On the 21st June 1677, Leibnitz sent to Oldenburg, to be communicated to Newton, a letter containing the first at tempts at a method which applied to every thing that could be done by that of Newton. This was his Differential Cal culus. The death of Oldenburg, which soon followed, put an end to this epistolary correspondence ; and seven years afterwards, viz. in 1684, Leibnitz published his me thod in the Leipsic Acts for October of that year, with this tide, " Methodus pro maximis ct minimis, itemque tangentibus, tpte nee fractas, nee irrationales quantitates moratur et singulare pro illis calculus genus." Thus, in whatever way Leibnitz came by his calculus ; whether he found it by the power of his own genius, which w as cer tainly very great, or availed himself of Newton's discove ry, which had in some measure transpired by his manu script memoir, "De analysi per equationes ?turner° termi forum in/initas," having been made known to many mathe maticians, although not printed ; certain it is, that his me thod was first given to the world ; for Newton's method of Iluxions only became generally known by the publication of his Princi/zia, in the end of the year 1686.
Leibnitz enjoyed, without contradiction, the honour of being the inventor of his calculus, until the year 1699; and even Newton himself, in the first edition of his Erin cipia, where he had occasion to give an example of his me thod of fluxions, allowed to Leibnitz the merit of his inven tion : For he says, " In the course of a correspondence, which ten years ago I carried on with the very learned geometrician Mr Leibnitz, having intimated to him that I possessed a method of determining maxima and minima, of drawing tangents, and resolving such problems, not only when the equations are rational, but also when they are irrational; and having concealed this method by trans posing the letters of the following sentence, An equation being given, containing any number of flowing quantities, to find their fluxions, and the contrary, this"celcbrated man answered, that he had found a similar method, which he communicated to me ; and which differed from mine only in the enunciation, and in the notation." To this, in the edition of 1714, was added, " and in the manner of con ceiving the quantities to be generated." It has been supposed that the claim of Leibnitz to the discovery would not have been called in question, if he had been just towards Newton : but in this respect he fail ed, and hence the origin of that quarrel which was carried on with such animosity between the British and foreign mathematicians. In some letters which he had written to persons in Britain, he had appeared to attribute to himself too exclusively the invention of his calculus, and this drew upon him some pointed remarks, respecting the prior claims of Newton. At length, a mathematician named Fatio de Duillier, who is said to have entertained a dislike to Leibnitz, on account of his having omitted to name him in an enumeration which he made of eminent mathemati cians, asserted, in a short tract on the curve of swiftest descent, and the solid of least resistance, that Newton was the first inventor of the new calculus, and that he would leave to others to decide what Leibnitz, the second inven tor, might have borrowed from the English geometer. To this attack Leibnitz gave a spirited answer, and complained to the Royal Society ; and there the dispute rested for a time. Afterwards, when Newton's treatise on the Quadra ture of Curves, and his Enumeration of lines of the third order, came out, in 1704, the Leipsic journalists gave an unfavourable account of it, and in effect said, that Newton had taken his method from that of Leibnitz, substituting fluxions for differences. This assertion called forth the in
dignation of the British mathematicians, and without doubt offended Newton himself. Accordingly, in 1708, Keill in serted in the Philosophical Transactions a paper, in which he stated formally, that Newton was the first inventor of the Fluxional Calculus, and that Leibnitz, in publishing it in the Leipsic Acts, had only changed the name and the no tation.
Leibnitz thus accused of plagiarism, addressed a letter to Hans Sloane, Secretary to the Royal Society, requiring that Kai should retract what he had said: But far from this, Keill replied in a long letter to Hans Sloane, in which he enumerated the reasons that led him to conclude, not only that Newton had preceded Leibnitz in the discovery,but that he had given so many indications of his method, as to bring it within the comprehension of a man of even mo derate capacity. This letter was sent to Leibnitz; who re quested that the Royal Society should put a stop to the clamour of a person, who was too young to know what had passed between him and Newton. The Royal Society judged that it would be proper to consult the original pa pers, and appointed a committee to select and examine them. The papers which they selected, were published by command of the Society, with this title, Commerciunz Epis tolicum de varia re Mathematica inter Ceteberrimos presentie Mathenzaticos, &c. And to this was added the report of time committee, which was to the following effect : " That Mr Leibnitz was in London in 1673, and went thence to Paris, where he kept a correspondence with Mr Collins, by means of Mr Oldenburg, till about September 1676, and then returned by London and Amsterdam to Hanover, and that Mr Collins was very free in communi cating to able mathematicians what he had received from Newton : That it did not appear that Mr Leibnitz knew any thing of the differential calculus, before his letter of the 21st of June 1677 ; which was a year after a copy of Newton's letter of the 10t December 1672 had been sent to Paris, to be communicated to him ; and about four years alter, Mr Collins began to communicate that letter to his correspondents, in which letter, the method of fluxions was sullicientiy described to any intelligent person : That Newton was in possession of his calculus before the year 1 669 ; and that those who had reputed Leibnitz the first inventor, knew little or nothing of his correspondence with Mr Collins and Mr Oldenburg long before, nor of New ton's having that method above fifteen y ears before Mr Leibnitz began to publish it in the LeipSic Acts: That for these reasons, they reckoned Newton the first inventor, and were of opinion that Mr Keill, in asset ting the same, had been in nowise injurious to Mr Leibnitz." In this report, the committee cautiously avoided giving any direct opinion upon the only point on which there could be any doubt, namely, whether Leibnitz had invent ed the calculus for himself, or had availed himself of the labours of Newton. The tcnour of their report seems to she•, that they were of the latter opinion. The Commer cium Epistolicum was circulated with great care over Eu rope, with a view to vindicate the claim of the British na tion, to the most important discovery that has ever been made in abstract science.