It was not to be supposed that Leibnitz would quietly submit to this decision, so unfavourable to his pretensions: He considered himself as grievously injured, and threaten ed to answer it in such a manner, as to confound his ad versaries. This feeling must have arisen from the insi nuation, that he had stolen the invention ; for, as to the right to priority of discovery, that is, beyond doubt, in fa vou• of Newton.
When this dispute was originally agitated, the natural feelings of patriotism, which protect nations against the encroachments and unjust pretensions of each other, pre vented that cool discussion which is necessary for the dis covery of truth. The British mathematicians were deci dedly averse to Leibnitz's claims, while the foreigners, on the contrary, supported them with as much acrimony as if it had been a dispute about a matter of faith rather than of testimony. Even Newton himself, who, for a time, does not appear to have taken an active part in the controversy, at last suppressed, in the edition of his Principia, printed in 1726, the passage he had inserted in the first edition, which admitted that Leibnitz had discovered the calculus by his own efforts. He probably' would have done this in the earlier edition of 1713, if it had not been brought out in a private manner by Crites and Bentley at Cambridge, while he was at a distance, with whose conduct, on this occasion, he was by no means pleased. It may be suppos ed, that, in suppressing the passage, he was actuated by a feeling of resentment for the undeserved abuse that had been bestowed on his writings by the friends of Leibnitz, and also by the unjustifiable conduct of that philosopher himself.
It is perhaps impossible now to determine with certain ty, were just grounds for the suspicion that Leibnitz had availed himself of Newton's invention. M on tucla, in his History of Mathematics, vol. ii. p. 381, 2d edit. says, "There are only three places of the Commer cium Epistolicum, which treat of flu4lons in so clear a way as to prove that Newton had found it before Leibnitz, hut too obscurely it seems to take from the latter the merit of the discovery. One of these is in a letter to Oldenburg, who had signified to Newton that Slussius and Gregory had each found a very simple way of drawing tangents. Newton replied, that he conjectured what the nature of that method was; and he gave an example of it, which spews that he was in possession of a method in effect the same as these two geometers had found. He adds, that this is only a particular case, or rather a corollary to a method much more general, which, without a laborious calcula tion, applies to the finding of tangents to all sorts of curves, geometrical or mechanical, and that without being obliged to free the equation from radicals. He repeats the same thing, without explaining himself farther, in another let ter; and he conceals the principle of the method under transposed letters. The only place where Newton has al lowed any thing of his method to transpire, is in his „dna lysis per vquationes numero ternzinorzenz infinitas. He here
discloses, in a very concise and obscure manner, his me thod of .fluxions ; but there is no certainty that Leibnitz saw this essay. His opponents have never asserted, that it was communicated to him by letter ; and they have gone no farther than to suspect that he had obtained a know ledge of it in his intercourse with Collins upon his second journey to London. Indeed, this suspicion is not entirely destitute of probability ; for Leibnitz admitted, that, in this interview, he saw a part of the Epistolary Correspondence of Collins. However, I think it would be rash to pro nounce upon this circumstance. If Leibnitz had confined himself to a few essays of his new calculus, there might have been some ground for that suspicion. But the nu merous pieces he inserted in the Leipsic Acts, prove the calculus to have received such improvements from him, that probably he owed the invention to his genius, and to the efforts he made to discover a method that had put Newton in possession of so many beautiful truths. This is so much the more likely, as from the method of tan gents discovered by Dr Barrow, the transition to the dif ferential calculus was easy, nor was the step too great for such a genius as that with which Leibnitz appears to have been endowed." In this opinion, we are disposed to agree with Montucla ; and we consider that we add to its weight by the following testimony in its favour, from one of the most elegant writers and able critics of the present time : celebrated La Place having asserted, in his Philoso phical Essay on Probabilities, that Fermat was the true in ventor of the Differential Calculus ; the writer to whom we have alluded, in a review of La Place's work, says, " Against the affirmation that Fermat is the real inventor of the differential calculus, we must enter a strong and so lemn protestation The age in which that discovery was made has been unanimous in ascribing the honour of it ei ther to Newton or Leibnitz; or, as seems to us much the fair est and most probable opinion, that is, to both, to each inde pendently of the other, the priority in respect of time being somewhat on the side of the English mathematician. The writers of the history of the mathematical sciences have given their suffrages to the same effect. Montucla, for instance, who has treated the subject with great impar tiality, and Bossut, with no prejudice certainly in favour of the English philosopher. In the great controversy to which this invention gave rise, all the claims were like ly to be well considered; and the ultimate and fair deci sion, in which all sides seem to have acquiesced, is that which has been just mentioned. It ought to be on good grounds, that a decision passed by such competent judg es, and that has been now in force for a hundred years, should all at once be reversed." Edinburgh Review, vol. xxiii. p. 324.