Draft letter from Sir Isaac Newton to Pierre des Maizeaux Isaac Newton c. 15,132 words The Newton Project Oxford 2020 Newton Project, University of Oxford

This text is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

 c. 1710-1720, in English and Latin with a little French, c. 15,132 words, 18 ff. 18 ff.

in English and Latin with a little French

 MS Add. 3968, ff. 420r-437v, Cambridge University Library, Cambridge, UK UKCambridgeCambridge University Library Portsmouth Collection MS Add. 3968, ff. 420r-437v c. 1710-1720 England English Latin French Isaac Newton Unknown Cataloguer (2) 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.
420

SrSir

Mr Leibnitz Letter of is like all the rest of his Letters & like the Libel of pub all of them like the Libel of (like the Libel of ) published in Germany without the name of yethe Author &Or Printer or place where it was purinted, vizt full of assertions accusations & his railing reflexions without proving any thing. No proof that he had I To avoid proving that he And as And by this character you may guess at the Author of that Libel.

He is unwilling to acknowledge himself the Aggressor, & complains that the Passage in the Acta Lipsiensia of Ianuary 1715 alleged against him, has been poisoned by a malicious interpretation of a man who would pick a quarrel. In the Preface Introduction to the the Book of Quadratures I affirmed that I found the Method of fluxions gradually in the years 1665 & 1666. And in opposition to this the Ac said Acta in giving an Actcount of the said Introduction we represent that for the better undingersstanding the said Introduction we must have recourse to the Differential Method cujus elementa ab Inventore Dn. Gothofredo Gulielmo Leibnitio in his Actis sunt tradita varijque usus tum ab ipso, tum a Dnom. fratribus Bernoullijs tum & Dno Marchione Hospitalio (cujus nuper sunt ostensi. Pro diffentijs igitur Leibnitianis Dn. Newtonus adhibet semperque adhibuit fluxiones quæ sint quamproxime ut fluentium augmenta æqualibus temporis particulis quam minimis genita; ijsque tum in suis Principijs Naturæ Mathematicis, tum in alijs postea editis eleganter est usus, quemadmodum et Honoratus Fabrius in sua Synopsi Geometrica, motuum progressus Cavallerianæ Methodo substituit. And then they go on to explain the method & character of Mr Leibnitz instead of that of Mr Newton. & But they that read & compare the Introduction to Mr Newton's book of Quadratures, the Account given thereof in wherein he affirms that he found the method gradually in the years 1665 & 1666, the Answer of Dr Keill, 24 May 1711 the whole Account given thereof in the Acta Eruditorum, the Answers of Dr Keill dated & the Answer of Mr Leibnitz to the Doctor dated 29 Decem. 16 1711, will find the contrary. The matter is sufficiently stated in the Acta E Commercium Epistolicum, & I need not repeat it. A In the Preface to the book of Quadratures I wrote that I had found the method of fluxions gradually in the years 16765 & 1666 Mr. The Acta gave a contrary account of the method, & M Dr Keill & wrote Mr justified justified this account & thereby made it his own.

& gives a contrary Interpretation of his own, saying that the words adhibet semperque adhibuit imply that I used fluxions not only after I had seen his differences, but even before; as if pro differentijs L . . . anis D. N . . . us adhibet semper ahdhibuit fluxiones quemadmodum I H. Fabrius motuum progressus Cavellerianæ Methodo substituit could signify that Mr Newton I used fluxions fe before Mr Leibnitz used Differences or I knew that he used them. In the Introduction to the Book of Quadratures I affirmed – – – instead of that of Mr Newton And Mr Leibnitz in his Letter of 29 Decem: 1711, has justified all this & made it his own. A If he that interpreted the word adhibuit by the word substituit has poisoned this Vassage in the Acta by a malitious interpretation the A crime is his that wrote the Passage.

And as for his suggesting that I might be willing to find a pretence to ascribe to my self the invention of the new calculus contrary to421421 to my knowledge owned in my Principles p. 253 in the first Edition: its well known here that this controversy was begun between him & Dr Keill before I knew what was had been published in the Acta Leipsica. And

Mr Dr Barrows method of tangents was published in the year 1670. Mr Gregory the same year in his Letter above mentioned gave notice that from Dr Barrows method of Tangents compared wthwith his own he had deduced a general method of tangents withou drawing tangents wthwithout calculation. Mr Slusius also in yethe year 1672 gave notice to Mr Oldenburg that he had also such an easy method of Tangents. Mr Collins the same year thereupon gave me notice of these methods of Tangents & desired that I would send me my method. Thereupon I wrote my Letter of 10 Decem 1672 wherein I I described my method & represented that I took the my method it to be the same wthwith that of Slusius & Gregory & added that it was a branch or rather a corollary of a general method wchwhich without any troublesome calculation extended tnot only to tangents of all sorts of Curves but also to other abstruser sorts of Problemes concerning the Curvatures, Areas, Lengths, centers of gravity ,of Curves &c Nor And was not (like the method of Hudde maxima & minima of Hudde) was restrained to equations free from surdes; & that I had interwoven this method with that of infinite series, meaning in my the Tract wchwhich I had written wrote the year before, as Mr Collins mentioned in his Letters of to Borellus & Vernon in December 1675 And Mr Leibnitz a year after he had seen these Letters received copies of these Letters & eight months after he had seen my Letter of 24 Octob 1676 in other Letters in the hands of Mr Collins (amongst wchwhich I reccone my Analysis per æquationes numero terminorum infinitas [& my letter of 24 Octob. 1676 the newly arrived at London but not yet copied) sent back his method of differences whi Dr Barrows method of tangents with the characteristick changed & explained how this method gave the readily gave the method of tangents of Gregory & Slusius, & might be improved tso as to proceed without taking away sur not to stop at fractions & surds, & faciliated quadratures, & from these characters he concluded that this method was like that wchwhich I had described in my Letters. And this it is the Differential method of Sl which was mentioned b in my book of Principles pag pag. 253, 254, & is now claimed by Mr Leibnitz as the first inventor thereof, notwithstanding that he had notice of the method all this by my Letters of of earlier date compared with that of Gregory & that I had written a treatise of this method & of the method of series together in the year 1671. He now pretends to have invented the method in the year 1676; & so he might in his journey from England through Holland into Germany: but

A few months after the Commercium Epistolicum came abroad Mr Bernoulli Leibnitz p inserted a Letter of a nameless Ma dated into a defamatory Letter pretended to be written dated 29 Iuly 1713 another written or pretended to be written by After the Commercium came abroad Mr Leibnitz appelaled from the R. Society to the judgment of a nameless Mathematician or pretended Mathematician of the first rank & inserted his judgment & into a defa & & inserted his judgment into dated 7 Iune 1713 into into a defamatory Letter dated 29 Iuly 16 1713 inserted the judgment of this mathematician dated 7 Iuly Iune 1713, & pred the L Letter with this judgment was published in Germany in the form ofa Libel without the name of the author or Mathematician or Printer or City where it was printed, & secretly dispersed inall over Europe in a clandestine manner by him & his correspondents. It was confuted by Dr Keill & & last winter I The Mathematician cited This judgment was given in a Letter to Mr Leibnitz dated 7 Iune 16713 & in this Letter Iohn Bernoulli was cited by the title of a certain eminent Mathematician, [but last winter it was re the judgment of the Mathematician was reprinted in] as distinct from the author of the Letter, M Dr Keill confuted & ythe last winter theis Letter of the Mathematician was reprinted in Holland without the citation & Iohn Bernoulli himself ascribed to Iohn Bernoulli himself.

I called The eminen Mathematician to whom Mr Leibnitz appealed from the R Society I called a MathemationMathematicion or pretended Mathematician not mean to disparage the skill of Mr Bernoulli but because the Mathematician in his Letter of 7 Iune 1673 cited Mr Bernoulli as a person distinct different from himself & now Mr Leibnitz tells us t leaves out has lately caused the Letter to be reprinted without the citation & tells us that the Mathematician was Iohn Bernoulli himself, & who whether the Mathematician or Mr Leibnitz is to be beleived I do not yet know.

Mr Leibnitz saith that the Letter wchwhich I call defamatory is nobeing no sharper then that Cor wchwhich has been published against him, I have no reason to complain. But the sharpness of the Commercium lies in the facts Letter lies in accusations & reflexions without any proofe wchwhich are calumny, & which is an unlawful way of writing, the sharpness of the Commercium lies in facts wchwhich are lawfull to be produced., The Letter such as is the fact that Mr Leibnitz after he Mr Leibnitz had received the series of Gregory twice from London, he sent it to me & published it in Germany as his own without mentioning that he had had received it from London: before. And further, the Letter was published in a clandestine backbiting manner without the name of the author or mathematician or printer or City where it was printed. And it was dispersed two years & an half quarter before the name we were told that the Mathematician is was Iohn Bernoulli.

He saith that when he was the first time in London he was not acquainted With Mr Collins as some have maliciously feigned. But who has feigned this or what need there was to feign it I do not know. Dr Pell gave him notice of Mercators series for the Hyperbola & he might have notice of mine within for the circle without b either in London or at Paris without being acquainted wthwith Mr Collins.

He saith that he found the series of Gregor arithmetical Quadrature of the Circle towards the end of yethe year 1673 & the met differential calculus towards the general method y arbitrary series & also the in the year 1676 & soon after the differential calculus in the same year & that in his Letter of 27 Aug. 1676 by the words certa Analysi he meant the differential Analysis. And am not I, & am not I as good an evidence that I found the method of fluxions in the year 1665 & improved it in the year 1666. And if I should add that before the end of that the year 1666 I wrote a small tract on this subject wchwhich was the grownd of that larger tract wchwhich I wrote in the year 1671, in& that in this smaller tract, tho I generally put letters for fluxions as Dr Barrow in his method of tangents put Letters for differe differences, yet in giving a general Rule for solv finding the curvature of curves I put the L letter x with one prick for first fluxions & with two pricks for second fluxions: I am not I as good an evidence for this as Mr Leibnitz is for what he affirms; especially since both thise Tracts isare still in being & ready to be produced upon occasion.

In the year 1684 Mr Leibnitz published only the elements of the Calculus differentialis & expl applied itthem to questions about tangents & maxima & minima but proceeded not to yethe higher Problemes. The Principia mathematica gave the first instances made publick of applying it to the higher Problemes & I understood Mr Leibnitz in this sense in what I said concerning the Acta Eruditorum for May 1700. But Mr Leibnitz observes that what was there said by him relates only to a particular artifice of de maximis et minimis with wchwhich Mr Leib he recconed only he there allowed that I was acquainted wthwith when I gave the figure of my vessel in my Principles. But this depending upon the differential method as an improvement thereof & being the artifice by wchwhich they solved the Problemes wchwhich they value themselves most upon (that of the linea celerrimi descensus & the Catenariæa, & vielaria) & wchwhich Mr Leibnitz there calls it a method of yethe highest moment & largely di of greatest extent, & both of them & which dependsing upon the Method in dispute I content my self with his acknowledgment that I was the first that proved by a specimen made publick that I had that artifice.

Dr Barrow had no Analysis in th printed his differential method of Tangents in 1670 Mr Gregory in his letter of 5 Sept 1670 gave notice to Mr Collins that from this method deduced a general method of TangtsTangents without calculation & by his Letter of 5 Sep. 1670 gave notice thereof to Mr Collins. Slusius in November 1672 gave notice of yethe like method to Mr Oldenburge. I in my Letter of 10 Decem 1672 sent the like method to Mr Collins & added that I tooke the Methods of Slusius & Gregory to be yethe same with mine, & that it was nbut a branch or rather a Corollary of a general method wchwhich without any troublesom calculation extended to not only to Tangents but also to other abstruser sorts of Problems concerning the crookednesses, areas lengths centers of gravity of Curves &c & thatis without stopping at curves surds: & added that I had interwoven theis method with that of infinite series. And after all this information meaning in my Tract wchwhich was written in 1671 Copies of these Letters were sent to Mr Leibnitz by Mr D. in the Collection of Gregories Lette Letters & Papers in Iune 1676 & what was Mr Leibnitz in Iune his Letter of 21 1677 sent nothing more back then what Barrows Method of Tangents extend to the method of Slusius & to Quadratures & equations involving surds: all wchwhich he had notice of by these letters. But this is not the case between me & Dr Dr Barrow. He saw my Analysis in the year 1669 & found no fault with it. And when he was publishing his Lectures I told him of my method of drawing Tangents without any computation, as I mention in my Letter of 10 Decem 1672. but he did not extend his method so far.

He tells us that in his Letter of 27 Aug. 1676 where he speaks of Problemes wchwhich depend not on equations nor quadratures he meant only equations of the vulgar Analysis. But the words rel he has for the words plainly relate to solving of Problems generally by infinite series tho the reducing of Problems to in generally not to vulgar equations but to infinite series & doing it in the difficulter cases without by other methods then yethe extracting the roots of vulgar equations. In the next words he said that he solved the Probleme of De Beaune certa Analysi & this Analysis & this Analysis he saith was the Differential. But the Probleme may be solved there is no need of tsuch an the Analysis in this case doth not require a differential equation. Any one may presently see that if the Ordinat Abscissa of this Curve increase in Geome Arithmetical proportion the Abs Ordinate shall increase or decrease in Geometrical, & therefore the Ordinate hath the same relation to the Abscissa as the Logarithm to its number its its Logarithm to its nNumber. & this is all the Analysis requisite.

In my Answer dated 24 Octob. 1676 I said Inversa de tangentibus Problemata sunt in potestate aliaque illis difficiliora. And a little after Inversum hoc Problema de Tangentibus quando Tangens inter punctum contactus et axem (it et [seu Abscissam] figuræ est datæ longitudinis non indiget his methodis. Est tamen Curva illa Mechanica cujus determinatio pendet ab Area Hyperbolæ. Ejusdem generis esto etiam Problema quando pars Axis [seu Abscissæ] inter Tangentem et Ordinatim applicatam datur Longitudine. Et quando Sed hos casus vix numeraverim inter ludos Naturæ. Nam quando inter in triangulo rectangulo quod ab illa Axis parte et Tangente ac Ordinatim Applicata constituitur, relatio duorum quorumlibet laterum per æquationem quamlibet definitur, Problema solvi potest absque mea methodo Generali: Sed ubi pars axis ad punctum aliquod positione datum terminata ingreditur vinculum; res aliter se habere solet; id est, Problema stur absque indigere solet mea methodo generali.

Pag. 191. lin 21. After the words year 1676 add Mr Iames Gregory in a Letter to Mr Collins dated 5 Sept 1670 & printed in in the Commercium Epistolicum pag 22 gave wrote thus [Barrovij Lectiones summa cum voluptate & attentione legi perlegi; atque omnes qui unquam hisce de rebus scripserunt infinito intervallo superasse comperio.] Ex ejusdem [Barrovij] methodis Tangentes ducendi cum quibusdam e proprijs collatis, inveni methodum generalem et Geometricam ducendi Tangentes ad omnes Curvas sine calculo & quæ complectitur non tantum Barrovij Methodos particulares, sed et ipsius generalem Methodum Analyticam, quam habes sub finem Lectionis decimæ [A copy of this Letter was sent to Mr Leibnitz at Paris 26 Iune 1676 in the aforesaid Collection of Letters Gregoris Letters 26 Iune 1676.] And two years after upon notice onthat Slusius & Gregory had Methods of drawing Tangents without calculation, Mr Newton wrote back to Mr Collins 10 Decem 1672 in these words Ex animo gaudeo D. Barrovij amici nostri reverendi Lectiones Mathematicas exteris adeo placuisse; neque parum me juvat intelligere eos [Slusium et Gregorium] in eandem mecum incidisse ducendi. Tangentes Methodum. Qualem eam esse conjiciam ex hoc exemplo percipies. And at the end of the example he added these words Hoc est unum particulare – – – – – – – ad series infinitas &c

Pag 192. After the words lin. 7 read. Copies of Mr Gregories Letter of 5 Sept 1670 & Mr Newton's Letter of 10 Decem 1672 were sent to Mr Leibnitz by Mr Oldenburg amongst the papers &c

Pag 192. lin. 10. – of Iune 13 1676, & amongst the same Letters was Mr Gregories Letter of 5 Decem 1670. Ib. l 19. . . . other method, & Mr Leibnitz Gegory having described how from Dr Barrows method of Tangents he had deduced th gave the Method Method being deduced from Dr Barrows method being the same with that Ib. l. 19 & that the method of Tangents of Slusius & Gregory was but a branch p. 196. lin ult. – – – general method, & Mr Gregory that he had deduced it from yethe Method of Dr Barrow. And thus far Mr Leibnitz described nothing more then what he might learn from Dr Barrow & Mr Gregory

But whereas Mr Newton had said

422

Dr Ke He fell foul upon Dr Keill & appealed to the prest the R. S. t R S cetet against him against him & chanlenged me to declare against him that is before I knew what had been published in the Acta Leipsica, & therefore he is the aggressor & ought to prove his accusation upon pain of being deemed guilty of calumny.

SrSir

Mr Leibnitz is unwilling to acknowledge himself the Aggressor & complains that the Passage [o d in the Acta Eruditorum of Ianuary 1705 alled [pro diffentijsrentijs igitur Leibnitianis, D. N . . . nus adhibet semperque adhibuit fluxiones] has for this end been poisoned by a malicious interpretation of a man who would pick a quarrel. In opposition to what I said in the Int themy Introduction to the book of Quadratures I affirmed the author of that passage said that represented that for better undestandingunderstanding that Introduction [In opposition to yethe antiquity of the method of fluxions repre maintained in the Introduction to my Book of Quadratures the author of the Passage represented that for better understanding the said Introduction in giving an account of that Introduction mentioned that represented that for better understanding it we must have recourse to the Differential Method, cujus elementa in his Actis sunt tradita ab Inventore Dn. Gothofredo Gulielmo Leibnitio in his Actis sunt tradita varijque usus tum ab ipso, tum a Dom. fratribus Bernoullijs, tum et Dn. Marchione Hospitalione sunt ostensai. Pro differentijs igitur IGITVR Leibnitianis Dn. Newtonus adhibet semperque adhibuit fluxiones quæ sint quamproximè ut fluentiam augmenta æqualibus temporibsus particulis quàm minimis genita, ijsque tum in suis Principijs Naturæ Mathematicis, tum in alijs postea editis eleganter est usus QVEMADMODVM et Honoratus Fabrius in sua Synopsi Geometrica motuum progressus Cavallerianæ methodo substituit. And then this Author goes On to explain the method & character of M]

SrSir

1 Mr Leibnitz is unwilling to acknowledge himself the Aggressor & complains that the Passage in the Acta Eruditorum of Ianuary 1705 [pro differentijs Leibnitianis L . . . tianis, D. N . . . nus adhibet semperque adhibuit] has for this end been posonedpoisoned by the Author of the Remarques upon the Commercium, who says (pag. 108) sensus verborum est quod N . . . nus Fluxiones differentijs L . . . tianis substituit. And This he calls a malitious interpretation of a man who would pick a quarrel, & pretends that the Author of the Passage words adhibet semperque adhibuit might relate as well to the my the time before I had the method seen Mr Leibnitz differences (he should have said, before Mr Leibnitz the differential method was known to Mr Leibnits as to that afterwards. But if I understand Where & f But the wor Author of the Paragraph Passage first tells saith tells his Reader that Mr N for better understanding the Prin Introduction to the Book of Quadratures we must have recourse to yethe Differential method, cujus elementa ab INVENTORE Dn. G. G. L . . . tio in his Actis sunt tradita, varijque usus tu And then adds: Pro Differentijs igitur L . . . tianis IGITVR L . . . tianis D. N . . . tonus adhibet semperque adhibuit fluxiones — QVEMADMODVM et Honoratus Fabrius in sua Syn in sua Synopsi Geometrica motuum progressus Cavallerianæ methodo S substicit The Author of the Passage by the word I IGITVR makes the words adhibet semperque dadhibuit a consequence of what went before & interprets them by the word QVEMADMODVM interprets them he makes them equipollent to substituit: Mr Leibnitz t take calls this interpretation a malitious one & interprets them in another sense wchwhich makes them no consequence of what went before now & spoils the sense of quemadmodum Fabrius substituit.: Certainly The plain meaning of the words are that M. N. uses at preent & always from the beginning of his having this method did did always use fluxions for the (or instead of) the Leibnitian Differences even as Faber substituted motions for the method of Cavellerius. And who ever wrote as this passage Mr Leibnitz by his Letter of 29 Decem 1711 has justified it & the accusation in this passage & made thise accusation it his own. He chalenged me also both in this Letter & in that of 4 Martch 16101 to give my opinion in this matter, & now I have at length given my opinion, he compares this takes my Letter this oi for an answer to his challenge saying that he was unwilling to enter the lists before I appeard my self with my forelorn hope before I appeared my self, & therefore hise is the aggressor.

The Libel dated 3. Mr Leibnitz insinuates that my probleme complaint of his accusing me of plagiary might be to gain attribute to my self the invention of the new calculus contrary to my knowledge avowed to the contrary in my book of Principles pag 253 of yethe first edition. And a little after he saisth that in the first Edition of my Principles p. 253, 254 I allowed him the invention of the Calculus of differences independantly of my own. But he here accuses me falsly. For In I there allowed that in his letter of in his Letter of 21 Iune 1677 he sent My words were these. In literis quæ mihi cum Geometra peritissimo G. G. Leibnitio annis abhinc decem intercedebant [i.e. anno 1676] intercedebant, cum significarem me compotem esse methodi determinandi Maximas & Minimas, ducendi Tangentes & similia peragendi quæ in terminis surdis æque ac in rationalibus procederet, & literis transpositis hanc sententiam involventalibus [Data æquatione quotcunque fluentes quantitates involvente, fluxiones invenire & vice versa] eandem celarem: rescripsit Vir clarissimus se quoque in ejusmodi methodum incidisse, & methodum suam communicavit a mea vix abludentem præterquam in verborum & notarum formulis. This I was reprinted in the second edition of my Principles & is still allowed by me. But I never allowed that Mr Leibnitz was the first inventor or found this method without receiving some light from mey Letters me. Mr Craige is a witness that in those days I looked upon the method as mine. He received also copies of myr Gregories Letter of 5 Sept in wchwhich Mr Gregory wrote to Mr Collins that from Dr Barrows methods of Tangents & his own he had found a general method of drawing Tangents to all Curves without any Calculus In Iunely 1676 MrheL.Mr L. received copies of my Letters dated 10 Decem. 1672 & 13 Iune 1676. In October following he came to London & saw some others of my Letters in the hands of Mr Collins. & particularly my Letter of 24 Octob. 1676 & had an opportunity of seeing my Analysis In March following he received a copy of my Letter of 24 Octob. 1676 & after all this in a Letter dated 21 Iune 1677 he sent me back his method Mr Mr Craig remembers that representing that it was like the method wchwhich I had given notice of. And what he sent back was nothing more then what he had sufficient notice of from my Letters & Mr Gregories together. In the year 16784 when Mr Leibnitz first printed the elements of his method, Mr Craige brought to m who was then at Cambridg brought me the Acta Eruditorum & desired me to explain thoseat Elements if I could. me method. to him I Whereupon I explained then it to him &] I told him that it the method would appere to be mine was mine, a in a new dress, [I could recover it if I would print the Letter wchwhich had passed between me & Mr Leibnitz seven or eight years before were printed. Mr Craig is still alive & remembers this, & therefore when I wrote the Scholium above mentioned, I did tho I forbore to accuse Mr Leibnitz yet I did not intend to say that he was the first Inventor or found the method without receiving light from me. The Royal Society & their Committee have acted by good authorriity & in a lregular manner & Mr Leibnitz has no authority to call them to account. If they would have condemned Dr at his requestdemand they would have condemned Dr Keill without ex- examining into the matter they would have been honest Gentlemen but when he declined refused to justify his accusation & put them upon a necessity of publishing appointing a Committee to exemin the ancient letters & papers about this matter & report their opinion thereupon that the Society might know what to do in the matter, ol If what the Committee published was sharp the sharpness was in was in the facts conteined in the ancient Letters & Papers wchwhich they published & if any thing was misrepre misinterpreted Mr Leibnitz was at liberty to set the interpretation right. But for him & his correspondent to publish a Libel against the Society defamatory Letter against the Committee of the Society, e void of facts & full of sharp reflexions without the n scurrilous reflexions, without the name of the place author or printer or place where it was printed, is an illegal & scandalous & infamous way of proceeding. & by the statu He saith that it was enough that the name of the author of the Letter inserted into the an excellent Mathematician whom he had desired to examin declare his opinion in this matter upon the Commercium & whose letter was inserted into the other Letter was sufficiently known. Iohn Bernoulli was cited by the great Mathematitian as the paper was first printed in Latin, three years ago & dispersed into all Europe, & half a year ago the in a French version printed in Holland423 the citation was omitted & the great Mathematician was said to be Iohn Bernoulli himself. Thiese doub dark tricking double-facted maskerading practises are not in use amongst honest men. He refuses positively to 4 The Royal Society & their Committee have acted by good authority & & in a regular manner & Mr Leibnitz has no authority to call them to account. If at his command they would have condemned Dr Keill without examining into the matter they would have been honest Gentlemen. But when he in his Letter of 29 Decem 1711 refused to justify his accusation & put them upon a necessity of appointing a Committee to examin old Letters & Papers relating to this matter & report their opinion thereupon that the Society might know what was fit to be done for them to do therein; & the Society ordered the letters & papers with the Report to be published: then he appealesd from them to a to another judge mathematician of his own chusing & by consequence a partiman party-man &tho he calls him & this Mathematician in & desiresd him to give his opinion upon the Commercium. And this Mathematician in his Answer dated 7 Iuly 1713 citesd Iohn Bernoulli as a man different from himself in these words [quemadmodum ab eminente quodam Mathematico dudum naotatum est)] And this Letter wsa inserted into a defamatory Letter dated 29 Iuly 1673 & published in Ger in Germany without the name of the Author or Mathematician or of the author of the defamatory Letter or Libeller or Printer or City where it was printed. Dr Keil ans t This was This & both the impression dispersed by Mr Leibnitz & his Agents & reprinted in French isn the Iournal Literair for Iuly & Au of November & December 1713 & ansrwedred by Dr Keill in the Iournal of Iuly & August 1714. And the Letter of the Mathematitian was reprinted in Latin in the Novelles Litterairs for 28 Decem 1675 [as written by Iohn Bernoulli without [& the citation of Iohn omitted above mentioned omitted whereby the author is distinguished from Iohn Bernoulli] without mentioning that it had been answered by Keill, & to give it authority, it is there saitd to have been written by Iohn Bernoulli & the citation above mentioned whereby the author distinguishes him self from Iohn Bernoulli is omitted. And therefore in my Letter of the 26 Feb. 1677 last And therefore being suncertain whether this Mathematician be Iohn Bernoulli or some other man, I called him (in my Letter of I 26 Feb: 1616 last) a Mathematician or pretended Mathematician. I d intending by those words not to detract from the skill of Mr Bernoulli but (as Mr Leibnitz complains) tobut to reflect touch upon the dark, tricking, double-faced, maskerading management of the Libel. 5 Mr Leibnitz represents that this paper being no sharper then the Commercium Epistolicum I have no reason to complain. But the difference is that this paper is has all the characters of a defamdefamatory Libel being full of reflecting affirmations without any proof offered & printed & dispersed in a clandestin manner without naming the author printer or City where it was printed. Mr Leibnitz saith that the Mathematician whose Letter was inserted into it was nkown wchwhich is sufficient but it was not known sooner till above two years after the Libel was dispersed And if it had been known sooner, yet the Mathematician is not answerable for the Libeller unless so far as he had a hand in it: whereas the Comerc. Epist. was published fairly at London by Order of the R. S. & has nothing of sharpness in it but what is grownded upon the in the facts comprehendeded in or proved by the ancient Letters & papers. or grounded upon them. Which Which And this way of writing is allowed by all mankingd. 120) 6. He complains of the Committee as partial, & set sup Iohn Bernoulli against them & to give the preference to this great Mathematicians send them challenges them to solve one of his Problemes. But I want the But what solving of Problemes has to do in this matter I do not understand. The Committee without much any skill in mathematicks might search out the old Letters & papers & shew them to witnesses who knew the hands, [& tell the Society that they met with nothing whereby it appeared that they Mr Leibnitz had the method before the year 1677, & that by my Analysis communicated by Dr Barrow to Mr Collins in the year 1669, & by my Letters of 10 Decem 1672 & by my L 13 Iune 1676 & 24 Octob. 1676 they were convinced that I had the method when I wrote those Letters & Papers. And all the Mathematical skill of Mr Bernoulli will not make good his pretenses to yethe contrary] & I want them they were wanted for nothing more. then their testimony is wanted in this matter. Mr Bernoulli with all his Mathematicks can be no eviden has brought no evidence to the contrary And all Bernoullis skill in Mathematicks avails nothing against this evidence. Without much skill in Mathematicks they might report that they met with nothing in all those Letters & Papers whereby it appeared that Mr Leibnitz had the method before the year 1677, & 7 But Mr Leibnitz represents that the Committe have omitted things wchwhich made against me & printed every thing wchwhich could be turned against him by strained glosses, & to make this appear he produced an instance in his last Letter, but finding confesses now that he erred in that instance affirming that the passage was omitted in the Commerc. he& now he produces another instance. He saith that I ow in one of my Letters to Mr Collins I owned that I could not find the second segments of Spheroids, & ytthat the Committee have omitted this Let If the Committee had omitted such a Letter I think they would have done right, it being nothing to the purpose. But there was no such Letter. Mr Collins in a Letter to Mr Gregory dated 24 Decem 1670 & printed in the Commercium pag. 24, wrote that my method extended to yethe second segments of round solids, & th he could I heare that the Letter in wchwhich I signified this to Mr Collins is still extant & conteins the dimension of the second segment of the Sphæroid., so that it makes as much for me as Mr Leibnitz pretends that it makes against me [Thus you see that the Committee (contrary to what Mr Leibnitz represents) have omitted a Letter wchwhich makes for me, & he ought to beg their pardon for accusing them falsly] & yet I do not complain of the Committee for omitting it. But I complain of Mr Leibnitz for accusing the Committee of partiality without being able to prove his accusation wh without knowing wherein they were partial. For this rashness shews the spirit of the Gentleman.
109424 SrSir Mr Leibnitz is unwilling to acknowledge himself the Aggressor & complains that the Passage in the Acta Eruditorum of Ianuary 1705 [pro differentijs L . . . tianis, D. N . . . nus adhibet semperque adhibuit] has for this end been poisoned by the Author of the Remarques upon the Commercium, who says (pag. 108) Sensus verborum est quod N . . . nus fluxiones differentijs L . . . tianis substituit. This he calls a malicious interpretation of a man who would pick a quarrel, & pretends that the words [adhibet semperque adhibuit] may relate as well to the time before I had seen Mr Leibnitzes differences (he should have said, before he invented them) as to that afterwards. But the Author of the Passage first tells his Reader that for better understanding the Indtroduction to the Book of Quadratures we must have recourse to the Book of Quadratures Differential Method, cujus Elementa ab Inventore INVENTORE Dn. G. G. L . . . tio in his Actis sunt tradita. And then adds: Pro Differentijs IGITVR Leibnitianis D. N . . . tonus adhibet semperque adhibuit fluxiones — QVEMADMODVM et Honoratus Fabrius in sua Synopsi Geometrica motuum progressus Cavallerianæ methodo substituit. The word I first sentence postpones the method of fluxions to that of differences & by the word INVENTORE gives the right of invention to Mr Leibnitz. The word IGITVR makes the second sentence a consequence of the first wchwhich it cannot be in the sense wchwhich Mr Leibnitz puts upon the words semperque adhibuit. And the word QVEMADMODVM interprets makes makes the words adhibet semperque adhibuit by equipollent to the word substituit, which interpretation Mr Leibnitz calls a malicious one. The plain meaning of the Passage is that Mr Leibnits invented the differential method & this method must be understood before Mr Newtons method can be understood well. Mr Newton therefore uses at present & always did use from thae beginning of hais having thie method did always use fluxions for (or instead of) differences the Leibnitian Differences even as Faber substituted motions for the method of Cavallerius. Mr In my Letter of 24 Octob 1676 I represented that five years before that time, that is in the year 1671, I wrote a Book of this Method & the method of Series together, but for the sake of quiet desisted from my publishing it designe of publishing it. The Book is still in being & conteins a very plain description of those two methods. The first Proposition of the book is, Relatione quantitatum fluentium inter se data fluxionum relationem determinare. In the year 16845 Mr Iohn Craig desired me to explain to him the elements of the differential Calculus then newly published in the Acta Eruditorum. I did so & told him that the method was mine as would appear if the Letters wchwhich past between me & Mr Leibnitz seven or eight years before should be published, & Mr Craig is still alive & remembers this. Dr Wallis in the Preface to the two first Volumes of his works printed in Spring, 1695, wrote that in those Letters (copies of wchwhich had been communicated to him by Mr Oldenburgh I had explained to Mr Leibnitz that Method found by me ten years before or above, that is, in the year 1666 or before. In the Account of these two Volumes published in the Acta Eruditorum the next year, this passage was taken notice of & not contradicted. Dr Wallis in a Letter dated 1 Decem. 1696 gave notice of this passage to Mr Leibnitz Leibnitz & in the Letters wchwhich followed between them it was not contradicted. Mr Fatio in the year 1699 published that I was the first oldest inventor by many years & confirmed his opinion by what he had seen in my manuscripts, & Mr Leibnitz in his answer did not contradict him And all this was done without any encouragement from me. In the year 167 1704 I published (in the Introduction to my book of Quadratures) that I found the method of fluxions by degrees in the year 1665 & 1666. For this was not yet disputed. But Dr Wallis, (the last of the old men who had corresponded with Mr Oldenburg & Mr Collins in these matters, except Mr Leibnitz & my self being now dead, somebody in the Acta Eruditorum for Ianuary 16 1705, in giving an account of the said said Introduction told his Reader that for the better understanding this Introduction we must have recourse to the Differential method cujus elementa ab INVENTORE Dn. G. G. L . . . tio in his Actis sunt tradita. And then added: Pro Differentijs IGITVR Leibnitianis Dn. Newtonus adhibet semperque adhibuit fluxiones — QVEMADMODVM et Honoratus Fabrius in sua Synopsi Geometrica motuum progressus Cavallerianæ methodo substituit. And hereby the world was told that I did not invent the method so early as has been beleived in England nor write a book upon it in the year 1671 nor mention it in my Letters of 13 Iune, & 24 Octob 1676 & 10 Decem 1672, nor was the first inventor, but do uses & have always used fluxions for the Leibnitian differences even as Faber substituted motions for the method of Cavallerius. With this accusation the dispute began, & Mr Leibnitz hath made this accusation his own by saying in his Letter 29 Decem 16711, Frustra ad exemplum Actorum Lipsiensium [Keilius] provocat ut sua dicta excuset; in illis enim circa hanc rem quickquam detractum non reperio sed potius passim suum cuique tributum. In the same Letter he refused to contend with Dr Keill because the Doctor was not authorised by me, & desired that I would give my opinion in this matter, that is, that I would either condemn Dr Keill & retract what Dr Wallis Mr Fatio & I had published some years before & what I had written in yethe year 1676 & before, or enter into the lists with him as he expresses the himself in his last Letter. And by this attaque he is A the Aggressor. He is very angry at the interpretation of the words adhibet semperque adhibuit by the word substituit. And yet the Author himself by the words igitur & quemadmodum hads made the interpretation his own interpreted them in that manner. Mr Leibnitz insinuates that my complaint of his accusing me of plagiary might be to attribute to my self the invention of the new calculus contrary to my knowledge avowed to the contrary in my Book of Principles pag 253 of the first edition. And a little after he saith that in the first Edition of my Principles p. 253, 254 I allowed him the invention of the calculus of differences independently of my own But he accuses me falsly. My words were these. In Litteris quæ mihi cum Geometra peritissimo G. G. Leibnitio annis abhinc decem intercedebant [i.e. anno 1676,] cum significarem me compotem esse methodi determinandi maximas & minimas, ducendi Tangentes, & similia peragendi quæ in terminis surdis æque ac in rationalibus procederet, & literis transpositis hanc sententiam involventibus [Data æquatione quotcunque fluentes quantitates involvente, fluxiones invenire, & vice versa] eandem celarem: rescripsit vir clarissimus se quoque in ejusmodi methodum incidisse, & methodum suam communicavit a mea vix abludentem præterquam in verborum f et notarum formulis. This was reprinted in the second edition of my Principles & is still allowed by me But I nevednever allowed that Mr Leibnitz was the first inventor or found this method without receiving some light from me. Mr Craige is witness that in those days I looked upon the method as mine. In Iuly 1676 Mr Leibnitz425 Leibnitz received copies of my Letters dated 10 Decem. 1672 & 13 Iune 1676., He received also & a copy of Mr Gregories Letter to Mr Collins dated 5 Sept. 1670. In October following he came to London & saw some others of my Letters in the hand of Mr Collins, & particularly my Letter of 24 Octob 1676 then newly arrived at London but not yet copied. In March following a copy of this Letter was upon notice of his being arrived at Hannover was sent to him. And after all this, in a Letter dated 21 Iune 16767, he sent me back his method of tang representing that it was like the method of wchwhich I had given him notice. And what he sent back was nothing else more then what he had sufficient notice of compo from my Letters compared with Mr Gregories Letter & Dr Barrows method of tangents. This method was published by Dr Barrow in the year 1670, & Mr Gregory the same year in his Letter above mentioned gave notice that from Dr Barrows this method compared with his own he had deduced a general method of drawing tangents without any calculation Mr Slusius also in the year 1672 wrote to Mr Oldenburg that he had such a ready method of Tangents. And thereupon Mr Collins gave me notice of these methods & desired that I would send them mine & I did so in my Letter of 10 Decem 1672, representing that I took it to be same wthwith that of Slusius & Gregory, & I added that it was a branch or rather a Corollary of a general method which without any troublesome calculation extended not only to tangents of all sorts of Curves but also to other abstruser sorts of Problemes concerning the curvatures, areas, lengths, centers of gravity of Curves &c and was not (like the method of tangents of Slusius Hudde's method of maxima & minima) restrained to equations free from surdes; & that I had interwoven this method with that of infinite series; meaning in the Tract which I wrote the year before. And Mr Leibnitz a year after he had received copies of these Letters & eight months after he had seen my other Letters in the hands of Mr Collins (amongst wchwhich I reccon my Analysis per æquationes numero terminorum infinitas) sent back Dr Barrow's method of tangents with the characteristick changed & explained how this method readily gave the method of tangents of Gregory & Slusius & might be improved so as not to stop at fraction surds & faciliated quadratures, & from these characters he concluded that this method was like that wchwhich I had described in my Letters. And this is the differential method wchwhich was mentioned in my book of Principles pag 253 & 254, & is now claimed by Mr Leibnitz as the first inventor thereof, notwithstanding that he had notice of all this by my Letters of earlier date && & was told that I had notice of all this written a Treatise of this method & of the method of fluxions series together in the year 1671. 113(1426 to Des Maizeaux ① SrSir When the Postscript to Mr l'Ab Leibnitz's first Letter was shewed to me, to Mr l'Abbe Conti was shewed to me, I did did not think my self concerned to meddle with it, partly because the Letter was not directed to me, & principally because I observed that his designe was to lay aside the Records in the Commercium Epistolicūum & engage me in a squabble about Questions nothing to the purpose such as were: whether he Mr Leibnitz found the Differential method proprio Marte, whether all bodies be heavy, whether I make gravity to be an occult Scholastic quality & a miracle Whether I make it a Miracle Whether God be intelligentia supramundana. Whether h I make him to be the Soul of the world, whether he I say that he has need of a sensorium. Whether I have demonstrated a Vacuum. Whether space be the order of things coexisting & time the order of things successive. Whether God has made the world so perfect as to last from all eternity to all eternity by the mere laws of nature. Whether there be atoms, & whether any body in England can solve the problems of Mr Iohn Bernoulli. However at length being pressed by Mr l'Abbé Conti to answer write an Answer that the Postscript with my answer might be shedwed to the King I wrote an Answer dated 26 Febr. 16716. But when my Answer was sent to Mr Leibnitz & he 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 more to be sent to him; & only wrote a paper of Remarks upon his Answer & shewed them privately to some of my friends to satisfy them that it was easy to have answered his Letter had it come hither directly. And because he had sent them to be communicated to his friends at Paris, I caused them to be published as soon as I heard that he was dead, & you may reprint them wthwith such other Letters as are fallen into your hands but I see no necessity of writing an Answer to those other Letters. The Remarks may serve for an Answer to the whole 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 which was dated 8 Novem 1676 & published by Mr Iones. He that compares that Letter with those Propositions & particularly with the second Corollary of the 10th Proposition, will easily see that I had composed those Propositions before I wrote that Letter. The Tables at the end of 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 Tsheoresms could be invented. The Book of Quadratures was therefore composed before Mr Leibnitz understood the Differential Method. For the Horologium oscillatorium of Mr Huygens was published in April 1673, & Mr Leibnitz began a little after to study(2427 to study to h igher Geometry, & never pretended to have had the differential Method before the year 1676; & when he wrote his Letter of 27 Aug. 1676, he placed the perfection of Analysis not in the differential Calculus, as he did after he found 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 humanarum. Mr Iames Gregory died in the end of the year 16765 & Mr at the request of Mr Leibnitz his papers were Letters were collected & the Collection sent to Paris & among them in Iune following & among them were copies of Mr Gregories Letter of 5 Sept 1670 & mine of 10 Decem 1672, & by those Letters Mr Leibnitz had notice that Mr Barrow's method of Tangents was capable of improvement so as to give the method of Tangents of Gregory & that the method of Tangents of Gregory was capable & Slusius was capable of improvement so as to give the Method my general Method of Analysis, & that this Analysis proceeded without sticking at surds, & that I had interwoven it with the method of Series, vizt in a Tract wchwhich I wrote upon this subject in the year 1671. Mr Leibnitz wrote also to Mr Oldenburg for the Demonstration of some of my sSeries, that is for the Method of finding them & promised him a Reward & told him that Mr Collins could help him to it, & therefore he had heard that Mr Collins had my Method, that is my Analysis per serires numero terminorum infinitas. For I had sent my Method to Mr Collins in no other tpaper then that. Mr Collins instead of sending what Mr Leibnitz desired, joyned with Oldenburg to so in solliciting me to answer Mr Leibnitz's Letter. And thereupon I wrote my Letter of 13 Iune 1676, & after I had described my method of Series & some other Methods (meaning principally the Method of fluxions) became so general as to extend to almost all Problemes except perhaps some numeral ones like those of Diophantus. And Mr Leibnitz in his Letter of 27 Aug. 1676 replied that he did not belive that the Method was so general, there being many Problems & particularly the inverse Problems of Tangents not reducible to equations. And this is another argument that he had not yet found the differential method. In October following he came to London & there met with Dr Barrows Lectures & saw my Compendium Letter of 24 Octob. 1676 & therin had fresh notice of the said method & of my Compendium of series sent by Dr Barrow to Mr Collins in the year 1669, under the title of Analysis per series &c. & consulting Mr Collins, 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 us his new Method with this Indtroduction: 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 this Method as his own without mentioning the correspondence which he had formerly had with the English about these matters He mentioned indeed a methodus similis; but whose that Method was & what he knew of it he did not say, as he should have done. And this his(3459 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. In my Letter of 24 Octob. 1676, when I had been speaking of the method of fluxions I added: Fundamentum harum operationum, satis obvium quidem, quoniam non possum explicationem ejus prosequi, sic potius celavi 6accdæ13eff7i3l9n404qrr459t12vx. And in the said Scholium I opened the ænigma, saying that it conteined thies sentence Data æquatione fluentes quotcunque fluentes quantitates involvente, fluxiones invenire, & vice versa. For I looked upon this as a sufficient security without entring into a wrangle: but Mr Leibnitz was of another opinion. p. 2 × 6 Duplicate of this passage in the Supplement to the Remarks 426 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 because he knew that I had it before him, he never claimed a right to it. 104428 Ad Lectorem At the end of the Remarks – – – – – – – – top of his skill at that time. The Book of Quadratures was written in the year 1676 being for the most part extracted out of D D a Tract wchwhich I wrote in the year 1671 but did not finish & out of some other older Papers. The The first Proposition is comprehended Data æquatione quotcunque fluentes quantitates involvente invenire fluxiones is comprehended verbatim in the AEgnigma which I set down in my Letter of the 24th of October 1676. In that Letter I set down a Series for squaring of figures wchwhich in some cases breaks of & becomes finite, & illustrated it with examples & said that I found it that & some others of the same kind by the Method of fluxions founded in the sentence in that Enigma comprised in theat Enigma that is by the Method of fluxions; & how I found thatem I explained in the first six Propositions of the book of Quadratures & I do not know of any other method whereby they could be found; & therefore when I wrote that Letter I understood the Method of fluxions so far as it is comprehended in those six Propositions. When I had finished the book & the 7th 8th 9th & 10th Propositions were fresh in memory I wrote upon them to Mr I. Collins that Letter which was dated 8 Novem. 1676, & printed by Mr Iones. The Theorems at the end of the tenth Proposition for compoaring curvilinear figures with the Conic Sections were copied known to me when I wrote the said Letter of 24 Octob 1676, the Ordinates of the Curves Figures being there set down. They were copied from the Tract wchwhich I wrote in the year 1671. To understand these two Letters & how to find those Theoremes requires skill in the Method of fluxions so far as it is comprehended in all the first ten Propositions of the Book. And the Book conteins but one Proposition more. In the Analysis per æquationes numero terminorum infinitas which was sent by Dr Barrow to Mr Collins in Iuly 17669 & published by Mr Iones The first Proposition of theis Book of Quadratures was with the solution & examples were printed almost verbatim in the second Volume of the works of Dr Wallis A.C. 1692 & came abroad the next year. And thus the Rule for finding second third & fourth fluxions came abroad was published some years before the Rule for finding second third & fourth differences, & was long before in manuscript. In the Introduction to this Book the method of fluxions is taught without the use of prickt letters; for I seldome used prickt letters when I considered only first fluxions: but when I considered also second third & fourth fluxions I distinguished them by the number of pricks. And this notation is not only yethe oldest but is also the most expedient expedite tho it was not known to the Marquess de l'Hospital when he recommended the differential Notation. Mr Collins in his Letter to Mr Berte wrote dated 26 Iuly 1672 wrote thisus of what I communicated to Dr Barrow in the year 1669 & before. Ex ijs [sc. Anal Mense Septembri 1668 – – – – haud integrum duilt ducit. Gregory found the Method of series proprio Marte but did not claim it because he knew that he was not the first inventor. By the testimony of Mr Barrow grounded upon papers communicated to him from time to time, it Mr Collins here re relatesd in this Letter said wrote that it appeared that I had the Method conteined in the Analysis per serie æquationes numero terminorum infinitas some years before the Doctor sent this Analysis to Mr Collins. And part of this Method is to square figures accurately when it may be done or else by perpetuall approximation: & this requires skill in the method of fluxions so far at least as it requires skill is conteined in the first six Propositions of the Book of Quadratures as was said above. Nothing has been said to prove that Mr 429 Leibnitz had the method before he came to London the second time. Then he met wthwith Dr Barrows Lectures & the Marquess de l'Hospital has said that where the DrDoctor left off Mr Leibnitz proceeded, but & that the improvement wchwhich he made to the Doctors methods of Tang consisted in shewing how to proceed without taking awa exclude radicals exclude fractions & radicals. But the Marquess did not know that by my Letters of 10 Decem 1672 & 24 Octob 1676 I gave him he had notice from me that theise things improvemtimprovement werase to be done.made. He might afterwards find it proprio Marte, but by that notice knew that I had it before him. And For in his letter of 21 Iune 1677 wherein he began first communicate his Method he has acknowledged that I knew it when I wrote my Letter of 24 Octob. 1676. [And therefore it has lain upon him to prove that he had the method before the date of that Letter was the first inventor: especially since in his Letter of 29 Decem 1711 he claimed a right to the method & thereby made himself the first inventor & justified what was published in the Acta Eruditorum for Ian. 1705 saying that it detracted from nobody but gave every man his due. For there the differential method is reprentedrepresented the easier method & Mr Leibnitz is called the Inventor & the differential method is represented the easier & thence is drawn this conclusion Pro differentijs igitur Leibnitianis Newtonus adhibet semperque [pro differentijs illis Leibnitianis illis] adhibuit fluxiones, – ijsque tam in suis Pri quæ sunt quamproxime ut fluentium agumenta æquabilsæqualibus temporis particulis genita quam minimis genita, ijsque tum in Principijs Naturæ mathematicis, tum in alijs postea editis [pro differentijs Leibnitianis] eleganter est usus; quemadmodum & Honoratus Fabrius in sua Synopsi Geometrica, motuum progressus Cavallerianæ Methodo substituit.] And a copy of my Letter of Iune 10 Decem 1672 was sent to him (amongst Gregories papers) in Iune preceding. And in the Scholium upon the second Lemma of the second Book of Principles I put him in mind of this in a friendly manner And yet in his Letter of 29 Decem 1711 he has claimed a right to the method as Inventor & justified what was published in the Acta Eruditorūum for Ianuary 16 1705, where he is called the Inventor, & thence from his being so is drawn this Conclusion: Pro differentijs igitur Leibnitianis Newtonus adhibet, semperque [pro ijsdem] adhibuit, fluxiones — ijsque tum in Principijs Naturæ Mahtematicis, tum in alijs postea editis [pro differentijs illis] eleganter est usus, quemadmodum et Honoratus Fabrius in sua Synopsi Geometrica, motuum progressus Cavallerianæ methodo substituit. At the end of the Remarks after the words du même genre de celles que nous venons de marquer, add. When Mr Leibnitz wrote his Letter of 27 Aug. 1676 he placed the perfection of Analysis in another method composed of Analytical Tables of Tangents & the combinatory Art. Nihil est, said he, quod norim in TOTA Analysi momenti majoris. And a little after: Ea vero nihil differt ab Analysi illa SVPREMA ad cujus intima Cartesius non pervenit. Est enim ad eam constituendam opus Alphabeto cogitationum humanarum. This was the top of his skill at that time. 105)430 At the end of the Remarks after the words du même genre de celles que nous venons de marquer, adde. When Mr Leibnitz wrote his Lettre of 27 Aug. 1676 he placed the perfection of Analysis in another method composed of Analytical Tables of Tangents & the Combinatory Art. Nihil est, said he, quod norim in tota Analysi momenti majoris. And a little after: Ea vero nihil differt ab Analysi illa suprema SVPREMA ad cujus intima quantum judicare possum Cartesius non pervenit. Est enim ad eam constituendam opus Alphabeto cogitationum humanarum. This was the top of his skill at that time. Before he had the differential method I wrote the Book of Quadratures For I wrote it in the year 1676, (except the Introduction & the Scholium at the end of it) extracting most of it out of old papers. And when I had finished it & the 7th 8th 9th & 10th Propositions were fresh in memory I wrote upon them to Mr Collins that Letter wchwhich was dated 8 Novem. 1676 & published by Mr Iones The Table in the end of the 10th Proposition for comparing Curvilinear Areas with the Conic Sections is mentioned in my Letter of 24 Octob. 1676 & the very words of the first Proposition of the Book are also there set down enigmatically; and the contents of these two Letters require skill in the whole book The first Proposition of the Book was also set down enigmatically in that Letter In the Introduction to this Book the Method of fluxions is explained without the use of prickt letters: For I seldome used prickt letters when I considered only first fluxions. But when I considered also second & third & fourth fluxions &c I distinguished them by the number of pricks. And this notation is the most expedite tho it was not known to the Marquess de l'Hospital when he recommended the differential Notation. to understand them. 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 & also the Method of extracting fluents out of equations involving fluxions mentioned in my Letter of 24 Octob. 1676 & copied from an older paper; & an explication of the method direct & inverse comprehended in the sentence Data æquatione quotcunque fluentes quantitates involvente invenire fluxiones, & vice versa: & the Doctor printed them all the same year in the second Volume of his works which was then in the Press & came abroad the next year (A.C. 1693) two years before the first Volume was printed off. And thus the Rule for finding second third & fourth fluxions was published some years before the Rule for finding second third & fourth differences & was long before in manuscript. In the Introduction to this Book the Method of fluxions is explained without the use of prickt letters. For I seldome used prickt letters when I considered only first fluxions But when I considered also second third & fourth fluxions, I distinguished them by the number of pricks. And this Notation is the most expedite & fit for use, but was not known to the Marquess de l'Hospital when he recommended the differential Notation. SrSir Vpon reading the Letters wchwhich you are printing I see no need of saying any thing further about itthat matter. When Mr Collins sent notice one of my series to Mr Iames Gregory wthwith notice that I had a general method of squringsquaring curvilinear figures by such series, Mr Gregory after a years study found out the method proprio Marte but yet never claimed a right to it because he knew that he was not the first Inventor. 125)432 Corrigenda Pag 8 lin 13 dele c'est a dire, commune ou superficiell. Pag. 16. l. 5 scribe A Londres Feb. 26, 171516 st. vet. Pag. 17. l. 13 scribe en Iuillet 1714. Pag 19 l. 20 desquelles. Pag. 46. l. 11 en 1677. P. 75 lin 15 scribe Iuin 1713. Pag. 78 l. 9 scribe 24, 26. Pag. 88 lin 2 Pag 8 lin 6 Post Nature adde et qui n'ont rien de marveilleux. Pag. 87 lin 6 & 9 dele designoient & scribe enveloppoient. Pag 88 lin 2, Adde, And that I usually put letters without pricks for fluxions where I considered only first fluxions, but where I considered also second, third, & fourth fluxions &c (as for instance in extracting fluents out of equations involving fluxions) I distinguished them by letters with one two three four or more points pricks; a notation wchwhich is more convenient then that of Mr Leibnitz tho not necessary to the method. And that in the year 1676 I wrote the book of Quadratures when Mr Leibnitz by his Letter of 12 Iune May 1676 had put me upon resuming the consideration of these things I wrote the Book of Quadratures (escept the Introduction & Conclusion) extracting most of it out of old papers; & when I had newly finished the tenth Proposition with its Corollaries, & they were fresh in my memory I wrote upon them my that Letter to Mr Collins which was dated 8 Novem. 1676 & published by Mr Iones; & that the Tables at the end of that 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, & that in the same Letter where I said that the general Theoremes there mentioned for squaring of Curves were founded on the method of fluxions, I had relation to the six first Propositions of the book of Quadratures: & that the invention of those Series is a demonstration that in those days I had this Method, there being no other way of finding them. In two Letters dated 27 Aug. & 17 Sept. 1692① ② In writing the book of Principle I made much use of this method direct & inverse but did not set down the calculations because the book was writ by the method of Composition as all Geometry ought to be. And At the request of Dr Wallis when he was printing the 2d Volume of his works I sent him in two Letters dated 27 Aug & 17 Sept: 1692 the first Proposition of the Book of Quadratures copied almost verbatim illustrated with examples in first & second fluxions, & the method of extracting fluents out of equations involving their fluxions printed in the fluxions mentioned in my Letter of Octob. 24, 1676, & the DrDoctor published printed them the next same year A.C. 1693) (vizt (vizt A.C. 1692) in the second Volume of his works pag 391, 392, 393, 394, 395, wchwhich Volume was printed two years before the first. & this was above two years before the DrDoctor heard any thing of the Differential method of Mr Leibnitz. [In the winter between the years 1665 & 1666 I invented the met Theory of Colours & almost at the same time with the Method of fluxions, & in the year 1671 was upon a designe of publishing them both, but soon after laid aside that designe for a reason mentioned in my Letter of Octob. 1676, & for the same reason forbore to publish them till the year 16 1704 [And as for the Method of fluxions I do not remember that I have improved it seince the year 1671, In the years 1684, 1685 & 1686 I made much use of it in writing the Book of Principles but did not there set down the calculations because the Book was writ by Composition as all Geometry outght to be & ever since that time I have been forgetting the Method it.] & then published both together. And for the method of fluxions I do not remember that I have improved it the method of fluxions since the year 1671. In the year 1677 I found by the inverse method the Demonstration of Keplers Met Proposition wchwhich is the 11th Proposition of the first book of Principles by the help of it, & in the yeare 16843; 84, 85, & 86 I I began to use at the request of Dr Halley I took that matter into fresh consideration I found som by it some other Propositions of the same kind which were communicated to the R. Society Mathematicians R. Society in the winter following && & entred in their books & in the years 1684, 1685 & 1686 I made much use of it in writing the book of Principles but did not there set down the calculations because I wrote the book was written by the method of composition as all Geometry ought to be; & ever since that time I have been forgetting not only this Method but almost all Mathematicks it; [& Mr Leibnitz doth not pretend to have found the me it before the year 1676., He thinks that he might [& in his Letter of 27 Aug. 1676 there are some things wchwhich satisfy me that he did not know it when he wrote that Letter. For in that Letter he mentions a Method by Analytical Tables & the Combinatory Art as the top of his skill in Analysis, says at that time. Nihil est, saith he, quod norim in tota Analysi momenti majoris. And a little after: Ea vero nihil differt ab Analysi illa suprema ad cujus intima, quantum judicare possum, Cartesius non pervenit. Est enim ad eam constituendam opus Alphabeto cogitationum humanarum after I had written to him. And in his Letter to Mr Oldenburg dated at Amsterdam Novem 1828 1676 he wrote that by these Analytical Tables the Method of Tangents of Slusius was to be perfected improved But after he had found the Differential Method he changed his language & wrote that in his Letter of Iune 21, 1677 that it was the Differential Calcuslus by wchwhich the Method of Tangents of Slusius was to be perfected improved.] Pag. 119 93. lin adde In his Letter of Pag. 93. After venons de marquer adde In that Letter of 27 Aug 1676 there are some things there are some things wchwhich satisfy me that he did not know it when he wrote it. For he did not duly deny that the difficulter Problemes could be reduced to converging series, but als & that inverse Problems of tangents & many others could be reduced to æquations but also mentioned a method by Analytical Tables & the Combinatory Art as the top of his skill in Alnalysis at that time. Nihil est, – – – to be perfected By the inverse Method of fluxions I found in the year 1677 the Demonstration of Keplers Proposition wchwhich is the eleventh Proposition of the Book of Quadratures & in the year 1683 at the importunity of Dr Hally I resumed the consideration of those things thereof & added some more Propositions about the motions of the heavenly bodies which were sent to him communicated by him to yethe R. Society & entred in their Books end of the winter or spring following & upon their request that they 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 finished th wrote that Book I have by disuse been forgetting the Methods by wchwhich I wrote it. Pag 93. After the words venons de marquer, add. In When he wrote that Letter he placed the top of perfection of his skill in Analysis at that time 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 nihil differt ab Analysi illa suprema SVPREMA ad cujus intima, quantum sentio judicare possum, Cartesius non pervenit. Est enim ad eam constituendam opus Alphabeto cogitationūum humanarum. 433 – as their Ancestors did before they corrupted themselves. For the first of the moral Precepts of the Noachides was to worship no other Gods then one. years before the first Methods by wchwhich I wrote it. When Mr Leibnitz wrote his Letter of dated 27 Aug. 1676, he placed the perfection of Analysis in not in the Differential Method but in another Method founded on Analytical Tables of Thangents & the Combinatory Art. Nihil est, saith he, – – – – – cogitationum humanarum. In October When he was in London the second time vizt in October 1676 he met with Dr Barrows Lectures, & Mr Iames Bernoulli in a Paper printed in the Acta Eruditorum for Ianuary 1691 wrote thus: Qui calculum Barrovianum intellexerit (quem decennio ante [i.e. ante editionem Elementorum Calculi Leibnitiani] in Lectionibus suis Geometricis adumbravit auctor, cujusque specimina sunt tota illa Propositionum inibi contentarum farrago) intellexerit, alterum a Dn. L. inventum ignorare vix potestrit; utpote qui in priori illo fundatus est, et nisi in differentialium notatione & operationis aliquo compendio ab eo non differt. The Marquess de l'Hospital, in the Preface to the Analysis des Infinitement pPetits published A.C. 1696, hath told us that the improve wchwhich Mr Leibnitz made to Dr Barrows Methods consisted in excluding fractions & surds from the calculation: but he did not then know that I had given him Mr Leibnitz notice of this improvement in my Letters of 10 Decem 1672 & 24 Octob. 1676. It has been sai When the Marquess de l'Hospital wrote his book de infinite Petites & affirmed that the Differential notation was more convenient then mine, he meant my Notation in the second Lemma of yethe second Book of Principles: for he had then seen no other. That notation I have not used in Calculations: I used it only in demonstrating that Lemma synthetically. The methdmethod of extracting fluents out of Equations involving fluxions I invented in the end of the year 1671 or beginning of the year following & at the request of Dr Wallis sent it to him in Septem. 17 1692 & he inserted it into the second Volume of his works wchwhich were printed the next year And he & came abroad two years after. And here I used prickt letters. In a Letter to Mr Collins dated Novem 8 1676 & published by Mr Iones In the year 1676 I wrote the Book of Quadratures ext except the Introduction & Conclusion wchwhich were written many years after I extracted most of it out of old Papers. And the same year in my Letter of Octob 24 I cited some things out of it And after I had finished the tenth Proposition with its Corollaries I wrote to Mr Collins my Letter of Octob. 8 1676 published by Mr Iones. This Letter contains things wchwhich were fresh has a particular relation to the second Corollary of that Proposition & conteins things wchwhich were fresh in memory when I had newly composed that Proposition & 434 Corrigenda. Pag. 8. lin. 6. After Nature add et qui n'ont rien de marvelleux Pag 8 lin. 13 omit c'est a dire, commune ou superficiell. Pag. 12. l. 23. dele par ordre de la Societé Royale Pag. 16. lin. 5 write the date of the Letter A Londres Feb. 26, 171516 st. vet. Pag. 17. l. 13 write en Iuillet 1714. Pag 19 l. 20 desquelles. Pag. 46 lin 11 write en 1677. Pag 75 lin 15 write Iuin 1713. Pag. 78 lin 9 write 24, 26. Pag. 87 lin 6 & 9 omit designoient & write enveloppoient. Ib. l. 12 write dans mes Lettres du 10 Decem 1672 & 24 Octobre 1676. Pag. 88. lin. 2. add. And that I usually In using the method of fluxions I commonly put letters without pricks for fluxions where I considered first only first fluxions, but where I considered also second third & fourth fluxions &c (as for instance in extracting fluents out of equations involving fluxions) I distinguished them by letters with one two or more pricks, a Notation which I reccon more convenient then that of Mr Leibnitz tho not necessary to the method. As I found the methods of Series & Fluxions in the b year 1665 & so I found the Theory of Colours in the beginning of the next year & in the y ear 1671 was upon a design of publishing them all; but for a reason mentioned in my Letter of 24 Octob. 1676 laid aside that designe till the year 1704. However, when Mr Leibnitz by his Letter of 12 May 16176 had put me upon resuming the consideration of the methods of Series & Fluxions I wrote the book of Quadratures extracting most of it (excepting the Introduction & Conclusion) extracting most of it out of old papers; & when I had newly finished the tenth Proposition with it's Corollaries & they were fresh in memory I wrote upon them that Letter to Mr Collins wchwhich was dated 8 Novem. 1676 & published by Mr Iones. The Tables at the end of that Proposition for squaring of some Curves & comparing others by the Invers 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 said represented that the generall Theoremes there mentioned for squaring of Curves were founded on the Method of fluxions, I meant the method described in the first six Propositions of the Book of Quadratures. For I know of no other method by which those Theorems could be invented ② At the request of Dr Wallis, when he was printing the second Volume of his works, 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 from the Book & the Method of extracting Fluents out of Equations involving fluxions mentioned in my Letter of Octob. 24. 1676 & copied from an old Paper: & the Doctor printed them both the same year (vizt A.C. 1692) in that Volume of his works, pag. 391, 392, 393, 394, 395, 396, & this was above two years before the Doctor heard any thing of the Differential Method of Mr Leibnitz. In writing the Book of Principles I together with an explication of the method of fluxions direct & inverse comprehended in the sentence Data æquatione fluentes quotcunque quantitates involvente in&venire fluxiones & vice versa. And this Volume came abroad in the year 1693 two years before the first Volume was printed off. ① By the inverse method of fluxions I found in the year 1677 the Demonstration of Kepler's Astronomical Proposition wchwhich is the eleventh Proposition of the B first Book of Principles, & in the year 1683 at the request importunity of Dr Halley 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 Books the winter following, & upon their request that things might be published, I wrote the Book of Principles in the435 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 by disuse been forgetting the Methods by which I wrote it. And at present I do not think my self further concerned about these matters then that it should be beleived that what I have published about them in the Book of Quadratures hath not so far as I know been taken from others men who had them before me Mr Leibnitz, & that I invented the Method of fluxions gradually in the years 1665 & 1666 as I affirmed in the Introduction to that book & as Dr Wallis affirmed nine years before in the Introduction to yethe first Volume of his works without being then contradicted] Pag. After the words venons de marquer, add. When he wrote that Letter he placed the perfection of Analysis 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 nihil differt ab Analysi illa suprema SVPREMA ad cujus intima, quantum judicare possum, Cartesius non pervenit. Est enim ad eam constituendam opus Alphabeto cogitationum humanarum. 436 In the second part of his Postscript he tells you that if all bodies be heavy gravity must be a scholastick occult quality & a miracle. notwithstanding that it may be supposed to act constantly by a certain law imprest by God upon the nature of things; that is to say it must a miracle tho it be no w miracles. For Miracles are so called because they happen seldome & thereby for that reason create wonder. All qualities are occult whose causes are not known, & Mr Leibnitz has not yet told us the cause of Gravity. But a Scholastick occult quality is that whose cause in our opinion cannot be found out because it was unknown to Aristotle, & no body can go beyond him. Mr Newton holds no such opinion, but leaves it to Mr Leibnitz every man to find out the cause of gravity if he can. But Mr Leibnitz tells us insinuates that gravity must be caused by the action or impulse of some other bo some bodies or subtile matter & & the matter wchwhich causes gravity cannot gravitate it self. He goes upon the Hypothesis of the materialists viz that all the phænomena in nature are caused by mere matter & motion & man himself is a mere machine It woul His body is not actuated by his mind any mind but moves by mere mechanism. And And his zeale for this precarious hypothesis makes him rail at Mr Newton's universal gravity. He denys none of Mr Newtons experiments. He denys not theis third Rule of Philosophy. &And yet from ex the ExperimtsExperiments & that Rule Vni universal gravity necessarily follows. But he has an extraordinary kn denys the conclusion. And indeed he has a very good faculty at denying conclusions. That third Rule is the Rule of Induction. And without it no Proposition can become general in Naturall Philosophy. Without it we cannot affirm that all bodies are impenetrable. And the argument by Induction for universal gravity is as strong as the argument for universal impenetrability. Yet Arguments from Induction are not Demonstrations. They are only to take place till some experimental exception can be found. And if Mr Leibnitz out of fondn zeale for the Hypothesis of the Materialists will except his subtile matter, th the exception will do Mr Newton's Philosophy no harm. tho it be an irregular ButAnd by theh same liberty any body else may except the Impenetrability of the particles of his subtile matter. He saith that God is Intelligentia supramundana because he is not the soul of the world & has no need of a Sensorium: as if the sens soul of a man would be the soul of the pictures of visible objects made in the sensoriūum if it were in the sensorium place where they are made, or as if any man (except the Anthopomorphites He saith that God hath no need of a Sensorium ever feigned that God had a Sensiumorium in a litteral sence. But what he means by banishing God out of the Vniverse world wants an explication Doth he mean that God is beyond the all space: a being that's nusquāam, And is he angry at Mr Newton for saying that heGod is every where. & that he is not far from any of every one of us: for in him we live & move & have our being. He saith that he is astonished that Mr Newton should beleive that God haveth made the world so ill that it should have made the world so ill that like a watch it would at length cease to go without the extraordinary hand of God; And & that this is to have very narrow Ideas of Gods wisdom & power. And by the same Argument any man may thin affirm that God was able to endow matter wthwith are a an active & self moving principle, & enable it to thingsk, & therefore has done it because he is wise & good, & that God created the world from all Eternity & made it a being absolutely perfect because he was able to do so, so Fo & & that to deny all this is to have narrow ideas of Gods power & wisdome & goodness. He commends experimental Philosophy, but adds that when experiments are wanting, it is allowed to imagin Hypotheses, & expecting till new experiments shall determin which of them are true. But & upon this account he thinks his philosophy may be justified. But he should consider that Hypotheses are nothing more then imaginations, conjectures, & suspicions & ought not to be propounded as Opi Truths or Opinions nor admitted into Philosophy as such untill they are verified & established by experiments. And if you consider his Philo Philosophy you will find that it consists in such opinions generally in such Hypotheses as cannot can never be established by experiments: Such as are That God is intelligentia supramundana, that there is the bodies of animals are moved not by the mind or will of the animal but mechanically by an Harmonia præstabilita that all the Phænomena in Nature are purely mechanical. That the world is so perfect that it wcan last for ever without running into disorder, thadt the Planets revolve in Vortices, That God has never intermedled with the frame of things since the first creation. It's not impossible but that an exception may be found in time. But the exception a mere hypothesis or supposition of an exception is no exception. The exception out to be grounded upon some phæ experimental. The meaning of con Conclusion dix from In made by Induction is that they are to be looked upon as general till some reall exception appeare. Mr New And in this sense gravity is to be looked upon as universal till some real exception appear. that is. To make an exception upon a mere Hypothesis is to feign an exception. It is to reject the argument for Induction, the & turn Philosophy without into a heap of Hypotheses, that is, into which are no better then a chimerical Romance.