An unpublished autograph by Christiaan Huygens: His letter to David Gregory of 19 January 1694

References

• Oxford, Bodleian Library 290 291 MS Tanner 25 (See also footnote 15.) We are grateful to the Bodleian Library for permission to publish this letter. The authors are grateful to Miss S. M. McNab (Utrecht University) for linguistic improvements.
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• Hall , M.B. 1980 . “ Huygens' scientific contacts with England ” . In Studies on Christiaan Huygens Edited by: Bos , H.J.M. , Rudwick , M.J.S. , Snelders , H.A.M. and Visser , R.P.W. 66 – 82 . Lisse in
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• Guerrini A. Newtonian Matter Theory, Chemistry, and Medicine, 1690–1713 Indiana University 1983 PhD dissertation and ‘The Tory Newtonians: Gregory, Pitcairne, and their circle, Journal of British Studies, 25 (1986), 288–311; also R. E. Schofield, Mechanism and Materialism: British Natural Philosophy in an Age of Reason (Princeton, New Jersey, 1970), pp. 40–62.
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• Gregory to Huygens, The Correspondence of Isaac Newton Turnbull H.W. Cambridge 1693 August 12/22 1959– [hereafter Correspondence], iii, 1688–1694 (1961), 276–7.
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• This is evident from notes made by Gregory during his visit and published in Correspondence III 272 275 see especially p. 274, note 1. See also Huygens to L'Hospital, 23 July, 1693, Oeuvres complètes de Christiaan Huygens, publiées par la Société Hollandaise des Sciences, 22 vols (The Hague, 1888–1950) [hereafter Oeuvres], x, 462.
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• Huygens . Oeuvres , X 462 – 463 . note 19. See also ibid., pp. 471–3.
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• Correspondence , III 275 – 275 . 277 (‘breviter alteram Methodi meae quadraturarum conditionem explicatam dedi’).
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• Correspondence , III 275 – 275 . ‘cuidam (ut postea intellexi) minus diligenti’. In the draft at Edinburgh (see footnote 9) the following phrase is crossed out: ‘mercatori cuidam haec leviora forsan’.
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• London, Royal Society 81 81 MS 247 (Gregory Volume) Edinburgh, University Library, MS Dc 1.161, 1801. (We are grateful to Edinburgh University Library for sending a copy of this draft, as well as some other papers concerning Huygens.) The first draft (London) is dated Oxford 12–22 August 1693. The second (Edinburgh) omits the mathematical part, and seems to preserve an earlier version. However, it bears the dates ‘Calendas Septembris’ (preceded by an ‘X’ and a large space; it might therefore also be read as ‘X Calendas Septembris’) on the front, and ‘10 September’ both on the front and the back.
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• Correspondence , III 275 – 278 .
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• In the draft at Edinburgh the following phrase has been crossed out: ‘fateor Nob. Vir. nec etiam methodo Newtoniano cessuram credo’. The back of the draft contains calculations on these two curves Edinburgh University Library MS Dc. 1.161.1802)
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• Wallis , Joannis . 1793 . De algebra tractatus; historicus & practicus Oxford reprinted Hildesheim/New York, 1972). This is the second volume of Wallis's Opera mathematica. Gregory's method, in the form of a letter from Gregory to Wallis, is on pp. 377–80. The extracts from Newton's work are on pp. 390–6.
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• Huygens to L'Hospital, Oeuvres July 1693 X 464 464 23 Huygens wrote that he had not received anything at that moment. See The Mathematical Papers of Isaac Newton, edited by D. T. Whiteside, vii (Cambridge, 1976), 10, note 33.
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• Huygens to Fatio, Oeuvres November 1693 X 567 567 30
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• Hackman , A. 1860 . Catalogi codicum manuscriptorum bibliothecae Bodleianae, IV: Codies viri admodum reverendi Thomae Tanneri, S.T.P. episcopi Asaphensis, complectens Oxford reprinted 1966), p. 976. It is not known how the letter arrived there. The Tanner manuscripts contain a few other letters to Gregory, all by Dutchmen.
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• A probable candidate would be Joannes Olyphant, who matriculated at Leiden University on 4 December 1693. Gregory had married into the Olyphant family. See Guerrini Newtonian matter theory Indiana University 1983 111 112
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• Huygens Oeuvres July 1693 X 462 463 23 Huygens did not give the rule itself, but simply stated to what kind of curves it applied.
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• Huygens Oeuvres August 1693 X 482 484 10 See further, ibid., pp. 492–3, 523, 549–50.
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• Oeuvres November 1693 X 565 565 25 ‘Au reste toutes ces suittes ne sont point necessaires lorsque c est un nombre entier, car je puis toujours prouver alors les quadratures sans en avoir besoin.’
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• Pitcairne had been Professor of Medicine at Leiden University from 1692 to 1693. He did not return from his holiday in Scotland in 1693. During his holiday, he married Elizabeth Stevenson, to whom he had been engaged before leaving for Leiden. It was said that he did not return to his chair because Elizabeth refused to follow her husband abroad. See Lindeboom G.A. Pitcairne's Leyden interlude described from the documents Annals of Science 1963 19 273 284 (p. 282). See also Guerrini, ‘The Tory Newtonians’ (footnote 3), p. 303.
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• For this project, see Westfall R.S. Never at Rest: A Biography of Isaac Newton Cambridge 1980 506 507 and I. Bernard Cohen, Introduction to Newton's ‘Principia’ (Cambridge, 1971), pp. 188–98.
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• These are Divers ouvrages de mathematique et de physique par Messieurs de l'Academie Royale des Sciences Paris 1693 Recueil d'observations faites en plusieurs voyages par ordre de Sa Majesté, pour perfectionner l'astronomie et la geographie. Avec divers traitez astronomiques. Par Messieurs de l'Academie Royale des Sciences (Paris, 1693); Veterum mathematicorum Athenaei, Bitonis, Apollodori, Heronis, Philonis, et aliorum opera, graece et latine pleraque nunc primum edita, ex manuscriptis bibliothecae regiae (Paris, 1693). The first work, contained, pages 303–36, several pieces by Huygens, who had sent them to De la Hire in 1687. See the correspondence in Oeuvres, ix, 91–2, 95–7, 167 (8 and 26 September 1686, 20 June 1687).
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• Philosophical Transactions 1673 8 97 and 98 contain a discussion between Sluse and Huygens about Alhazen's problem, with Oldenburg acting as go-between. Huygens probably refers to his letter on pages 6143–4, which is not from 1673, but from 1672, July 1. It is also printed in Oeuvres, vii, 187–9, and in The Correspondence of Henry Oldenburg, ix, 120–5 (with translation). The solution in Divers ouvrages, 336, has been reprinted in Oeuvres, xx, pp. 270–1. On its provenance, see ibid., p. 207. See also ibid., pp. 218, 265–9, 328–33. For Huygens's dissatisfaction with the publication, see Huygens to L'Hospital, Oeuvres, x, 497 (3 September 1693) and Huygens to De la Hire, ibid., p. 548 (5 November 1693).
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• Concerning this watch, see Oeuvres XVIII 592 596 and the notes (with drawing) Gregory made on it resulting from his visit to Hofwijk on 6 June 1693 (Edinburgh University Library, MS Dk 1.21.A41). The instrument maker concerned was Bernardus van der Cloesen. It was a sea-watch for finding longitude at sea, but it never seems to have been offered to the authorities for their consideration. Over the years, Huygens had spent much time and energy on the problem of longitude, but he was never really successful. See M. S. Mahoney, ‘Christiaan Huygens: The measurement of time and of longitude at sea’, in Studies on Christiaan Huygens (Lisse, 1980), pp. 234–70; and J. H. Leopold, ‘Christiaan Huygens and his instrument makers’, ibid., pp. 221–33.
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• 1689 . De la théorie de la manoeuvre des vaisseaux Paris a work by B. Renau, published anonymously. Its title page bears the words: ‘De l'expres commandement de sa majesté’. Huygens's refutation was published in the Histoire universelle et historique of September 1693. See the text in Oeuvres, x, 525–31, and the correspondence with L'Hospital on the subject, ibid., pp. 478, 523, 464–5. In 1694 the matter still gave rise to polemics. Renau's answer is printed ibid., pp. 588–696, Huygens's rejoinder pp. 654–8, a further reaction by Renau pp. 690–3. See also pp. 585, 624, 686, 694–5, 705–6.
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• Huygens's . Cosmotheoros sive de terris coelestibus, earumque ornatu, conjecturae which was to appear posthumously at The Hague in 1698.
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• See Wallis Joannis De algebra tractatus; historicus & practicus Oxford 1793
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• Edinburgh 1688. We have not been able to trace a copy of this paper, nor of its re-edition at Leiden in 1693. Both editions are mentioned in Pitcairne's Opera omnia The Hague 1722 (2 parts which do contain the paper, but nothing by Gregory; probably Gregory's series was left out by the editor as not being by Pitcairne.
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• The Mathematical Papers of Isaac Newton Vol. VII , 3 – 10 . Also discussed in Westfall (footnote 22), pp. 400, 469–70, 513–14.
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• No. 2812. Oeuvres X 471 473 The editors of the Oeuvres say that this document is ‘probablement de la main de David Gregory’. They print it as an appendix to Huygens's letter to L'Hospital (No. 2810, 23 July 1693). Publishing it at this position is logically correct (for the subjects of the letters 2810 and 2812 agree), but the chronology cannot be right, since Huygens first revealed the contents of Gregory's method in his letter of 3 September 1693 (Oeuvres, X, 492–3). It is possible that the document was written by Gregory, particularly because of its contents, but after comparing the handwriting we remain in doubt. In a private communication J. G. Yoder (Renton, WA) points out that a third person, Pitcairne for example (see footnote 4), may have written No. 2812, which would explain the reference to Gregory (‘iuxta Canonem Gregorianum’). We have not yet been able to check this suggestion.
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• It is discussed, together with a modern proof based on partial integration, in Oeuvres x 473 473 note 5
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• Correspondence , III 278 – 278 . note 4
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• Huighens , Hubertus . Paucæ quædam Observationes circa Proportionem, quam ad Rectilineas habent Figuræ Curvilineæ, breviter traditæ Medioburgi [i.e. Middelburg], Apud Simonem Brulois, Bibliopolam aan de groote Beurs. [1692]. Thanks to the help of P. M. Gouk (Oxford) we could consult the copy at Oxford, Christ Church (AG.5.12(3)), which is said to be the only surviving copy.
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• Correspondence III 276 277 the antiderivative of The area of the other curve has logarithmic divergence as well, but of lower order a 2 ln |x 2 - a 2| (in both cases for x→a).
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• For further details and references to Huygens's notebooks, see Oeuvres X 462 463 For Gregory's calculations, see above, footnote 11.
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• Letter of 24 June 1687; Oeuvres IX 167 171
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• Oeuvres , X 457 – 468 .
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• Repeatedly, even in his letter of 23 July 1693 to L'Hospital. Oeuvres X 457 468
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• Letters of 23 July and 3 September 1693, Oeuvres X 464 468 493-4
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• Letters of 22 October and 29 December 1692 Oeuvres X 328 328 352-353
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• Letter of 12 May 1693 Oeuvres X 446 451 In a commentary to this letter the editors show in note 12 how both differential equations can be solved with modern techniques.
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• Oeuvres , X 511 – 511 .
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• Oeuvres , X 538 – 543 .
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• See Oeuvres X 542 542 note 18
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• Oeuvres , X 609 – 615 . Because of differences between the draft, preserved in Leiden, and the letter that Huygens sent, we also consulted a copy of the actual autograph letter, preserved in the Niedersächsische Landesbibliothek Hannover. We are grateful to J. G. O'Hara of the Hannover Leibniz Archiv for supplying this copy.
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• In his letter of 11 October Oeuvres X 539 539 Leibniz had paid Huygens a compliment that started with the solemn Latin words (in a letter the rest of which was in French) ‘Voti damnatus sum’', i.e. ‘My wishes have been fulfilled’, and continued ‘that you have decided to make use of my calculus’.
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• Leiden University Library Hug. 45; see also Oeuvres, X, 610, note 15.
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• Found in Oxford, Bodleian Library 290 – 291 . MS Tanner 25
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