② Mr Iames Bernoulli in the ge Acta Eruditorum mensis Ianuarij 1691 pag. 14, gave thean account of the Differential method in these words Quanquam, ut verum fatear, qui calculum Barrovianum (quem decennio ante [i.e. ante annum 1784] in Lectionum inibi contentarum farrago) intellexerit alterum a Dn. Leibnitio inventum ignorare vix poterit; utpote qui in priori illo fundatus est, & nisi forte in differentialum numero notatione & operationis aliquo compendio ab eo non differt.. ① And that very candid Gentleman the Marquis de L'Hospital in the Introduction to his Analysis, tells us that Mr Fermat found a method of Tangents wchwhich Des Cartes allowed to be often better then his own. That Dr Barrow made it more simple & adopted a proper calculation to it, but wanted this was still wanting, viz to exclude fractions & radicals in disit in the application in d in using this method. In default of wchwhich the calculus of Mr Leibnitz succeeded who began where Dr Barrow left off.

These two Gentlemen knew nothing of what Mr Leibnitz mighthad received from England by the means of Dr Olden Mr Oldenburg. Mr Leibnitz never acknowledged to them any thing of that knid. In the Acta Leipsica Eruditorum he never made any acknowledgmtacknowledgment of any thing advantagewchwhich he had received either from Dr Barrow or from Mr Newton or from Mr Gregory or from Mr Collins or Mr Oldenburg or any body else in England, unless where he could not avoid it. He never acknowledged any thing more of that knid then what was published by Dr Wallis, & therefore it is but just that the world should know it from other hands what he has further received from England Mr Oldenburgh

Mr Newton in his Letter of 10 Decem. 1672 & (a copy of wchwhich was sent to Mr Leibnitz by Mr Oldenburge amongst the Papers of Mr Gregory in Iune 1676,) & in his Letters of 13 Iune & 24 Octob. 1676 wchwhich Mr Leibnitz received the next year in spring gave notice to Mr Leibnitz that he had a method whereof the method of Tangents of Slusius was but a branch or Corollary, & that this Method stuck not at extended to the abstruser sorts of Problemes about the curvatures, areas lengths, areas, solid contents, & centers of gravity &c of lines & figures & to inverse problemess of Tangents & others more difficult & succeeded in & extended to mechanical curves as well as oin others & proceeded without sticking at surds, & made the method of Series so universal as to reach to almost all Problemes except perhaps some numeral ones like those of Diophantus. And he gave examples of this Method in drawing of Tangents & squaring of Curves & the foundation of this method he compehended in this sentence exprest a enigmatically, Data æquatione Æ quotcunque fluentes quantitates involvente fluxiones invenire & vice versa. And a part of the inverse method he exprest enigmatically in this sentence Ex æquatione fluentes quantitates involvente fluxiones invenire et vice versa Ex æquationes fluxiones involvente fluxentesm extrahere Extrahere Fluentem quantitatem ex æquatione simulo involvente fluxionem ejus. In both wchwhich sentences the word fluxiones relates to the second third & following fluxions as well as to yethe first. And if all this be added to Dr Barrows Lectures published N.C 1670, there will be nothing more left for Mr Leibnitz but a new notation Leibni

When Mr Leibnitz received this information he could not at first believe Mr Newtons Method was so general: for he wrote back in his Letter dated 27 Aug 1676 th Quod dicere videmino plerasque difficultates (exceptis Problematibus Diophantæis) ad Series infinitas reduci, id mihi non videtur. Sunt enim multa usque adeo mira et implexa ut neque ab æquationibus pendeat neque ex Quadraturis: qualia sunt (ex multis alijs) Problemata methodi tangentium inversæ; quæ etiam Cartesius in potestate non esse fossus est. And Mr Newton in his Letter of 24 Octob. 1676 made answer: Vbi dixi omnia pene Problemata solubilia existere; volui de ijs præsertim intelligi circa quæ Mathematici se hactemus occuparunt vel saltem in quibus ratiocinia Mathematica locum aliquem obtinere possunt. Nam alia sane adeo perplexi conditionibus implicata excogitare liceat, ut non satis comprehendere valeamus; et multo minus tantarum computationum anus sustinere quod ista requirerent. Attamen ne nimium dixisse videar, inversa de Tangentibus Problemata sunt in potestate alioque illis difficiliora. Ad quæ solvenda usus sum duplici methodo; una concinniori altera generaliori. Vtramque visum est impræsentia literis transpositis consignare ne ne propter alios idem obtinentes, institutum in aliquibus mutare cogar [Una methodus consistit in extractione fluentis quantitatis ex æquatione simul involvente fluxionem ejus: altera tantum in assumptione seriei pro quantitate qualibet cognita ex qua cætera commode derivari possunt, et in collatione terminorum homologorum æquationis resultantis ad eruendos terminos assumptæ seriei] And of all these things being added to Dr Barrows Lectures & method of Tangēents published A.C. 1670, 12 there will be was very little more remaining besides a ne left for Mr Leibnitz to find out besides a new notation & a new name of the method. [Certainly if the Marquess de L'Hospital had seen these thre Letters of Mr Leibnitz left off began where Dr Barrow left off, the other & tang & improved the method by teaching to avoyfractions & radicals & the other would not have ascibed to Mr Leibnitz that little wchwhich was wanting to make Dr Barrows method compendious.] By the words of Mr Leibnitz Sunt enim multa usque adeo mira et implexe ut neque ab æquationibus pendeant neque ex quadraturis: qualia sunt (ex multis alijs) problemata methodi tangentium inversœ, its manifest that he did not understand when he wrote his Letter of 27 Aug. 1676 he did not understand any thing more the differential method.