Pag. 1. lin. 5. Almost two years after the Principia Philosophiæ came abroad, Mr Leibnitz published the principal Propositions thereof as his own & to make himself the first inventor of this science gave it the name of Dynamic, & now instead of making restitution complains of the English as if they would pass for the sole inventors.

Ib. lin. 7. Dr Keill hath proved that M. Ber Mr Leibnitz changed the differential characters of Dr Barrow a, e, i, o, u into the characters dz, dy, dx, dv, dt: Mr Newton puts any Letters for fluxions & the rectangles under those letters & the letter o for moments or differences: but thinks it ridiculous to place the invention of the method in the invention of words & symbols. See Transact. N. 342. p. 204, 205.

Ib. l. 8. Dr Keill hath proved that Mr Bernoulli was in an error himself The candor of these Gentlemen is taxed by Mr L & Mr Newton charged with plagiary by Mr L. & the evidence against them is Mr Newton's testimon the testimony of Mr Leibnitz. for himself grounded upon his candour. And in all Courts of Iustice the Persons accused are allowed to enquire into the credit of the Witnesses. And the English think the following objections against his candor very material vizt 1 that he endeavoured to make himself a witnesse in his own cause; that he declines to make good his charge against Dr Keill; 2 that so soon as he had found the Differential method he pretended to have found it jam tum a multo tempore a long time before;3 that he did not pretend to have found it before Mr Newton when he published the Differential method, he did not name Mr Newton;4 that he then made no further mention of Mr Newton's methodus similis then was necessary to save his own reputation;5 that he has not to this day acknowledged Dr Barrows the light he received from Dr Barrows method of Tangents;6 that he changed Dr Barrows differential notation into the his own differential notation without ever acknowledging it,7 that he did not dispute wthwith Dr Wallis the antiquity of the method of fluxions asserted by the DrDoctor nor began to dispute it before the Doctor's death;8 that he denyed in his dispute wthwith Mr Fatio he pretended that in the year 1684 when he first publshed his differential method he knew nothing more of Mr Newtons inventions in that kingd then that he could draw Tangents without taking away irrationalls;9 that after he had granted to Mr Fatio that Newton invented the Differential method apart wthwith of fluxion by himself wthwithout receiving any light from the differential method, he afirmed in the Acta Eruditorum that Mr Newton had from the beginning used fluxions instead of Differences as Honoratus Faber had substituted motions for yethe instead of the method of Cavallerius;10 that Mr after he had twice received from Mr Old. a series of Mr Gregory for squaring the circle & knew that Mr Gregory had found it in the year 1671 he published it as his own without naming Mr Gregory;11 that in his Letter of 26 Octob. 1674 he pretended to have invented a series for finding any Arc of a circle whose sine is given, but afterwards when he received this series first from Mr Oldenburg & again from Mr Collins by Mr Mohr, he did not know it to be his own, but in his Letter of 15 May 1676 desired Mr Oldenburg to procure from Mr Collins the method of finding it. And 12 That when Mr Newton at the request of Mr Oldenburg & Mr Collins sent to him his Method illustrated with examples of various series Mr Leibnitz pretended that he had invented four of those series before he received them from Mr Newton, & 13 that he did not yet understand the method of finding all those series but desired Mr Newton to explain it further; 14 that so soon as he understood it, he wrote back that he had found it before as he understood by his old papers, but had forgot it till he received it from Mr Newton; 15 that he changed Dr Barrow's differential notation into a new differential Notation ll, that he might not seem obliged to the DrDoctor for his method of Tangents; 16 that when Mr Newton's book of Principles came abroad he selected the principlall things out of it & published thesem in another form above a year after in three papers, as his own: 17 that he changed the name of vis centripeta used by Newton into that of sollicitatio paracentrica , not because it is a fitter name, but to avoid being throught to build upon Mr Newtons foundation; 18 that he has set his mark upon this whole science of forces calling it Dynamick, as if he had invented it himself, & is frequently setting his mark upon things by new names & new Notations; that & 19 that he has adapted an erroneous demonstration to the 11th XIth Proposition of Mr Newton the first of Mr Newtons first Book of Principles to make it his own; 20 & that he has takemtaken from Mr Newton his general method of series, & endeavoured to explode the rest of Mr Newton's series methods of series as useless. For

Pag. 1. lin. 17, he tells us that Mr Newton indeed was before him in the invention of series, but he had since invented a general method of series & had no need of Mr Newtons extractions. methods. But this general method is Mr Newtons For Mr N invented by him above 44 years ago or above. For in his Letter of 13 Iune 1676 he tells us that his method of Series was not altogether universal wthwithout some further methods of then those described in that Letter, & wchwhich he there omitted because he was then weary of those studies & had then absteined from them almost five years. And what those methodmethods were he described in his Letter of De OetOct 24 1676 in the two following sentences exprest enigmatically, vizt, Vna methodus consistit in extractione fluentis quantitatis ex æquatione simul involvente fluxionem ejus: altera tantum in assumptione seriei pro quantitate qualibet incognita ex qua cætera commode derivari possunt & in collatione terminorum homologorum æquationis resultantis ad eruendos terminos seriei. The first of these two methods is a branch of the method of fluxions, the other is that very method whereof Mr Leibnitz pretends to have been the first inventor. And by all these instances of the candor of Mr Leibn. you may judge what reason he had to say that the English would be almost the sole inventors. Mr413 Mr Newton found out alll these methods between the years 1664 & 1672, Mr Leibnitz owns that he knew nothing of the advandced Geometry in the year 1673, & yet he would be the first inventor. Mr N Mr Newton began to study these things nine years before Mr Leibnitz & grew weary of them before Mr Leibnitz began to think of them & yet Mr Leibn. would go for the first inventor. All All these methods are but several branches of Mr Newton's general method, Mr Leibnitz teares this general method in piences that he may go for the first inventor of the principal parts of it & make the rest insignificant & useless, & this is his candour.

But Mr Leibnitz complains of the English for not printing the the Letters entire, & saith that they only published what they thought capable of a bad interpretation & particularly, saith he, when I was the second time at London Mr Collins shewed me part of his correspondence wthwith Mrs Gregory & Newton & I observed that Mr Newton acknowledged his ignorance in many things, & said amongst other things that he had found nothing about the dimension of the celebrated Curvelines except the dimension of the Cissoid. But, saith he, they have suppressed all this. And this is another instance of his candor. For they did not omit all this, but published it, as you may see in the Commercium pag. 74. Mr Leibnitz came to London the second time in October 1676 & there saw these things in Mr Newtons Letter of Octob 24 1676 in printed written to Mr Oldenburg & put into the hands of Mr Collins, Mr Oldenburg to be copied. He did not stay in London till a copy of the Letter could be copied, but so soon as they knew whether to send a copy after him, it was sent. This whole Letter is published in the commercium

Pag 1. l. 7. Mr Leibnitz changed the differential characters of Dr Barrow into a, e, i, o &c into the characters dz, dy, dx, dv: Mr Newton puts any letters for fluxions & the rectangles under those letters & the letter o for s moments or differences; but thinks it ridiculous to place the invention of the method in the invention of wortds & characters. See Transact. N. 342. p. 14 204, 205.

Ib. l. 8. Dr Keill hath proved that M. Benoulli was in an error himself. See Iournal Litt. Iul. & Aust 1674, p. 343, 344.

Ib. l. 13. Is it by a forc't interpretation that Mr Leibnitz received the Series of Gregory from Mr Oldenburg, & published it as his own?

Ib. l. 14 By the laws of all nations, if he will not prove his accusation against Dr Keill, he is guilty of calumny & If he will not write a publick answer to what has been published against him his writing against the English in private Letters to his correspondents, ought also to go for calumny backbiting.

Ib. l. 18. His general method was found by Mr Newton many years before. See Transact Num 342 p. 212.

Ib. l. 21. That dispute was occasioned by Dr Wallis's affirming to NB. There was no dispute at that time tho Dr Wallis affirmed that Mr Newton found the method of fluxions in yethe year 1666 or before. & Mr Leibnitz did not then deny it or affirm that he himself knew it before yethe year 1677.

Ib. l. 240, 24. ② If the Mr Leibnitz ③ hath any Letters in the hand writing of Mr Collins or Mr Oldenburgh wthwith whom he corresponded, & will send the Originals to any friend in England that the hands may be viewed before the R. Society & attested copies taken thereof, ② And ② if he ① will appoint any friend to vieue view the Letters kept in the Archives of the Society & extract what he thinks material to be published & is not yet published; ④ I do not question but the Society at his request will publish the same.

Pag. 2. l. 2. Mr Leibnitz corresponded wthwith Mr Oldenburg from yethe year 1670 to yethe year 1677 & with Mr Collins from the year 1673 or 1674 & in yethe year 1674 began to write about Mr Newton's series, wchwhich was three or four years after Mr Collins began to communicate those series to the Mathematicians both at home & abroad & particularly to some at Paris.

Ib. l. 6. Since Mr Collins in yethe year 1676 shewed Mr Leibnitz part of his correspondence wthwith Mr Newton, he might shew him the tract De seriebus infinitis.

Ib. l. 7, 8, 9. What Mr Newton there said, was not suppressed but printed in the Commercium pag 74 lin. 10, 11.

Pag. 1. l. 5. Almost two years after the Principia Philosophiæ came abroad Mr Leibnitz published the principal Propositions thereof as his own, & would can pass for almost the sole inventor, but has not succeeded. His adapting an erroneous can he & to make the science of forces his own has christened it by the new name of Dynamik, & can he complain of the English. His adapting an erroneous demonstration to Prop. XI Lib. 1 Princip. discovers that he tried in vain to make itthese things his own.

Pag. 2. l. 11. Mr Newton is not so vain as to keep a correspondence for propagating philosophy. Mr Leibnitz keeps an universal correspondence, & instead of defending him self fairly & above board, endeavours in a clandestine manner to k by means of his universal correspondence to keep up his reputation & back-bite Mr Newton.

IbPag. 2. l. 1. Therefore Mr Leibnitz knew nothing of the advanced Geometry before the year 1674.

P. 1. l. 5 Mr Leibnitz complains that yethe English would be sole inventors. But he will not suffer them. They can invent nothing He puts in his claim upon all occasions of being cal first inventor or at least Coinventor of every thing. After he had received the series of Gregory from Mr Oldenburgh he published it as his own wthwithout mentioning his receipt hereof having receaved it from Mr Oldenburgh. When Mr Newton in his Letter of Iune 13 1676 sent him several series he prendedpretended to have invented four of them, before he understood the method of inventing them. In the year 1674 He intedvented pretended to a series for finding the arch of a circle by the sine, & yet afterwards wrote for the method of finding it. Almost two years after Mr Newtons Principia Philosophiæ came abroad he published the principal Propositions thereof as his own & adapted an erroneous Demonstration to the chief of them to make it his own Galileo began to consider the effect of Gravity upon Projectiles, Mr Newton in his Principia Philosophiæ improved that consideration into a large science Mr Leibnitz christened the child by new name as if it had been his own calling it Dynamica. Mr Hygens gave the name of vis centrifuga to the force by wchwhich bodies revolving bodies recede from the centre of their motion Mr Newton in honour of that author retained the name & called the contrary force vis centripeta Mr Leibnitz to explode this name calls it sollicitatio Paracentrica, a name much more improper then that of Mr Newton. But his mark must be set upon all new t inventions And if one may judge by the multitude of new names & characters invented by him, he would go for a great inventor.

Ib. l. 7

Pag. 1. l. 7, 8. He saith that it appears not that Mr Newton invented the infinitesimal Notation & Arithmetick before him as Mr Bernoulli has well judged. The English say that Mr Newton in his Tract communicated by Dr Barrow to Mr Collins in the year 1669 put letters for fluxions & the rectangles under the symbols of fluxions & the letter o for infinitesimals, that Dr Barrow in his method of Tangents published in the year 1670 put the vowels a, e, i, o, u for infinitesimals, & that Mr Leibnitz in the year 1677 began to put dz, dy, dx, dv, dt &c for infinitesimals & to call them differences & the method the Differential Method. They say also that Mr Newton in the same Tract, represented the summs of Ordinates of Curves by inscribing the Ordinate in a square rectangle in this manner $\boxed{\frac{\mathrm{a}\mathrm{a}}{64\mathrm{x}}}$ & that it doth not appear that Mr Leibnitz represented the same thing by the summatory symbol $\int \frac{\mathrm{a}\mathrm{a}}{64\mathrm{x}}$ before yethe year 1686., from wchwhich symbol They say also that Mr Newton in the same Tract gave a specimen of this new Arithmetic, that Dr Barrows method of Tangents is another specimen, & that Mr Newton in his Letter to Mr Collins dated 10 Decem 1672 (a copy of wchwhich was sent to Mr Leibnitz by Mr Oldenburg 13 Iune 1676) described the same method & how it extended to all sorts of Problems & proceeded without sticking at surds, & gave the method of Tangents of Slusius as a branch or Corollary thereof. They say also that Mr Newton in his Letter to Mr Oldenburgh dated 24 Octob 1676, mentio represented that his method readily gave the method of Tangents of Slusius, & maxima & minima & Quadratures & sother Problemes & stuck not at surds & that it was comprehended in this sentence enigmatically exprest Data æquatione quotcunque fluentes quantitates involvente, fluxiones invenire & vice versa; & that this method gave him the series for Quadratures there set down & illustrated with examples & that the book of Quadratures shews how the method of fluxions gives this series, & no man hath hitherto shewn how to find it by any other method of fluxions, & that Mr Newton five years before those days that is in the year 1671 wrote a book of this Method & of the method of series together. T & that it doth not appear by any arguments that Mr Newton Leibnitz knew the Differential method before the year 1677. They say also that when Mr Leibnitz wrote his Letter of 27 August 1676, he could not beleive that Mr Newton's methods wasere so general as Mr Newton had represented & ytthat inverse Problems of Tangents could not be reduced to quadratures or equations, & therefore he had not yet found the differential Method, that at his second coming to Lodndon wchwhich was in the latter part of October 1676 he saw Mr Newtons Letter of 24 of that month in the hands of Mr Collins (For it was in that Letter that Mr Newton said that in the figures vulgarly celebrated he found little new concerning their dimensions except the dimension of the Cissoid,) & having also a copy of Mr Newtons Letter of 10 Decem. 1672 in his return from London through Holland into Germany he was meditating417 meditating how to make the method of Tangents of Slusius general & extend it to all sorts of Problems, & in a Letter to Mr Collins dated from Amsterdam 16 28 Novem. 1676, proposed to do it by a table of Tangents, & therefore had not yet found the differential method; & that the next year when he had newly found this method, he wrote back that he took Mr Newtons the method wchwhich Mr Newton concealed, to be like it. They say also that all these things are taken out of Letters & Papers printed entire, (the extracts or fragments of Letters relating to the Questions about infinite or converging Series,) & that it lies upon Mr Leibnitz to prove that he had the Differential method before the year 1677.