PHYSICAL SCIENCE. 



Newton was the first discoverer, and Leibnitz 

 the second ; both were originals, and both inde- 

 pendent of each other. The algorithm of Leib- 

 nitz was much more perfect than that of Newton ; 

 and it had the great advantage of being first 

 made known to the world an account of it 

 having been inserted in the first volume of the 

 Acta Eruditorum, for 1684. 



Thus, while Newton's discovery was known 

 only to a few friends, Leibnitz's was rapidly 

 spread over the continent. John and James 

 Bernoulli joined their talents to those of the 

 original inventor, and illustrated the new method 

 by the solution of a great number of difficult and 

 interesting problems. Leibnitz's methods ac- 

 quired perfection, while those of Newton remain- 

 ed unknown. The first work on the new 

 geometry, was by Craig, who drew his informa- 

 tion from the writings of Leibnitz and his friends. 



Nothing however like hostility appeared be- 

 tween the two great discoverers, and Newton in 

 the passage of the Principia above referred to, 

 gives a highly favourable opinion on the subject 

 of the discoveries of Leibnitz. A remark of 

 Fatio de Duillier, in a paper presented to the 

 Royal Society in 1699, lighted up a flame which 

 a whole century has been scarcely sufficient to 

 extinguish. In a paper on the line of swiftest 

 descent, there occurred this sentence, " I hold 

 Newton to have been the first inventor of this 

 calculus, and the earliest by several years, in- 

 duced by the evidence of facts ; and whether 

 Leibnitz, the second inventor, has borrowed any 

 thing from the other, I leave to the judgment of 

 those who have seen the letters and manuscripts 

 of Newton." Leibnitz replied to this charge in 

 the Leipsic Journal, without any asperity, simply 

 stating himself to have been, as well as Newton, 

 the inventor. 



In the year 1705, on the publication of New- 

 ton's Quadrature of Curves, the same journalists 

 insinuated, though with politeness and ambiguity, 

 that Newton had been led to the notion of fluxions 

 by the differentials of Leibnitz; just as Honora- 

 tus Fabri had been led to substitute the idea of 

 progressive motion, for the indivisibles of Caval- 

 leri. A charge so entirely unfounded, could not 

 but call forth the indignation of Newton and his 

 friends. In that indignation they were perfectly 

 justifiable. But when the passions are heated, 

 the injustice on one side is generally retali- 

 ated by an equal piece of injustice on the 

 other. Accordingly, Keill who undertook the 

 defence of Newton's claims, instead of en- 

 deavouring to establish the priority of his dis- 

 coveries by an appeal to facts Jind to dates that 

 could be accurately ascertained ; undertook to 

 prove- that the communications of Newton to 

 Leibnitz, were sufficient to put the latter in 



possession of the principles of the new analysis, 

 after which he had only to substitute the notion 

 of differentials, for that of fluxions. But in 

 support of these charges he had nothing to offer 

 but equivocal facts, and overstrained arguments, 

 capable of convincing those only, who were 

 already disposed to believe. They were accord- 

 ingly received as accurate in England ; rejected 

 as absurd in Germany, and read without con- 

 viction by the mathematicians of France and 

 Italy. 



Leibnitz complained of Keill's statements to the 

 Royal Society of London, who declined giving 

 any opinion ; but appointed a committee of its 

 members to draw up a full and detailed report of 

 all the communications which had passed between 

 Newton and Leibnitz, or their friends, on subjects 

 connected with the new analysis, from the time 

 of Collins and Oldenburgh, to the date of Keill's 

 letter to Sir Hans Sloane in 1711, of which 

 Leibnitz had complained. This report forms 

 what is called the Commercium Epistolicum. It 

 was published the year following by order of 

 the Royal Society and, though in the main just 

 and fair, seemed rather to lean to the side of 

 their own president. Leibnitz complained of 

 this publication, and alleged, that though nothing 

 was inserted which was not contained in the 

 original epistles, yet certain passages were sup- 

 pressed which were favourable to his pretensions. 

 He threatened an answer, but it never appeared. 

 Some notes were added to the Commercium 

 Epistolicum, which contained a good deal of 

 asperity, and the review of this book inserted in 

 the Philosophical Transactions for 1715, is still 

 more liable to the same censure. 



In the year 1713, a paragraph was circulated 

 among the mathematicians of Europe, written 

 by John Bernoulli. It amounted to this, " That 

 there is no reason to believe that the fluxionary 

 calculus was invented before the differential." 

 Bernoulli was doubtless well acquainted with the 

 subject; but he was too much connected with 

 Leibnitz, and had contributed too much to the 

 progress of the differential calculus, to be an 

 impartial judge. 



The German mathematicians injured their 

 own cause by attempting to fix on Newton a 

 charge of plagiarism, which could be so trium- 

 phantly refuted. As much were the English 

 mathematicians to blame when they retorted the 

 same charge upon Leibnitz. It was not indeed 

 physically impossible that Leibnitz might have 

 borrowed his calculus, as Newton undoubtedly 

 preceded him ; but the assertion is not supported 

 by the slightest shadow of a proof. 



We shall pass over the subsequent defiances 

 which passed mutually between the English and 

 Continental mathematicians, and the harsh and 



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