p. 258 lin, 54. Facuit Newtonus pacis gratia, et seriem Gregorij Leibnitio quæ Collinius & Oldenburgus cum Leibnitio tunc communicabat ignoravit. Supra (impressa sunt Newtoni Consulat Lector Epistolas Newtoni ss pam fuisset tunc ignoravat. supra impressas.

ib. lin 11. Meditationes illæ A methodo fluxionum et æque nascebantur et prius nascebantur:

ib. lin 19. Lineæ illæ Newtoniana primum methodo primum medthodum æquationibus æquationibus finitis sunt expressæ & sub leges Analyseos redactæ. Vide supra, pag.

p. 258 lin. 4. Facuit Newtonus pacis gratia, et quæ Collinius & Oldenburgus eo tempore cum Leibnitio communicabantverant ignoravit. Tantum abest ut Leibnitius Postulabat Leibnitius methodum perveniendi ad series quas acceperat ab Oldenburgo acce quus a, et quamprimum methodum illam acceperat cœpit a Newtono, cœpit series per methodum illam illam inventas sibi arrogare.

p. 258. lin 4 Facuit Newtonus verbi pacis gratia. & sed iIn epistolis illis suis Leibnitium primum esse methodi vel methodi quam differentialem vocat inventorem esse primum minim nam vel methodi serierum primum esse inventorem nullibi agnovit, Et series suas Certe Leibnitius series Newtonianas et Gregorianas Anno 1675 & forte an ad ipsum missas ab Oldenburgo accepit fuisse ignorabv tunc ignoravit ivit. Certe Leibnitius & unam earum earum pro sua ventavit, et anno proximo methodum primum ind. ad series illas ad se mitti postublabit, & seriem Gregorianam ad se missam pro sua venditavit. Quæ omnia Newtonum lutebant.

ib. l. 11. Quasi methodo fluxionum nihil debeatur.

ib. l 19. Non primum Quasi Leibnitius ignoraret Newtonum methodum fluxionum prius invendtum fuisse. Newtonum hæc omnia hæc omnia præstare per methodum fluxionūum ib. l. 29. præstari & Newtonum prius præstare potuisse. Vide ejus Epistolas p & , et Analysin p.

ib. l. 19 Hæc Leinbitius, quo est candore, sub nomine Editorum Actorum.

p. 259. l. 3. Quadraturam aut per seriem infinitam a D. Brunkero inventam Mercator per divisionem Wallisianam tantum demonstravit & ut supra nihil præterea.

Pag. 64554 lin. 4. Ignoravit WallisisusWallisius Gregorium hanc seriem cum anno 1671 cum Collinio Oldenburgum Anno 1675 cum Leibnitio communicasse, & Leibnitium in Anglia fuisse anno 1673 ubi methodus veterum Collinius de methodo serierūum libe loqui & series aliquas cum amicis libere communicare cpt ubi Collinius de methodo serierum libere loqui cœperat et series aliquas cum amicis communicare.

Pag 673. lin. 15, 16, 19. Annon Newtonus hujusmodi æquationes prius invenit qui docuit fluentem ex æquationiebus fluxionem simul involvente extrahere? Annon tota fluxionum methodus inversa, ubi de Curvis agitur, pendeat ab hujusmodi series æquationibus ad Curvas applicatais. Annon Newtonus Curvas omnes mechanicas ad æquationes reducere docuit pergendo ad ab hujusmodi æquationibus finitais ad series infinitas. vide pag 86. Interea Nicolaus Mercator . . . . . non possunt.

Pag 674. Literas tuas . . . . . . . nam secus est. — Vbi dicitur Nicolaum Mercatorem . . . . . . . . sed res eadem est. — Et ni faller (sic saltem mihi nunciatum est) . . . . . . . . . præjudicio esse debet.

Ad p 675 l. 44 38. Ipsa Series ipsa quæ N. Mercatori passim toties tribuitur a D. Brunkero primum inventa fuit – ut supra dictum est.

Pag 679 Methodum fluxionum . . . . . differunt in nonnullis.

Ad pag 679 lin 20. Hoc advertit & agnovit Leibnitius Quasi Leibnititus hoc non advertisset Anno 1677 ubi primum dit incidit in methodum Newtoni? ut Vide literas ejus supra impressas pag leguit patebit pag. 17, 18, Vide etiam pag 18, 19, 52. Sed nunquam adduci pot pag 90, 91. Cæterum Newtonum primum esse inventorem nunquam agnovit. Et quamvis D. Wallisius sæpius incult caret methodos utriusque rem eandem esse vel quam simillimam, adduci tamen non potuit Leibnitius ut differentiam aliquam realem assignaret. Si Newtonus est primus inventor, medthodus ipsi debebitur. Si Leibnitius aliquid addiderit hoc erit Leibnitianum. Doceat igitur tandem Leibnitius quid addiderit huic methodo ac desinat tandem methodum sibi arrogare, nisi nomen methodum fluxionum New

Pag. 681. Optaverim item ut . . . . . . intelligamus

Ad pag. 681 lin. 17. Vt Leibnitius quid suum sit exponat Wallisius iterum postulat sed frustra.

Newtono relinquere. Methodum differentialem Moutoni olim sibi olim arrogavit.. A D. Pellio ob id reprehensus. In Reductionibus æquationum ad radices non affectas Gregorius & Tschurnhausius. olim sd Cum Gregorius et Tschunhausius in reductionibus æquationum ad s radices non affectas occupati esset; ipse eos prævenire conatus est ob id reprehensus a Collinio. Cum Newtonus methodum serierum invenisset & Leibnitius ipso sero ab Collinio Oldenburgo et Mohro series aliquas accepisset & spatio omnie toto unius methodum perveniendi ad series illas invenire non potuisset; postulavit ab Oldenburgo meth odum dad se mitti, et interea serierum acceptarūum unam (quam forte per methodum trans divisionem invenire didicere transmutationem figurarum invenire didicerat) pro sua vulgo cum amicis in Gallia communicare cœpit. Deinde accepta methodo generali Newtoni series alias per methodum illam inventas, mutatis s(levi facta mutatione) sibi rapere conatus est, et in Actis Leipsicis se inter inventores serierum passim numerat , ob id merito reprehendus. Ex litteris Newtoni ad Collinium et Newtonum Oldenburgūum missis, noverat Newtonum in methodum incidisse ante annum 16 Anno 16711 librum de methodo serierum & met alia methodo alia huic affini solvendi problemata difficillima & cum ex characteribus & exemplis methodi illius per Newto ipse tand anno 1677 in eandem methodum incidit, Newtonum prævenit & anno 1684 pro et methodum ob id merito reprehen et methodum pro sua venditat.

ib lin 27 Litera Newtoni primam lucem affuderant.

Ib lin 27 Hæc et quæ sequuntur Leibnitius ante annum 1677 minime advertit. Et Literæ Newtoni primam lucem afuderant. Anno 1676 credidit inversa tangentium problemata ad æquat et similia ad æquationes reduci non posse.

And the Letters & Papers wchwhich follow shew it appears that in the year 1671 at the desire of his friends he composed a larger Treatise on yethe this method (p ) ) that it was very general & easy without sticking at surds (p ) & extended to problemes of Tangents direct & inverse (p ) & to the finding the lengths areas lengths centers of gravity & curvatures of curves & solving other more difficult problems (p )② that it extended to the extracting of fluents out of equations involving their fluxions (p )③ & proceeded in difficulter cases by assuming the terms of a series gradually & determining them by the conditions of the Probleme (p )① that in Problemes reducible to Quadratures it proceeded by the Propositions since printed in the bokok of Quadratures (p ) that it extended to mechanical curves & (p ) & was was so general as to extend to almost all Problemes except the numeral ones of Diophantus & such like (p ) [& that it proceeded in extended to mechanical curves as well as others (p ) & by consequence proeeded by the consideration of the indefinitely small particles of quantity called Indivisibles by Cavallerius & Leibnit Augmenta momentanea & momenta by Mr Newton, Infinitesimas & Differences by Leibnitz. For there is no other way of drawing Tangents to Mechanical curves or find of finding the areas lengths centers of gravity & curvatures of any Curves then that of by considering the moments or infinitesimal particles of Quantities & their proportions to one another.] And all this was found out by Mr Newton before Mr Leibnits knew any thing of the method. For when Mr Oldenburgh had sent him some of the series found out by this method, the next year he desired Mr Oldenburg to procure him the method (p ) & in his Letter dated 27 Aug 1676 he wrote that he did not beleive that Mr Newtons method was so general. For, said he, there are many Problemes & particularly the inverse Problems of Tangents that cannot be reduced to æquations or quadratures (p ) & in the years 1675 & 1676 he wrote communica a piece of this se in a vulgar manner concerning a series which he had received of that year of Mr Oldenburg & continued to polish it the next year (p ) but after he found out the Differential method, thought it not worth publishing p. In all the Letters In all the Letters & papers there is not one word of his knowing the Differential method before his The first The first mention of his knowing the Differention is in his Letter of 21 Iune 1677. There he began to In all these Letters & Papers there appears nothing of his knowing finding or knowing the Differential Method before yethe year 1677. It is first mentioned by him in his Letter of 21 Iune 1677, & he began his description of it with these words. Hinc nominando IN PSTERVM dy differentiam duarum proximarum y &c. p 88.

If it be said that Mr Leibnitz notwithstanding notwithstanding these things might find out the method apart & so far have a some right to it as he was a second Inventor: it must be considered that the first Inventor hath the sole right till another a second Inventor arises, & no mans right to any thing is to be taken from him without his consent it would be is an act of injustice to take away any mans right to any thing & divide it between him & others without his consent, besides that to do it in this cases of this nature would encourage Perretenders & per perpetually imbroyl the first inventors in disputes with contentious people. But however it doth not appear that Mr Leibnitz invented the method alone without receiving some light from Mr Newton.

For he had se at his request Mr Newton communicated to him one half of the method in plain words in his Letter of 13 Iune 1676, namely that half wchwhich consists in the invention of ser inf reduction of Problems to infinite series so far as he could describe it without mentioning discovering the other half. For he concealed his Theorems for Quadratures derived from the other part of it & his he way of extracting fluents out of Equations involving their fluxions (p. 56. & Mr I. Gregory by having . . . . . . . . & how he derived reciprocal series from one another. About the

Abou Mr Newtons Letter of 10 Decemb 1672 was also sent him about the same time (p. 30, 47) in wchwhich Letter he had a general description of the method wthwith its large extent & an example of it in drawing of Tangents to mechanical Geometrical curves & was told that this method of Tangents was but one particular or Corollary of the general method. And by this method he un Letter he understood also that Mr Newtons method was agreed wthwith that of Slusius but was much in Geometrical Curves but was more general in extending to mechanical Curves & not sticking at radicals. And after thise sight of this Letter, D his mind ran upon the improvement of Mr Slusius method; p 87, 88.

Mr Newton also in his two letters of 13 Iune & 24 Octob 1676 mentioned some Propositions in his book of Quadratures & gave him a notable of example of his method in a Rule found by it for the squaring of Curves & another notable example in the inverse method of Tangents & let him know that this method was so general that it extended to almost all Problemes except the numeral ones of Diophantus & such like. ✝ ✝ He told him also that his method extended to mechanical curves as well as others. (p. 530, 52, 54) whence it was obvious to conclude that it lay in proceeded by the consideration of . . . . . . proportions to one another. And And now when he had discovered communicated one half of his method in words at length & made so large a description of the other half as endangered the losing it; to secure it th to himself till he could have time to communicate it in open words at length he concealed it in ænigmas. And yet he discovered by circumstances what he thought to have concealed

pag 673. Intere Nicolaus Mercator . . . . . . . promittere non possum.

Ib. Ad lin. 15, 16, 19. Annon Newtonus hujusmodi æquationes prius invenit qui docuit fluentem ex æquatione fluxionem involvente extrahere, & Curvas areas Mechanicas ad series inf æquationes reduxit pergen numero terminorum infinitas reduxit pergendo ab hujusmodi æquationibus finititis? Annon tota fluxionum methodus inversa ubi de Curvis agitur pendeat ab hujusmodi Curvis æquationibus ad Curvas applicatis?

Pag 674 & 675. Literas tuas . . . . . . . . . nam secus est. — Vbi dicitusdicitur Nicolaum Mercatorem . . . . . . . . . . . . . . . . Quod tamen neutri prejudicio esse debet.

Ad p 675 l. 38. Series ipsa quæ D. Brunkero tribuitur M Mercatori tribuitur, a D. Brunkero primum inventa fuit ut supra dictum est.

Pag 679, 670 Methodum fluxionum . . . . . . . . . . vellim non fraudari posteri sed publice quoque est professus.

Ad p 679 lin 20. Quasi Leibnitius hoc non advertisset anno 1677 ubi primum incidit in methodum Newtoni. Vide Literas ejus supra impressas pag. 90, 91. Cognationem methodorum & Newtono deberetur et methodum fluxionum Newtoni ante quod antnnum 1671 inventam fuisse agnoscere debuit Anno 1684 ubi primum medthodum differentialem in Actis Leipsicis exposuit, Et.

Ib lin 24. Hic agnoscere videtur Leibnitius methodum utramque esse unam et eandem paucis exceptis, sed inter ideoque communi nomine Analyseos infinitesimalis a se designari, differre tamen in nonnullis. Quatenus inter se una et eadem s non different, methodus erit primi tribui debet inventori primo, quatenus differunt, aliqua erunt addita ad Inventore secundo

Ad pag 679 lin 20. Quasi Leibnitius hoc non advertisset anno 1677 ubi primum incidit in methodum Newtoni. Vide Literas ejus supra impressas pag 90, 91. Certe methodum Newtoni ante annum 1671 inventam fuisse ex literis ejus Leibnitius intellexiterit (pag ) sed in Actis Leipsicis hoc nunquam agnovit. Vide supra pag. 70, 71, 72.

Ib. lin 24. Quæritur, quis sit methodi hujus Analyseos hujus infinitesimalis addidit Nam Certe Newtonus tractatus hoc titulo insignitum Anno supra impressum anno 1669 cum Collinio communicavit Nam At Leibnitius methodum totam subo nomine methodi differentialis sibi arrogatus assumit & nil nisi nomen nudum methodi Infinitesimalis fluxionum Newtoni relinquit. Ad Et adduc non potest at differentiam detbat relinquere conatur. Ib lin 26 Novimus quid Cartesius addidit Analysi Vietææ, addidit dicat tandem Leibnitius quæn quid ipse Analysi addidit Analysi fluxionum.

Ib. lin 27. Literæ Newtoni primo Leibnitio Consideratio Literarum Newtoni incidit in methodum quam i differentialem vocavit. Newtoni primam lucem Leibnitsio affuderant Leibnitio. His admonitus et exemplis quibusdam methodi fluxionum adjutus incidit in methodum differentialem Leibnit quam nomine methodi differentialeism vocavit a summatorio distinxit.

Ib. lin 35. Anno 1676 Leibnitius Leibnitius ante 16767 – – – – – hoc non vidit. Scripsit enim anno 167 inversa tangentium problemata & alia multa ab æquationibus non pendere. Rescripsit Newtonus hujusmodi problemata in potestate esse nempe per æquationes suias. Et tum demum Leibnitius a Newtono admonitus hæc vidit. Vide pag. 65 lin 14.

Ib p 679 lin 49. Novit Leibnitius se primum Quando d Diu ante receptum ejus calculum Mirum est hæc a Leibnitio dici, qui novit legerat ex literas Newtoni intellexerat methodum solvendi hujusmodi problemata ante annum 1671 Newtono innotuisse, & Newto hunc primum a Vide supra pag. 71 lin 1 Certe Sed et Newtonus etiam ex Libro e Principijs ejus ipsum primum noverat ipsum primum per hanc methodum problemata primus felicitur tractaitsse quæ ad transitum pertinet ada Geometria ad Naturam.

Ib. lin 5 54. Hugenius Literas quæ Newtonum et Leibnitium mediante Oldenburgo intercesserant nunquam vidit.

Ib l. 24. Methodum fluxionum et Methodum differentialem esse nonnullis quidem differre sed licet in nonnullis differre possuint esse tamen unam et eandam methodum hic agnoscit Leibnitius & ideoque se communi, nomine designare solere Analyseos infinitesimalis, licet in nonnullis differre possint ut Analysis Vietæ et Analysis Cartesij in nonnullis differunt Quæritur qu Quæritur quis sit methodi hujus infinitesimal inventor primus & quid alter alterius cinventis addidebit. Novimus quid Cartesius addidit Analysi Vietæ, dicat tandem Leibnitius quid ipse addidit Analysi fluxionum.