl. Wolfio significavit se Anglos famam ipsius lacessentes reipsa refutaturum: quamprimum enim a laboribus historicis vatcaturus sit, daturum se aliquid in Analysi prorsus inexpectatum et cum inventis quæ hactenus in publicum prostant, sive Newtoni, sive aliorum nihil quicquam affine habens.] But Mr Leibnitz pretends that the always [allowed that I found the Method by my self] words semperque substadhitbuit imply that I always used the method without substituting fluxions for differences. It has been satid that Mr Leibnitz found the method by himself. But this is not the Question. The Committee of the R. S. should not have medled with it did not enter into this Question, But On the contrary they said And yet in the year 1684 he began to published it as his own in the year 1686 without making any mention of the correspondence wchwhich had been between us by mean eight about this method about it eight years before, & thereby he put me upon a necessity of mentioning that correspondence in the Scholium upon the second Lemma of the second book of Principles, & gave just occasion to the Committee of the R. S. to take notice of his concealing silence about that correspondence. Mr Ia. Bernoulli — before he found it Mr Collins in the year 1669 sent one of my series to Mr Ia. Gregory with notice that I had a general method of squaring figures by such series; & Mr Gregory after a years study found out the method proprio Marte, but never laid claim to it because by that notice he knew that I had it before him & without that notice he had not found it nor serched after it Gregorius autem Newtonum primum ejus Inventorem anticipare haud integrum ducit. So Collins in his Letter wrote to Mr Strode 26 Iuly 1672. Mr Leibnitz had much more light into yethe Method of fluxions but laid yet laid claim to it before because he found it proprio Marte. It has been further objected against the Commerc. Epist. – – – – without writing another book as big. He has complained indeed that the book attaques his candor in not allowing that he found the method proprio marte. But this was not the Question. The Committee of the R. Society did not enter into this question but omon the contrary said: We take the proper Question to be not who invented this or that Method but who was the first inventor of the Method. And we beleive – – – – in the Acta Eruditorum of Leipsic. It was the duty – – – – – making himself the first Inventor. And their complaint was just. When Mr Leibnitz came to London the second time – – – – of this improvemtimprovement from me. Mr Leibnitz after all the notices wchwhich he had received from England concerning this Method, might find out the rest by himself: for I told him in my Letter of 24 Octob 1676 that the foundation of the Method was obvious: but his finding it after me gives him no right. And his concealing all the notices wchwhich he had from England of my having the method before him in order to give himself a right, put me upon writing the Scholium upon the second Lemma of the second Book of Principles to give the world notice of what I wrote to him about this method before he found it. So then the complaint of the Committee of the R. Society was just & the Commercium Epistolicum remains firm & untoucht. Mr Iames Gregory Collins sent Mr Iames Gregory one of my series with notice that I had a general method of squaring all figures all figures by such Series. And after this notice Mr Gregory spent a year in find searching after this method & at length found it proprio Marte but because by the notice he knew that I had it before him he never laid claim to it. Gregorius Acri Studio, said Mr Collins, eandem acquisivit multumque in ea enodanda desudavit. – D Gregorius autem Newtonum, primum ejus inventorem anticipare haud integrum ducit. Mr Leibnitz had much more light into the method of Fluxions, & after his being in England the second time had eight months time to find it before he wrote his Letter of 21 Iune 1677, & has been complained of not because after the notices wchwhich he had from England he did not find the remainder proprio Marte, but because Newtonum primum ejus inventorem anticipare integrum duxit. Add 3968399 Le 9e de xbreDecembre 1720Bernoulli chiavous the letter to M Des Maizeau From M. Des MaizeauFrom M. Des Maizeau Mr le Dr. Clarke ayant publié en 1717 un Recueil contenant quelques Ecrite de Mr Leibnitz sur les Principles de la Philosophie & de la Religion naturelle, avec ses Responses; je conseillai au sieur du sauzet, Libraire de la Haye, de les reimprimer: & il les annonça dans ses Novelles Literaires du 27 Mars 1717 p. 208. Ie lui proposas aussi d'y joindre une Traduction François des Recherches sur la lLiberté due l'Homme par Mr Collins et des Rémarques de Mr Collins Clarke sur ces Recherches. Dans ce temps-là Mr le Chavalier Newton fit imprimer une Version Francois de deux Ecrits sur l'invention des Fluxions ou du Calcul Calcul differentiel, qu'il avoit oposes a deux LettersLettres de Mr Lebniz adressees a Mr l'Abbé Conti: Ces 4 petites pieces qui avoient deja eté publieè ici, me parurent tres proper a etre ajouteés aux autres. Ie ne doutai point qu'elles ne fussent bien recues dans le Pys etrangers, ou l'on n'avoit que des idées confuses de celle dispute. Mr l'Abbé Conti gouta fort ce dessein, & pour le rendre plus utile il me donna quelques Letteres de Mr Leibnitz qui avoient du rapport avec celles dout j'ai parlé, & pouvrient servir d'eclarissement; Vne entr'autres ecrit d à Madam de Kielmansegg, ou il faisoit l'e histoire de son demêtre avec Mr Newton; & une autre a Monsr le Comte de Bothmer qui rouloit sur la meme matiere. Il avoit d deja fourni des Copies de ces mêmes Lettres a Mr Newton. Monsr l'Abbé etant ensuit allé à Paris, au commencement de l'Annee 1718, il m'envoye par Mr l'Abbé Greco plusieurs autres Pieces de Mr Leibniz pour augmenter mon Recueil; savois, des dissertations & des Lettres a Mr Remond. Ie l'en remerciai par la Lettre, qui est imprimeèé dans le II Tome pag 362 & suiv. Aussi tot que le 4 primieres feuilles de ce second Tome furent imprimimeè, le Libraire me les envoye le 14 Iune 1718. Ie les communiquai à Mr Newton, a fin qu'il fut à tems de faire corriger les fautes qui avoient pû se glisser dans les deux escrits qui etoient de lui; & pour savoir en meme tems ce qu'il persoit sur l'assemblage des pieces contenues dans ces quatre feuilles. En general, il ne' approva pas le maniere dout on les avoit placeés: il auroit souhaite que les deux Lettres de Mr Leibniz qui le regardoient, & ses deux Responses, eussent ete misess ensemble, & que la suite n en eut éte interompuè par les Lettres à Madam de Kielmansegg & a Mr le Comte de Bothmar. Il ne parut pas maeme fort content de l'impression de ces dernier Lettres, par ce qu'il y trouvoit cetrtain facts dont il ne convenoit point, & qu'il ne jugeoit pourtant pas a propos de refuter. C'est ce qui m'a oblige d'en advertis le Lectures dans la PefacePreface pag. LXVI. Divers incidents ont fait trainer l'impression de se Recueil, qui n'a ete fini qu'au Mois de May de cette année. Au reste, la petite Lettre du 7 de Iune 1713 inserée dans la Lettre à Madam de Kielmansegg pag. 36, & attribuée à Mr Bernoulli; avoit eté publieé sous le nom de Mr Bernoulli dans les Novellles Literairs de 28 Decembre 1715 comme je l'ai remarqué à la Marge: et il ne faut que lire ce qui la precede dans ces Nouvelles pour se convaincre que Mr Leibniz l'avoit envoyeé au Iournaliste. Mr Leibniz atribue encore cette Lettre a Mr Bernoulli dans cette qu'il a dressa à Mr l'Abbe Conti le 9 d'Avril 1716 pag 51, pour repondre à la Lettre de Mr Newton. On connoit assez dit il parlant de la feuille volante publieé en Latin, le nom & le lieu de l'Auteur de la Lettre y insereé d'un excellent Mathematicien que j'avoit prié de dire son sentiment sur le Commercium. Ainsi nous n'eumes pas le moindre souçon, Mr l'Abbé Conti & moi, que cette Lettre ne fut effectivement de lui. Cependant ayant sû avant que d'envoyer ma Preface in Hollande, que Mr Bernoulli la desavouoit; je crûs que l'equité demandaoit que j'en avertis le Public, comme j'ai fait pag. XLVIII. 401 Kuy to Maizeau SrSir You know that when Mr l'Abbé Conti had received a Letter from Mr Leibnitz with a large Postscript against me full of accusations forreign to the Question, & the Postscript was shewed to the King, & I was pressed for write an answer to be also shewed to his Majesty, & the same was afterwards sent to Mr Leibnitz: he sent it with his Answer to Paris declining to make good his charge & pretending that I was the Aggressor, & saying that he sent those Letters to Paris that he might have neutral & intelligent witnesses of what passed between us. I looked upon this as an indirect practise & forbore writing an Answer in the form of a Letter to be sent to be sent to him, & only wrote some Observations upon his Letter to satisfy my friends here that I it was easy to have answered him had I thought fit to let him go on with his polyiticks. As soon as I heard that he was dead I caused the Letters & Observations to be printed least they should at any time come abroad imperfectly in France. You are now upon a designe of reprinting them with some other Letters whose written at the same time, whose Originals have been left in yoryour hands for that purpose by Seignier Mr l'Abbé Contyi for making that Controversy complete & I see no necessity of adding any thing more to what has been said, especially now Mr Leibnitz is dead. When he wrote his Letter of 27 Aug. 1676 he placed the perfection of Analysis not in the Differential Calculus but as he did afterwards but in a Method founded on Analytical Tables of Tangents & the Combinatory Art. Nihil est, saith he, quod norim in tota Analysi momenti majoris. And a little after: Ea vero non differt ab Analysi illa SVPREMA ad cujus intima Cartesius non pervenit. Est enim ad eam constituendam opus Alphabeto cogitationum humanarum. And this looks like an Argument that he did not then he would scarce have said had he then understanood the differential method Analysis. When he was in London the second time (wchwhich was in October 1676,) he met with Dr Barrow's Lectures & saw my Letter of October 1676,) he met with Dr Barrow's Lectures & saw my Letter of Octob. 24, 1676, & three months before received a copy of my Letter to Mr Collins dated 10 Decem. 1672. Mr Iames Bernoulli in the Acta Eruditorum for Ianuary 1691 pag. 14 said that the Calculus of Mr Leibnitz was founded in that of Dr Barrow & differed not from it except in the notation of Differentials & some compendium of operation. And the Marquess de l'Hospital in the Preface to his Analysis of infinite petits published A.C. 1696 represented that the improvement wchwhich Mr Leibnitz made to Dr Barrows Analysis consisted in excluding fl fractions & surds: but he did not then know that Mr Leibnitz had notice of this improvement from me by my two Letters above-mentioned, dated 10 Decem. 1672 & 24 Octob. 1676. I wrote the Book of quadratures in the year 1676, except the Introduction & Conclusion; extracting most of it out of old Papers, & when I had finished402 finished it & the 7th 8th 9th & 10th Propositions wthwith their Corollaries & they were fresh in memory, I wrote upon them to Mr Collins that Letter wchwhich was dated 8 Novem. 1676 & published by Mr Iones. The Tables at the end of the 10th Proposition for squaring of some Curves & comparing others with the Conic Sections, were invented by the inverse method of fluxions before the year 1671 as may be understood by my Letter of 24 Octob. 1676. And in the same Letter where. I represented that the general Theoremes there mentioned for squaring of Curves were invented by the Method of fluxions, I meant the direct & inverse method described in the first six Propositions of the Book of Quadratures. for I know of no other Method by which those Theoremes could be invented. At the request of Dr Wallis I sent to him in two Letters dated 27 Aug. & 17 Sept. 1692, the first Proposition of the Book of Quadratures copied almost verbatim from the Book & the Method of extracting fluents out of equations involving fluxions mentioned in my Letter of 24 Octob. 1676 & copied from an older Paper, & the Doctor printed them both the same year (vizt A.C. 1692) in the second Volume of his works, pag. 391, 392, 393, 394, 395, 396, subjoyning an explication of yethe method of fluxions direct & inverse comprehended in the sentence, Data æquatione fluentes quotcunque quantitates inolvente, invenire fluxiones, & vice versa. This Volume came abroad in the year 1693 two years before the first Volume. And this is a demonstration that in those days I used prickt letters & understood second third & fourth fluxions. When I considered only first fluxions I seldom used letters with pricks, but when I considered also second third & fourth fluxions I distinguished them by letters with one two or more pricks. And for fluents I put the fluxion either included in a square or with a square prefixed or with an oblique line upon it. And these notations are the best yet used, but were not known to the Marquess de l'Hospital when he recommended the differential notation, nor are necessary to the Method. By the inverse Method of fluxions I found in the year 1677 the demonstration of Keplers Astronomical Proposition, vizt that the Planets move in Elliplses, wchwhich is the eleventh Proposition of the first book of Principles; & in the year 1683 at the importunity of Dr Halley I resumed the consideration thereof, & added some other Propopsitions about the motions of the heavenly bodies, which were by him communicated to the R. Society & entred in their Letter-book the winter following; & upon their request that those things might be published, I wrote the Book of Principles in the year 1684, 1685 & 1686, & in writing it made much use of the method of fluxions direct & inverse, but did not set down the calculations in the Book it self because the book was written by the method of composition, as all Geometry ought to be. And this Book was the first specimen made public of the use of this method in the difficulter Problems. When Mr Leibnitz was If it be asked why I did not publish the Book of Quadratures before the year 16704, I answer: For the same reason that I did not publish the Theory of colours before that year. I found that Theory in the beginning of the year 1666, & in the year 1671 was upon a designe of publishing it together with the methods of series & fluxions, but the next year for a reason given in my Letter of 24 Octob. 1676, I first suspended & then laid aside my designe of publishing them till the year 1704. And for the same reason I am very averse from medling with these matters any further. 403 pag. 1. lin. 47 – sections. And in my said Letter to Mr Ol to Mr Oldenburg of 24 Octob 1676 I set down the first Proposition of theis Book with its invese verbatim & reprentedrepresented theat the method was founded in that Proposition taken directly & inversely in the in this sentence Data æquation fluentes quotcunque fluentes quantitas involvente invenire fluxiones & vice versa & represented it with the the foundation of the method then spoken of. And in my Letter to Mr Co & that added that & then I added the fundamento conatus sum etiam reddere speculationes de quadratura Curvarum simpliciores; pervenique ad Theoremata quædam generalia. And ... I set down the first of those theorems for quadratures a Theorem for squaring Curves whose ordinates were any dignities of any Binomials & illustrated it wthwith examples & then added that I had other such like Theorems for Trinomials. And all this implies the knowledge of the method of fluxions so far as it is conteined in the first six Propositions of the Book of Quadratures. In the same Letter I said also that I had At quando hujusmodi Curva aliqua non potest Geometrice vel saltem cum alijs Figuris simplicissimis cum quibuscum potest comparari — et dudum retuli. And then I set down the Ordinates of the Curves in the latter part of the second second Thable set down in the 10th Prop. for comparing Curves wthwith the Conic Sections set down in the 10th Proposition of this book wchwhich is a profof that I had that Table some years before I wrote that Letter. And in my Letter to Mr Collins dated 8 Novem. 1676Pag. lin 11 About three years after I the writing of these Letters by the help of this method of Quadratures I found the Demonstration of Keplers Propositions that the Planets revolve in Ellipses describing with a Radius drawn to the sun in the lower focus of the Ellipsis, areas proportional to the lines And wi in the year 1686 I set down the Elements of the Method of Fluxions & moments, & demonstrated them synthetically in the second Lemma of the second Book of Principles in order to make use of the Lemma in demonstrating some following Propositions. & And because Mr Leibnitz had published those Elements in the Acta Eruditorum two years before without taking any notice of the corresondence wchwhich had passed between him & me ten by means of Mr Oldenburg ten years before: I added a Scholium to that Lemma not to give away the Lemma but to put me Mr Leibnitz in mind of making a candid & publick acknowledgment & publ of that correspondence before And in the demonstrating the XIV Prop. of that second Book I considered the differentia momentorum arearum or momentum differentiæ, & therefore when I wrote theis Book I was no stranger to second moments or differences. ‡ ‡ After this Book came abroad, Mr Leibnitz acknowledged that I w it by the After this, in the year 1691 the Book of Quadratures was in the hands of Dr Hally & Mr Ralphson at Cambridge &as one of them hath attested in print before his death & the other still attests. And in the year 1692 – – – – – the best [but the Book of Quadratures continued in MS till the year 1704. [In the meane time Dr Wallis in the Preface to the first Volume of his works (wchwhich came abroad two years after the second )& was published in April 1695) inserted the following Paragraph. Quæ in secundo volumine habentur – – – – – – ab ipso excogitatam. And so soon as this volume came abroad he sent to me the following Letter] In the mean time Mr Leibnitz wrote to me the Book following Letter dated March 7th In Theis year 1693 M I receedived from Mr Leibnitz the following Letter dated 17 Mart. 1693 st. n. Quantum tibi scientiam rerum mathematicarum totiusque naturæ scientiam debere abrbitrem occasione data etiam publice sum profsessus. Mirifice ampliaveras Geometriam tuis seriebus, sed edito Principiorum opere ostendisti patere Tibi etiam quæ analysi receptæ non subsunt. Conatus sum ego quoque notis commodis adhibitis quæ differentias & summas exhibent, Geometriam illam quam Transcendentem appello, Analysi quodammodo subjicere, nec res male processit. &c Here Mr Leibnitz acknowledged himself convinced by the Book of Principles that I had this Method & gave the preference therein to me Add 3968404 to Des Maizeau an Me Copy SrSir Since you are upon a d about publishing the some Letters of Mr Leibnitz out of the Originals left in your hands by Seignior l'Abby de Comitibus together wthwith my Answer & my my Answer wchwhich I wr at the importunity of the said Abby I wrote to a Poscript of his a Letter of Mr a Le You know that when Seignior Mr l'Abbé Conti had received a Letter from Mr Leibnitz wthwith a large abusive Postscript against me wchwhich full of accusations ☉☉ forreign to the question & the Postscrip was shewed to the the King, & at the importunity of the I was pressed to write an answer to the said Postscript that it might be also shewed to the King, & the same being was afterwards sent to Mr Leibnitz he sent it with his Answer to Paris declining to make good his charge & pretending that I had attaqued him, wchwhich indirect p was the Aggressor & saying that he sent those Letters to Paris that he might have impartial witnesses of what passed between us! I looked upon this as an indirect practise & forbore writing toan Answer in the form of a Letter to be sent to him & only wrote some Observations upon his Letter to be communicated to private satisfy my friends here that his Letter was easil it was easy to have have answered his Letter had it him, had I thought fit to let him go on with his polyticks. As soon as I heard that he was dead I caused those the Letters & Observations to be printed lestast they should at any time hereafter come abroad in Fr imperfectly in France. And now You are now upon a designe of reprinting them wthwith some other Letters whose originals have been left in your hands for that purpose by Sen Mr L'Abbé Contei, I have read them all over & see no necessity of saying any thing more about this matter but I intend to meddle with this dispute no further but I see no reason why I should meddle with this dispute any further, especially now Senr Mr Leibnitz is dead. & For I have always indoustriously avoided these disputes. If any thing more were to be said added, it should be what follows the following Declaration. ② I wrote the Book of Quadratures in the year 1676, except the Introduction & Conclusion; extracting most of it out of old Papers, & when I had finished the seventh eighth ninth & tenth Propositions with its their Corollaries & they were fresh in memory, I wrote upon them to Mr Collins that Letter which was dated 8 November 1676 & published by Mr Iones. The Tables at the end of that the tenth Proposition for squaring of some Curves & comparing others with the Conic Sections, were invented by the Inverse Method of Fluxions before the year 1671 as may be understood by my Letter of 24 Octob. 1676. And in the same Letter where I represented that the general Theoremes there mentioned for squaring of Curves were invented by the Method of fluxions, I meant the direct & inverse Method described in the first six Propositions of the Book of Quadratures: for I know of no other Method by which those Theoremes could be invented. At the request of Dr Wallis I sent to him, in two Letters dated 27 Aug. & 17 Sept 1692, the first Proposition of the Book of Quadratures copied almost verbatim from the Book, & the Method of extracting fluents out of Equations involving fluxions mentioned in my Letter of 24 Octob 1676 & copied from an older Paper, & the Doctor printed them both the same year (vizt A.C. 1692) in the second Volume of his works pag. 391, 392, 393, 394, 395, 396, subjoyning an explication of the method of fluxions direct & inverse comprehended in the sentence Data æquatione405 æquatione fluentes quotcunque quantitates involvente, invenire fluxiones, et vice versa. And This Volume came abroad in the year 1693 two years before the first Volume. And this is a demonstration that in those days I used prickt letters & understood second & third fluxions. When I considered only first fluxions I seldome used letters with pricks, but when I considered also second third & fourth fluxions I distinguished them by Letters with one two three or more pricks. And for fluents I put the fluxion either included in a square or with a square prefixed or with an oblique line upon it. ✝ ✝ And these notations are the best yet extant, but were not known to the Marquess de l'Hospital when he recommended the differential notation, nor are necessary to the Method. ③ By the inverse method of fluxions I found in the year 1677 the Demonstration of Keplers Astronomical Proposition vizt that the Planets move in Ellipses, wchwhich is the Eleventh Propopsition of the Book of Principles; & in the year 1683 at the importunity of Dr Hally I resumed the consideration thereof & added some more Propositions about the motions of the heavenly bodies wchwhich were by him communicated to the R. Society & entred in their Letter-Book the winter following, & upon their request that those things might be published, I wrote the Book of Principles in the years 1684, 1685, 1686, & in writing it, made much use of the method of fluxions direct & inverse, but did not set down the calculations in the Book it self because the book was written by the method of Composition, as all Geometry ought to be. [And ever since I wrote that Book I have been forgetting the Methods by which I wrote it.] If it be asked why I did not publish the Book of Quadratures before the year 16 1704, I answer; For the same reason that I did not publish the Theory of colours before that year. I found that Theory in the beginning of the year 1666, & in the year 1671 was upon a designe of publishing it together with the Method of Series & Fluxions, but the next year for a reason given in my Letter of 24 Octob. 1676 I first suspended & then left off my designe of publishing them till the year 16 1704. And for the same reason I intend fro am very averseI am very averse fro meddling with these matters anony further. ✝ ✝ ① When Mr Leibnitz wrote his Letter of 27 Aug. 1676 he placed the perfection of Analysis in a Method founded on Analytical Tables of Tangents & the Combinatory Art. Nihil est, saith he, quod morim in tota Analysi momenti majoris. And a little after: Ea vero non differt ab Analysi illa suprema SVPREMA ad cujus intima, Cartesius non pervenit. Est enim ad eam constituendam opus Alphabeto cogitationum humanarum. Would he have said this if he had then understood the differential calculus? When he was in London the second time When Mr Leibnitz was in London the second time (which was in October 1676,) he met with Dr Barrows Lectures & saw my Letter of 24 Octob. 1676 & three months before received a copy of my Letter to Mr Collins dated 10 Decem 1672, Mr Iames Bernoulli in the Acta Eruditorum for Ianuary 1691 sa pag 14 said that the Calculus of Mr Leibnitz was founded in Dr that of Dr Barrow & differed not from it except in the differential notation of differentials & some compendium of operation. ,And Mthe Marquess de l'Hospital in thies Preface to the his Book Analysis des infinitement petits published A.C. 1696 represented that the improvement wchwhich Mr Leibnitz made to Dr Barrows Analysis consisted in excluding fractions & surds, For the Marquess but the Marquess but he did not then know that Mr Leibnitz had notice of this improvement from from me by my two Letters above mentioned.. He commended also the differential Notation of Mr Leibnitz but he had seen no other Notation of mine then what he was in the book 406 I have read over the printed Letters wchwhich you have put into my hands, & since Seignior l'Abby Contyi found means to engage me in writing o writing part of them, & Mr Leibnitz has in his Letter to the Madam la Comptess de Kilmansegger pag. 34 & 35 has told his own story at large I give you leave to publish also the following narration at the end of what what I take to be matter of fact. Mr Leibnitz was in London in the beginning of the year 1673 & being went thence to Paris in March in in or about March to Paris where he carrying MeratorsMercators Logarithmotechnia along with him. At Paris he kept a correspondence wthwith Mr Oldenburg about Arithmetical matters till Iune being not yet acquainted with the higher Geometry. It [The Horologium oscillatorium of Mr Huygens cam was published in April 1673 & Mr Leibnitz] but began about that time he began to study it being entred into it by Mr Huygens, & begining wthwith his Horologium oscilllatoriumoscillatorium which was published in April p 1673. And the next year he renewed his correspondence wthwith Mr Oldenburg by two letters dated 15 Iuly & 26 Octob. representing that as the Lord Brounker & Mr Mercator had found an infinite series of rational numbers equal to yethe area of the Hyperbola so he had done the like for the circle & added that by the same method the arch of a circle might be found whose sine was given tho the proportion of the arch to the whole circumference was not known. Thereupon Mr Oldenburg in letter dated 15 Apr. 1675 sent to him from Mr Collins several series invented by me & Gregory one or two four of which were for finding the Arc whose sine or tangent was given & the sine or tangent whose Arc was given. And Mr Leibnitz in his Answer dated 20 May 16765. acknowledged the receipt of this Letter. And the next year in a Letter dated May 12 he desi comemended the two series above mentioned for finding the arc whose sine was given & the sine whose arc was given as very ingenious especially the latter wchwhich had a singular elegance & desired Mr Oldenburg to procure from Mr Collins & the Demonstration thereof, that is the Method of finding it. And in recompence for the same, he promised to send his own meditations upon the same subject, the demonstration whereof he was then polishing for that purpose. But Mr Oldenburg & Mr Collins wrote earnestly to me to send to my him my method & after much sollicitation I wrote my Letter of 13 Iune 1676 Mr Gregory died in the end of the year 1675, & at the request of Mr Leibnitz Mr Collins collected his Letters & Papers & Mr Oldenburg sent the Collection to Paris at the same time with my Letter. In this Collection was a Copy of Mr a Letter of Mr Gregory to Mr Collins dated 15 Feb. 167071 in which the series above mentioned for finding the arc any arc of a circle whose tangent is given. There was also a copy of my Letter to Mr Collins dated 10 Decem. 1672 in wchwhich I represented that the method of tangents of Slusius & Gregory seemed to be the same wthwith mine & that it was but a branch or corollary of my general method wchwhich extended to the asbstruser sorts of Problems & stuck not at surds & wchwhich I had interwoven with my method of infinite Series, meaning in a Tract wchwhich I had written upon this subject the year before vizt A.C. 1671. In the same Collection was also a Letter of Mr Gregory to Mr Collins dated 5 Sept. 1670 in wchwhich Mr Gregory represented that his method of Tangents406 Tangents was deduced from that of Dr Barrow. Mr Leibnitz wrote back to Mr Leibnitz Aug. 27. 1676 & in recompence for my method of Series sent me the Series of Gregory for finding the Arc whose tangent was given, without letting me know that he had received it twice from England. And I looked upon it as invented by Mr Leibnitz till some of the Committee appointed by the R. Society to search their Archives abotut found their original Letters by wchwhich it appeared that the series was Gregories. And by this Letter dated Aug. 27 & one of Mr Tschurnhause dated 1 Sept 1676, it appears that the aforesaid Collection came to their hands. 117)407 I have read over the printed Letters wchwhich you have put into my hands. & since Mr Leibnitz in his Letter to Madam la Comtesse de Kilmansegger pag 34 & 35 transcribes the Scholium upon the 2d Lemma of the second Book of my Principles & then adds: Ainsi, Mr Newton ne me contesta point d'avoir trouvé le chose de mon chef. , & upon this representation has by this representation And by this argument he has constantly pretended that in this Lem- Scholium I granted him the method. But whether he found the method by himself or not was not the Question. The true Question was whether he was the first inventor or not, & this Question he endeavours has constantly endeavoured to avoid; So till Mr Bernoulli gave him the precedence in time chusing rather to put the issue upon the Question whether he invented it by himself or not, as if it must be his if he invented it by himself though he was not the first inventor. He has often allowed that I invented the method by my self: but he never would allow that I was the first inventor. And the designe of that Scholium was to prove that so far I was the first that discovered that I had the Method. And it proves it by this argument, that I wrote of the Method to Mr Leibnitz before he wrote of it to me in the year 1677. I represented in my Letters that I had written a Tract of it in the year 1671 Mr Leibnitz never did pretend that he knew had it before the year 1676. And there are very strong arguments to prove that he had it not when he wrote his Letter of 27 Aug. 1676. For in that Letter he mentions a method by Analytical Tables & the Combinatory Art & saith of it Nihil est quod norim in tota Analysi momenti majoris – – – Ea vero nihil differt ab Analysi illa suprema ad cujus intima quantum judicare possum Cartesius non pervenit. Est enim ad eam constituendam opus Alphabbeeto cogitationum humanarum. This was therefore at that time the to top of his skill in Analysis. And in his a Letter to Mr Oldenburg dated at Amsterdam Novem. 1828 1676 he wrote that by this the Differential this method was that by wchwhich the the yethe Method of Tangents of Slusius was to be perfected. But after he had found the Differential Method he changed his opinion & language & wrote in his Letter of 21 Iune 1677 that it was the ts Differential CalculisCalculus [was the method] by wchwhich the Method of Tangents of Slusius was to be perfected. In his journey therefore from [Now of the Committee of the R. S. have represented that besides my two Letters dated 13 Iune & 24 Octob. 1676 Mr Leibnitz received also in Iuly 1676 the same year in Iuly a copy of my Letter to Mr Collins dated 10 Decem. 1672, it & that in this Letter the Method was sufficiently described to any intelligent person,] London to Hannover, he after he had when he had newly received my L.Letter of 13 Iun 1676 & a copy of my Letter of 10 Decem 1672 & of Gregories of 5 Sept 1670 & seen my Letter of 24 Octob 1676 & what he seems to have been upon the enquiry after the Method by wchwhich the method of Tangents of Gregory & Slusius might be perfected, & might to have found it in the end of theat year or beginning of the year following. But whether he found the method by himself or not is a question wchwhich doth not concern me. He knew by my Letter of 24 Octob. 1676 that I had the method five years before that time or above & it appears by his own confession that he had it not before the year 1676, & by his Letter of 27 August 1676 that he had it not when he wrote that Letter. [408]408 Epistola septimo Iunij 1713 data, quæ in Epistola Dni Leibnitij ad Dnam Kilmansekgg legitur Gallice versa legitur, impressa fuit in Belgio in Novelles Litterairs 28 Decem. 1715, pag. 414, cum hoc titulo: Lettre de M. Iean Bernoulli de Bále du 7 de Iuin 17313. Epistolæ D. Leibnitij ad Dominam Kilmansegg & D. Baronem Bothmar missæ a D. Leibnitio missæ missæ lucem non viderunt nisi post annos quatuor, & nihil amplius continent ad D. I. Bernouli spectians quam quod in Novelles Literairs impressum fuerat. ✝ ✝ Mense Septembri anni 1716 vel Octobri anni 16 1716 D. Des-Maiseaux accepit a D. Leibnitio Exemplar disputationis quam inter ipsum et D. Clark. [ut ex ejus Epistola ad D. Des-Maiseaux 27 Aug. 1716] data intelligo.] Et menseibus Martio vel Aprili & Iulio anni 16181718 Accepit etiam a D. l'Abbé Conti mense Martio vel Aprili Anni 1718, epistolas D. Leibnitij ad Abbatem illum, et ad Dominam Kilmanseg, et D. Baronem Bothmar, scriptas, aliasque nonnullas eo fine ut Epistolarum et scriptorum D. Leibnitij Collectionem aliquam in Hollandia imprimi curaret. ne prorsus Concilium eorum nesciente Hæc omnia me latebant donec schedæ aliquot hujus Collectionis impressæ sunt et ex Hollandiæa missæ sunt et mihi ostensæ. Id quod fiebant Mense Iulio vel Augusto anni 1718. Et in his schedis impressæ extabant Epistolæ illæ duæ ad D: Kilmanseg & D. Bothmar mi missæ. Anno vero sequente accepi a te Epistolam D. I Bernoulli datam 5 Iulij 1719 & post alios novem menses Collectio illa lucem vidit. Amicis m Amicis meis dico me fidem habere D. Bernoulli in prædicta Epistola 5 Iulij 1719 data asserenti se non scripsisse Epistolam 7 Iunij 1713 datam. Et quamvis aliqui eorum mihi nondum credant tamen ijs author non sum ut mihi contradicant. Vide Epistolam D. Leibnitij ad D. Maiseaux 27 Aug. 1716, Et Epistolam D. l'Abbe Conti ad D. Des Maizeaux ad D. l'Abbe Conti 21 Aug. 1718, idque in Has vide in secundo Collectionis Tomo pag 356 & 362. Dnus Des-Maizeaux easdem a D. L'Abbé Conti mense Martio vel Aprili Anni 1718 accepit eo fine ut Epistolarum Dni Leibnitij Collectionem aliquam in Hollandia imprimeiret Et hujus me prorsus insciente, curaret me prorsus consilium eoruum nesciente donec literæ illa duæ schedæ aliqut hujus collectionis ex impressæ sunt & h ex Hollandia missæ sunt mense Iulio ejusdem anni & mihi ostensæ iIn quibus erant his schedis Epistolæ illæ duæ extabant expressæ. Et Et aAnno sequente, accepi a te Epistolam D. I. Bernoulli datam 5 Iulij 1719, & post alios novem menses Collectio illa lucem vidit. Amicis meis dico me fidem habere Epistolæ prædictæ asserenti Dno Bernoulli in prædicta Epistaola 5 Iulij 1719 data asserenti se non scripseisse Epistolam 7 Iun. 1713 datam. Et quanquam aliqui eorum hic mihi nondum credant, tamen ijs author non sum ut meihi contradicant. D. Leibnitius exemplar eorum quæ inter ipsum & Disputationis quam habuit cum D. Clark, misit ad D. Des-Maiseaux ut ex ejus Epistola ad D. Des Maiseaux 27 Aug. 1716 data intelligo ad Dominam Dilmangseg & Dominum Baronem Bothmar. scriptas, aliasque scriptas eidem paulo post ad eundem ex Gallia misit at eo fine ut D. Des-Maiseaux collectionem aliquam Epistolarum D. Leibnitij in Hollandia imprimi curaret. Pictam tui effigiem jam tandem accepi [409a] Has duas Epistolas D. Desmaizeaux accepit ab AD Abbate de Comitibus circa menmensem Maioūum Anni 1717. Et anno sequente circa Mensem Iulium accepit etiam ab eodem Abate Epistolas alias & alia scripta D. Leibnitij eo fine ut Epistolarum et scriptorum ejus collectionem aliquam in Hollandia imprimi curavit. MrLeibnitz in his life time sent the dispute bewteen him & Dr Clark to Mr Desmaiseaux as you may perceive by his Letter to M. desmaizeaux dated 21 Aug. 1716 in order to their being printed in Holland. & D. Abbas de Comiti When I heard that Mr Leibnitz was dead I caused what had passed between him & me to be printed in Hollan at the end of Ralphsons book because copies thereof had been dispersed by Mr Leibnitz. And at that time wWhile this was doing Mr Desmaiseaus consulted with D. Abby Conti about p reprinting the same in Holland together wthwith other Letters of Mr Leibnitz in Holland & for that end he then received from Abbe Conti the Letters to Madam Kilmanseg & B. Bothmar. And in Iune or Iuly following he received from Mr L Abbe Conti then at Paris some other Letters to be added to yethe former wchwhich were then in the Press. Hæc omnia me latebant. The letter of 7 Iune 1713 inserted into the Letter of Mr Leibnitz to Madam Kilmanseg, was printed in Holland in the Novelles Literairs 28 Decem. 1715 pag 414 with this Title: Lettre de M. Iean Bernoulli de Bále du 7 de Iuin 1713. The Letters to Madam Kilmanseg & Baron Bothmar did not come abrodad till above four years after, & contein nothing more concerning the Letter of 7 Iune 1713 then what had been printed in Holland. M. DesMaizeaux received copies of them from M. L'Abbé Conti in order Spring 1718 in order to print a copy collection of some remains of Mr Leibnitz And I knew nothing of the designe of printing them untill they were shewed me in prnt print wchwhich was in August 1718. They ne about a year before I received from you M I. Bernoulli's Letter of 5 Iuly 1719. &And a year & three quarters of a year after that last before they came abroad For my part tho they did not come abroad till may I tell my friends have that I acquiesced in Mr I. Bernoulli's Declaration that he was not the author of the Letter of 7 Iune, 1713, And th tho some of mythem Friends do not yet beleive me, yet I have encouraged none of them to contradict me. 409 Bernulli 1717 to Epistola septimo Iunij 1713 data, quæ in Epistola Dni Leibnitij ad Dnam Kilmanseg Gallice versa legitur, impressa fuit in Belgio in Novelles Literairs 28 Decem. 1715 pag 414, cum hoc Titulo: Lettre de M. Iean Bernoulli de Bâle du 7 de Iuin 1713. Epistolæ D. Leibnitij ad Dnam Kilmanseg & D. Barronem Bothmar missæ lucem non viderunt nisi post annos quatuor, & nihil amplius continent ad D. I. Bernoulli spectans quam quod in Novelles Literairs impressum fuerat. Mense Septembri vel Octobri anni 1716 D. Des-Maizeaux ✝✝ Vide Epistolam D. Leibnitij ad D. Des-Maizeaux 27 Aug. 1716, et Epistolam D. Abbatis de Comitibus ad Des-Maizeaux ad D. Abbatem de Combitus 21 Aug. 1718. Has vide in secundo Collectionis Tomo pag. 356 & 362. accepit a D. Leibnitio Exemplar Disputationis inter ipsum et D. Clark. Et mensibus Aprili et Iulii anni 1716 proximo vere is accepit etiam a D. Abbate Conti de Comitibus, epistolas D. Leibnitij ad Abbatem illum, ad Dnam Kilmanseg, & ad D. Comitam de Bothmar & ad D. Remond scriptas Accepit autem Et anno proximo accepit etiam alias. ab eodem Accepit autem eo fine ut Epistolarum et Scriptorum D. Leibnitij Collectionem aliquam in Hollandia imprimi curaret. Et Hæc omnia me latebant donec schedæ aliquot hujus Collectionis impressæ sunt et ex Hollandia missæ sunt & mihi ostensæ. Id quod fiebat mense Iulio vel Augusto anni 1718. Et in his schedis impressæ extabant Epistolæ illæ duæ ad D: Kilmanseg & D. Bothmar, missæ. Anno vero sequente accepi a te Epistolam D. I. Bernoulli datam 5 Iulij 1719; quo tempore Collectio fere tota impressa fuit: Et post alios novem menses eadem lucem vidit. Amicis meis dico me fidem habere D. Bernoulli, in prædicta Epistolis Iulij data, asserenti, se non scripsisse Epistolam 7 Iunij 1713 datam. Et quamvis aliqui eorum mihi nondum credant; tamen ijs author non sum ut mihi contradicant. Mense Augusto et Septembri annoi 16716 D. Leibnitius dispationemdisputationem inter ipsum et D. Clark misit ad D. Des-Maizeaus The design of publishing M. Des-Maizeaux's collection was set on foot by Mr Leibnis & a little before his death & carried on by Mr Abbé Conti a little after For this end Mr Leibnitz sent Mr Leibnitz a copy of the dispute between himself & Dr Clark as 410 le Mathematicien ou pretendu Mathematicien] l'auteur ou le pretendu auteur] Gratiæ meæ multis nominibus tibi debentur; tum quod mediante R. Patre Reynau accessum & ejus amico applicasti te ad Patrem D. Cancellarium Galliæ & prælongo Memoriali rem hanc casum causam Bibliopolæ Montela ei explicuisti & ejus auctoritate obtinuisti ut ejus auctoritate Bibliopola flecteretur: tum quod negotium, cum Bibliopola ad finem perduxisti & longe plura Libri exemplaria pro me obtinuisti quam expectabam tum etiam quod magnum illum laborem in te suscipere digneris conferendi Librum cum correctionibus misseis, in quo faciendo spero & precor ut proprio utaris judicio & libere corrigas quæcunque tibi in correctionibus missis corrigenda videntur. Nam D. Maivreus omnia judicio tuo submittit. Pactum tuum cum Bibliopola ratum habeo & vice duodecim librarum sterlingarum dabo illi viginti. Et nummus paratus mitte solvetur erit ubicunque volueris. Epistolam Et ubi libe Epistolam inclusam D. Cancellario tradas precor una cum gratijs meis quamplurimus pro favoribus quibus me decoravit. Gratias etiam meas tradas reddas precor Dno Re Patri Reynau ut et ejus amico qui cujus mediatione accessum habuisti negotium delatum est ad D. Cancellarium, & D. Abbati Daguesseau D. Cancellarij fratri quod causaæm meaæm coram D. Cancellario faveret. Ex Epistola tua ad D. Moivreum data intelligo quod D. Bernoullio displicet me ipsum vocasse [the Mathematician or pretended Mathematician] quamvis his id est quamvis his verbis nihil aliud intellexi erim quam quod esset [the Author or pretended Author] quam Ipsi etiam displicet quod me illum vocasse hominem novum & rerum anteactarum parum peritum, ut Leibnitius Keilio objecit id est hominem qui post tempora Oldenburgij floruit et rerum ejus tempore ante mortem ejus int Leibnitium et Anglos gestarum minime peritus ab initio parum penitus cognitor fuisset, esset, quemad Leibnitius contra Keilium debet locutus est. scientiam non habuit nisi ex scriptus antiquis. Sed ipsi maxime displicet quod ipsum de ipso tanquāam equite errabundotico locutus essem: cum tamen non contra Bernoullium, ibi locatus sim sed contra LeibnitiūmLeibnitium ibi locutus sum, & qui Ber qui [ qui utique nomen Iudicis a se constituti diurnavit biennio ac tandem Iudicem hunc in tandem nominando non Iudicem produxit sed ducem exercitus, Et dum Bernoullius ipse sileret nec Iudicem se nec ducem constituens. Bernoullius utique Problema suum proposuerant in Actis Libsiensibus pro mense Maio 16797. p. 211, Leibnitius ad solutionionemsolutionem hujus Problematis primo Nicolaum Fatium provocavit anno 1700 mense Maio anni 1700 in ijsdem Actis p. 204 & jam demum Mathematicos omnes anglos omnes Anglos provocavit in eadem controversia cum Newtono] Is enim feclicitatemfelicitatem suam in disciplis Newton me feliciorem esse, Iactavit enim numerum de seipulorum suorum Epistolam Newtoni meam ad Abbatem de Comitibus vocavit une espece de Cartel, dixit se nolle Pell congredi pugnam in arenam descendere cum amicis in eis Concessu a amicis meis militibus in eis emissarijs, (sit enim vocavit Concessum a Regia Societate constitutum & D. Cot Cotes,), sed cum ipse tandem apparerem, satisfactionem mihi reddere se paratus esset. Et ad hæc ejus vebrba alludens, non culpavi D. Bernoulliaum quod anno 1697 Problema suum edidisset, [sed quod in Leibnitium culpam scripsi qui & Questionem non testibus & monijs et argumentis ex scriptis veteribus desumptisendis coram judice desumendis, sed bello inter cum exercitu discipulorum ejus, terminari voluit & Leibnitium ipsum cum equite errante contuli, & quid magnum illeūum Mathematicusm quem Leibnitius judicem prius constituerat jam velo detracto jam Miles constituerat Miles agmen duceret voluit ut Milesitem, & Le si Leibnitio credendum esset Ma misso Problemate Mathematicos Anglos provocarsset si Leibnitio credendum est. cum tamen ille Bernoullius non mistteriet sed misisse fingeritur a Lebnitio.] sed in Leibnitium sic scripsi. D. Leibnitius Consessum a Regia Societate constitutum accusat: quod Epistolas antiquas non totas imprimeret edidissent sed quo Commercium utique mole multum auctum fuisset, sed cum respondere debuitsset, quæritur llibrum nimit magnum jam prægrandem esse et Responsum requireri moleis non minusoris requirere. Et sic Epistolæ et chartæ antiquæ [ex mente Leibnitij] rejiciendæ sunt et Quæstio in qu rixiam deducenda est circa Philosophiam & Bres alias; & Mathematicus qui in Epistola ad Leibnitium 7 Iun 1713 nomen suum celaverat ut judex æquus haberi posset, jam velum deponere fingitur debet [secundum Leibnitium] in& in hac rixa non amplius judicem sed militem agere & per Leibnitium Mathematitcos Anglos provocare: quasi duellum vel forte prælium inter milites meos emissarios & exercitum discipulorum ejus in quorum numero se felicem prædicat, methodus esset magis idonea veritatem determinandi quam provocatio ad scripta antiqua et authentica; & scienti Mathesis imposterum vice Demonstrationum factis nobilibus equitum erraticorum vice Demonstrationum implerunda deberet sit. Non voco Bernoullium equitem erraticum, sed culpo Leibnitium quod is Bernoullium discipulos suos ut ejus talem equitems ostenderet militem eret idque eo fine ut Quæstio de MethoMethodo Diff.Differentiali sepositis non ex antiquis monumentis testimonijs per duellum ad per bellum, refereatur cum Leibnitio et ejus discipulis referatur determinanda sit determinaretur rixando. circa Quæstiones Metaphysicas Physicas & Mathematicas determinaretur, quod is discipulos suos ut equites jactaret, & sepositis antiquis testimonijs, Quæstionem de methodo differentiali per bellum ruando ea ad bellum determinaretur deducere conaretur contendendo circa quæstiones Metaphysicas & Physicas& & Physicas & Problemata Mathematica Mathematica: quod is sepositisa Qu testimonijs antiquis quæstione de methodo differentiali quod is discipulos suos jactaret tanquam milites ult Equites jactaret, & seposita Quæstione de Methodo differentiali, proponeret pQuæstiones novas Metaphysicas & Physicas & Problemata mathematica de quibus belligerandum esset rixando. In literis ad D. Conti, vocandi Bernoullium Mathematicum vel fictum mathe id est aut Mathematicum Iudicem intellexi Iudicem vel fictum Iudicem quem Leibnitius Mathematicum primarium vocabat, & Bernoullius ipse scripsit se Iudicium illud 13 Iunij 1713 nrdatum non dedisse. Vocavi ipsum hominem novum & rerum anteactarum parum peritum eodem quo Keil leibnitius sic Keilium sic vocavit: id est, ut significarem illum post temporisa Oldenburgij floruisse, & rerum eo vivente actarum nihil scrivisse nisi per epistasepistolas antiquas. Non vocavi ipsum equitem errabundum, sed culpavi Leibnitium q quod Bernoullium tanquam equitem errabundum tractaret. In Epistola sua prima ad Abbatem de Comitibus, scripsit eas qui co Commercio Epist respondere recusavit Questionem de primo inventore deserutit, quæstiones novas non paucas proposuit ad rem nihil spectantes, qual vizt de gravitatgravitate, occultis qualitatibus miraculis vacuo, spatio, perfectione mutidi, de & & Problemate Bernoullij ex actis Eruditorum desumpto & jactabat se discipulis felicem esse. Et ubi postquam Abbas de Comitibus qui Mediatoris officium in se susceperat, responsum a me extortum missesset ad Leibnitium, Leinitius epistolam Abbatis vocabat une espece de cartel de la part de M. Newton. Et addidit se nolle in arenam descendere cum militibus meis emissarijs sed cum ipse apparerem se paratum esse mihi satisfactionem dare. Hanc Ob hoc duellum Leibnitium ridebam quasi comparando disputationes de tot quæstionibus ad rem nihil spectantibus intros discipulos inter nostros discipulos cum duello gladiatoriumo ad veritatem determinandam minime idoneo Editionem Librorum semper dedei Bibliopolæ vel Bibliopolæ vel ei qui editionem curabat Pactum cum Bibliopola quovis quovis nunquam feci, sed beneficium editionis Pactum tuum cum Bibliopola ratum habeo, et e libris quos reservast sed cum pro libris duodecim circiter pulchre tectis dabo illi quos in animo habeo amicis apud vos donare, dabo adhuc insuper Bibliopolæ libros octo Sterlingas reliquos inter amicos tuos distribuos precor et nummus solvetur quandocunque volueris. Reliquos libros reservatos amicis tuis distribuas precor. In literis meis ad D. Conti Abbatem de Comitibus, non vocavi Bernoullium Equitem errantticcumerranticum, sed Leibnitium culpavi qui Bernoullium ut equitem erratntem fjactabat, [idque mittendo Bernoullio Problema Bernoullij ex Actis eruditorum desumptum, ut ab Anglis mathe] D. Chamber ab Abba lain a Leibnitianis primas constitasconstitutas fuerat Moderatur inter me et Leibnitium et me dolis malis circumveniret, sed frustra. Secundus Moderator a Leibnitianis constitutus Moderator fuit Leib Abbas de Comitibus. Ille ad Quæ a D. Des Maizeaux cum Leibnitio commercium & ab eo habuit & ab eo D. Leibnitius Epistolas inter ipsum et D. Clark ad misit ad D. de Maizeaus ut ab eo in lucem ederentur, qu dein Abbas de Comitibus quem Leibnitiani inter Moderatorem int'er Leibnitium et me constituerant, D. Des Mazeaux cum Leibnitio commercium habuit & mihi ignotus erat antequsam paginas primas 88 88 octoginta octo Voluminis secundi suæ Collectionis, & mihi impressuas mihi ostendit. Amicum esse Leibnitij exinde demonstratūrdemonstratur quod 2 Chartas. Leibni plures Leibnitij ad me nil spectantes edidit, & 1 Literas inter Clark Leibnitium et Clarkiu in primo volumine editas accepit a Leibnitio, ut easdem in lucem emitteret. Præfationem qua me defendit moleste habuit, tum meam et sæpe rogavi ut disisteret tum quod non esset Mathematicus tum quod amicus esset Leibnitij, & & meus tamen amicus videri cuperet. D. Des maizeaux mihi ignotus erat antequam p Epistolam inter Leibnitium et me, adusque pagi- octo Schedas quatuor paginarum antequum epistolas inter Leibnitium et me paginis 88 impressas mihi osten D. Des Maiseaux commercium cum Leibnitio olim habuit & litteras inter Leibnitium et Clarckkium in primo collectinoum Tomo impressas accepit a Leibnitio ut easdem in lucem mitteret, & pmihi ignotus erat priusquam epistola partem prima To Literas inter Leibnitium et me impri in prima parte Voluminis Tomi secundi ad usque paginasm 88 octogesimam octavam impressas ad me detulit mihi ostendit, et in secunde parte quæ priore major est edidit Collectionem chartarum Leibnitij quæ ad me nil spectant. Et ex his demonstratur eum amicum fuisse Leibnitij Nam tota Collectio ex Actis Leibnitij non ponitur nobilibus Leibnitij componitur.. Præfationem quo me defendit, moleste habui tum quod non esset mathematicus Controversiam non satis intelligeret sed aliorum argumenta tantum colligeret recitaret, tum quod amicus esset Leibnitij & meus tamen amicus videri cuperetur eo nonum minime idoneus qui me defenderet. D. Leibnitius Problema Bernoullij ad ex Actis Eruditorum desumptum ad determinandam veritatem alterius generis primo ad bis proposuit, primo contra N. Fatium anno 1700 deinde M contra Consessum a Regia Societate constitutum, anno 1715 quasi hi nec judices nec testes esse possent nilsi Problemata Bernoullij possent prius possent solvere, et] anno 1715 quasi testimonia Wallisij Barrovij, Collinij, Wallisij, Fatij alioumque ex scriptis antiquis desumpuptadesumpta re pro nihilo habenda essent et Qu veritas determinanda esset pro pro victorias in solutione problematum, & disputationibus metaphysicis determinanda estset. 411 Pactum tuum cum Bibliopola ratum habeo & ad libras duodecim sterlingas addam alias octo tibi mittendas nummumque mittam quandcunque volueris. D. Moivreus tibi mittet catalogum nominum plus minus quindecim amicorum meorum. Et expensas tegnitinum librorum compingendi exemplaria liborum librorum ijds. donandaum ex libris illis octo illis octo libris sterlingis desumi velim possunt. Exemplaria alia sex in schedis solutio ad me mitti cupio & reliqua exemplaria d pro lubitu tuo distribuasenda precor In schedula Iudicis Mathematici accusor plagiarij idque publice. Leibnitius hunc judicem in schetdulo illo Gallice edita Bernoullium esse dixit. Bernoullius d Injuriæ fuit publica & satisfactio debetuit esse publica. Satisfationem non quærebatm. Bernoullius sponte obtulit. & offerendo licentiam mihi dedit epistolam ejus in lucem emittendi. Quæritur quod Ostendi tantum amico privato una & altere privatim. D. Leibnitius Problema Bernoullij ex Actis Eruditorum desumptum ad determinandam veritatem alterius generis bis proposuit, primo contra N. Fatium Anno 1700 deinde anno 1715 contra Concessum a Regia Societate constitutum, quasi testimonia Barrovij, Collinij, Wallisij, Fatij, aliaque ex scriptis antiquis desumpta pro nihilo habenda essent, et veritas non per testimonia & argumenta sed per victorias in solutione Problematum et in disputationibus metaphysicis determinanda esset, ut fit in bellis ac duellis rixis militum quarum decisio ad pugnas referri solet. ut ea lege ut libros viginti tego vel viginti quinque tegat ornate pro deonis. to you 12Li already promised to yethe Bothmars I shall add 8Li more to bee paid you when you think fit, Mr De Moivre will send you a List of about 15 Names, I desire that yethe Charges of yethe bindings may be taken of yethe may be taken out of yethe 8L, as for yethe rest of yethe Copies in sheets which of 36, . 6 for my self unbound you may dispose of them as you shall thinke fit I desire to have 6 for my self, and that you would dispose of yethe rest as you of yethe Papres as you thincke fit in I understand by your letter to Mr Moiver that Mr Bernoulli iscomplains of me for calling him the a Mathematician (or pretended Mathematician) & homo novus & rerum anteactarum parum peritus & a Knight errant. But I And yet by the first I meant only that he was to call him the author or pretended author of the judgment published in the flying paper & said to be given written by a great mathematician And this was in his favour: For he has since declared that he was not the author. If he was the Iudge then the Iudge was in a conspiracy wthwith Mr L. to be carried on agtagainst Dr Keill & the ComeCommittee of yethe R. S. by concealing the name of the judge, for two years together: And by calling Mr Bernoulli the pretended Iudge I absolved Mr B. from being in such a conspiracy And by the second I meant that he was risen up since the days of Mr Oldenburg & unacquainted wthwith the transactions of those days, as Mr Leibnitz objected against Dr Keill. And by the third I meant only to t correct Mr Leibnitz for treating M Bernoulli as a Knight errant referring the matter in question to a battel duell or battel instead of deciding it by reason & old records, & making Mr Bernoulli at one & the same time an impartial judge between the two parties & the commender of the army of one of them parties a partiman in whose name he sent a challenge to yethe English Mathematicians. Mr Bernoulli's Problem was published in Leipsic Acts for May 1697 p. 211. Mr Leibnitz this in the year 1700 challenged Mr Fatio to solve this Probleme. It reflects not upn upon Mr Leibnitz for appealing from (not upon Mr Bernoulli) for appealing from the evidence wchwhich Mr Fatio offered to a Mathematicall Duell, & thereby treating Mr Bernoulli as a Hero or Don Quixot in Mathematicks. And the same thing Mr Leibnitz repeated by sending the challenging the English Mathematicians to solve the same Probleme I understand by your letter to Mr Moivre that Mr Bernoulli complains of me for calling him Mathematician or pretended mathematician, Homo novus & rerum anteactarum parum peritus, & a Knight errant. And yet by by the first nothing more was meant then to call him the author or pretended author of the judgemtjudgement published in the flying paper & saiascribed to a great mathematician, by the second nothing more then to cal that he was risen up since the days of Mr Oldenberg & unacquainted with the transactions of those days, as Mr Leibnitz had objected against Dr Keill & as for yethe third, it was not directed against Mr Bernoulli for being byut against Mr Leibnitz