Catalogue Entry: OTHE00075
Chapter XIV
[1]
Guldinus gave this theorem in 1635, and seeing that he was acquainted with Pappus, Montucla and others were disposed to regard him as a plagiarist. Had they studied Pappus in Condamine's Latin, in place of that of Halley, they never would have known the theorem but from Guldinus.
[2]
Roberval's concealment of his discovery, and his forgery of a work of Arist{illeg}, greatly lower his credit, when he bears testimony in his own favour.
[3]
These methods were published in the sixth or supplemental volume of the second edition of Herigon's Cursus, Paris, 1644, 8vo; and an example was given by Schooten in the second edition of his Commentary on the second Book of Descartes's Geometry, in 1659.
[4]
Vol. i. pp. 23-26.
[5]
Vol. i. p. 36, and note 3, p. 27.
[6]
This task seems to have been pressed upon him by some friends in London. In sending to Collins the notes upon the book, in July 1670, he wishes his name to be suppressed, and suggests that in the title page, after the words Nunc e Belgico Latine versa, the words et ab alio authore locupletata should be added. In a letter to Collins, dated September 5, 1676, he thus speaks of the work: — "I have nothing in the press, only Kinckhuysen's Algebra I would have got printed here, to satisfy the expectation of some friends in London, but our press cannot do it. This, I suppose, is the book Dr. Lloyd means. It is now in the hands of a bookseller here to get it printed; but if it do come out, I shall add nothing to it." Maccles{illeg}eld Correspondence, vol. ii. p. 398.
[7]
Pemberton's Account of Sir Isaac Newton's Discoveries, Pref. p. 6.
[8]
It is entitled Method of Fluxions and Infinite Series. Lond. 1736, 1737, 4to.
[9]
Wallisii Opera, tom. i. Præf. pp. 2, 3; and tom. iii. cap. xciv. xcv. See also Letter Of Wallis to Newton, April 10, 1695, in Edleston's Correspondence, &c., p 809, and part of it in Raphson's Hist. of Fluxions, pp. 120, 121.
[10]
Newtoni Opera, tom. i. pp. 333-386.
[11]
Ibid. tom. i. pp. 531-560.
[12]
Ibid. tom. i. pp. 1-251.
[13]
He probably discovered them among the Lucasian papers when be succeeded Newton in that chair, and found his manuscript lectures.
[14]
Newtoni Opera, tom. i. pp. 388-519.
[15]
"Acutissimis qui toto orbe florent Mathematicis."
[16]
John Bernoulli had already published, in the Leipsic Acts for June, p. 266, a solution of the most simple case in which the exponent of the power was unity.
[17]
Acta Lipsiensia, in June, p. 269.
[18]
The original manuscript of this letter with the solution of the problem is preserved at the Royal Society; and one of the two papers, a folio printed half-sheet, still exists in their archives. At the bottom, in Newton's hand, are the words, "Chartam hanc ex Gallia missam accepi, Jan. 29, 1696-7." Edleston's Correspondence, &c., &c., p. lxviii. For a copy of the document, see Newtoni 0pera, tom. iv. pp. 411-418.
[19]
Dated London, March, 1716.
[20]
Wallis to Newton, April 10, 1695. See Edleston's Correspondence, pp. 301, 302.
[21]
Two years before this, in 1671, Leibnitz presented to the Academy of Sciences a paper containing the germ of the differential method, so that he must have been able to appreciate the information he received in England. — See page 80.
[22]
Dated February 3d and 20th, 1673.
[23]
March 30, April 26, May 26, and June 8, 1673.
[24]
July 15, 1673.
[25]
October 26, 1673.
[26]
May 20, 1675.
[27]
Henry Oldenburg, whose name is so intimately associated witli the history of Newton's discoveries, was born at Bremen, and was consul from that town to London during the usurpation of Cromwell. Having lost his office, and been compelled to seek the means of subsistence, he became tutor to an English nobleman, whom he accompanied to Oxford in 1656. During his residence in that city he was introduced to the philosophers who established the Royal Society, and, upon the death of William Crown, the first secretary, he was appointed, in 1663, joint secretary along with Mr. Wilkins. He kept up an extensive correspondence with more than seventy philosophers and literary men in all parts of the world, — a privilege especially given to the Society in their charter. The suspicions of the Government, however, were somehow or other, excited against him, and he was committed to the Tower on the 20th June 1667, "for dangerous designs and practices." Although no evidence was produced to justify so harsh a procceding, he was kept a close prisoner till the 26th August 1667, when he was discharged. "This remarkable event," as Mr. Weld remarks, "had so much influence on the society as to cause a suspension of the meetings from the 30th May to the 3d October." It is remarkable that there is no notice of this fact in the council or journalbooks of the Society.
Oldenburg was the author of several papers in the Philosophical Transactions, and of some works which have not acquired much celebrity. He died at Charlton, near Greenwich, in August 1678. See Weld's History of the Royal Society, vol. i. pp. 200-204.
[28]
This article was entitled "Nova methodus pro maximis et minimis, itemque tangentibus quæ nec fractas nec irrationales moratur, et singulare pro illis calculi genus, per G. G. L." — Acta Erudit. 1684, pp. 472, 473.
[29]
"A mea vix abludentem" — the same expression which Leibnitz used in his letter to Oldenburg of June 21, 1677, "ab his non abludere." The similarity of the Method of Fluxions and the Differential Calculus, may be considered as admitted both by Newton and Leibnitz.
[30]
These words were inserted in the 2d edition of the Principia.
[31]
Letter to the Abbé Conti, April 9, 1716, and to Madame de Kilmansegg, April 18, 1716.
[32]
We have, fortunately, Newton's own opinions on the subject. "And as for the scholium upon the second lemma of the second book of the Principia Philosophiæ Mathematicæ, which is so much wrested against me, it was written not to give away that lemma to Mr. Leibnitz, but, on the contrary, to assert it to myself. Whether Mr. Leibnitz invented it after me, or had it from me, is a question of no consequence; for second inventors have no right." — Raphson's History of Fluxions, 1715, p. 122, see also p. 115; and Newtoni Opera, tom. iv. p. 616.
[33]
In a manuscript of seven closely written pages, entitled, "A Supplement to the Remarks;" that is, to some observations upon Leibnitz's letter to Conti, dated 9th April 1716, published in Raphson's Fluxions, p. 111.
[34]
The title of this addition, which occupies more than a folio page, is, "In the end of the Scholium in Princip. Philos., p. 227, after the words, Utriusque fundamentum continetur in hoc Lemmate, add, Sunto quantitates datæ, a, b, c; fluentes x, y, z," &c.
[35]
A copy of this letter was sent to Tschirnhausen in May 1675, thirteen months before it was sent to Leibnitz.
[36]
"Doubts have been expressed," Mr. Edleston remarks, "whether these papers were actually sent to Leibnitz." That papers were sent and received by Leibnitz, his own testimony and that of others prove; but there is some reason to believe, as first indicated by Mr. Edleston, and made much more probable by Professor Do Morgan, that Newton's letter of the 10th December was sent, without the example of drawing a tangent to a curve, which it actually contained, and which was relied upon as giving Leibnitz a knowledge of the new calculus. In support of this opinion, we find that what are called the originals, said to have been received by Leibnitz, and Collins' draught of the papers preserved in the Royal Society, contain merely an allusion to that method. These originals have been printed in Leibnitz's Mathematical Works, published at Berlin in 1849, but fac-similes have not been given to enable us to judge of their genuineness. It is difficult to reconcile with these statements that of Newton himself, who declares that the originals of the letters in question were sent to Leibnitz in Paris to be returned, and that these originals were in the archives of the Royal Society. Leibnitz may have retained imperfect copies of these originals, which must have contained the method of tangents. If it be true that the original letters of Newton were sent to Leibnitz, we have nothing to do with the copies either at Hanover or the Royal Society.
With regard to the seven "study exercises by Leibnitz, on the use of both the differential and integral calculus," as Professor De Morgan calls them, dated November 11, 21, 22, 1675, June 26, July, November 1676, wliich were published by Gerhardt in 1848, we cannot, without seeing the originals or proper fac-similes of the hand writing, receive them as evidence. Gerhardt admits that some person had been turning the 5 of 1675 into a 3, (from an obvious motive;) and when we recollect how Leibnitz altered grave documents to give him a priority to Bernoulli, as we shall presently see, we are entitled to pause before we decide on any writings that have passed through his hands. But even if we admit these documents to be genuine, the allegation of Newton's friends that copies of his papers were in circulation before 1675, requires to be considered in the controversy. We recommend to the reader the careful study of Mr. Edleston's statement in the Correspondence of Sir Isaac Newton, p. xlvii., and of the very interesting paper by Professor De Morgan, on the Companion to the Almanac for 1852, p. 8.
To these observations we may ad, that Keill published in the Tournal Littéraire for May and June, 1713, vol. i. p. 215, the extract from the letter of December 10, 1672, as the chief document upon which the report of the committee of the Royal Society was founded, and at the same time distinctly stated that this letter was sent to Leibnitz. Now Leibnitz, as we know, read this letter, and never contradicted the allegation of Keill. If the paper actually sent to him had been merely an abridgment of that letter, from which the example was omitted, he would undoubtedly have come forward, and proved by the production of what he did receive, and what we know he possessed, that the principal argument used against him had no foundation.
Three years afterwards, in 1716, when Newton had challenged him to the discussion, he had another opportunity which he did not use, of disowning the reception of the letter
[37]
See APPENDIX, No. 1.
[38]
On a separate folio sheet I have found the following form of the scholium. The words in italics are not in the printed scholium, in which there is the word eandem here omitted. "In literis quæ mihi cum geometra peritissimo G. G. Leibnitio annis abhinc decem intercedebant, cum significarem me compotem esse methodi determinandi maximas et minimas, ducendi tangentes, quadrandi figuras curvilineas, et similia peragendi quæ in terminis surdis æque ac in rationalibus procederet, methodumque exemplis illustrarem sed fundamentum ejus literis transpositis hanc sententiam involventibus [Data æquatione quotcunque fluentes quantitates involvente, fluxiones invenire, et vice versa] celarem: rescripsit vir clarissimus, anno proximo, se quoque in ejusmodi methodum incidisse, et methodum suam communicavit a mea vix abludentem, pæterquam in verborum et notarum formulis. Utriusque fundamentum continetur in hoc Lemmate." This copy does not contain the few words added in the second edition of the Principia.
[39]
In the Acta Eruditorum for January and February 1689, Leibnitz published two papers, one "On the Motion of Projectiles in a resisting Medium," and the other, "On the Causes of the Celestial Motions." Newton regarded the propositions in these papers, and in a third, De Lineis Opticis, as plagiarisms from the Principia, Leibnitz, as he said, "pretending that he had found them all before that book came abroad," and "to make the principal proposition his own, adapting to it an erroneous demonstration, and thereby discovering that he did not yet understand how to work in second differences. — See Raphson's Fluxions, p. 117; and Recensio Commercii Epistolici; Newtoni Opera, tom. iv. p. 481, No. lxxii.
[40]
See APPENDIX, No. 11. "At the request of Dr. Wallis," says Newton, "I sent to him in two letters, dated 27th August and 17th September, 1692, the first pro position of the Book of Quadratures, copied almost verbatim from the book, and also the method of extracting fluents out of equations involving fluxions, mentioned in my letter of 24th October, 1676, and copied from an older paper, and an explication of the method of fluxions direct and inverse, comprehended in the sentence, Data equatione, &c. &c., and the Doctor printed them all the same year, (viz. anno 1692) in the second volume of his works, pp. 391-396. This volume being then in the press, and coming abroad the next year, two years before the first volume was printed off and this is the first time that the use of letters with pricks, and a rule for finding second, third, and fourth fluxions, were published, though they were long before in manuscript. When I considered only first fluxions, I seldom used letters with a prick; but when I considered also second, third, and fourth fluxions, &c., I distinguished them by letters with one, two, or more pricks; and for fluents I put the fluxions either included within a square, (as in the aforesaid analysis,) or with a square prefixed as in some other papers, or with an oblique line upon it. And these notations by pricks and oblique lines, are the most compendious yet used, but were not known to the Marquis de l'Hospital when he recommended the differential notation, nor are necessary to the method." A Supplement to the Remarks, p. 4.
[41]
Acta Eruditorum, Jan. 1691, p. 14.
