‘There are great alterations in the geometry of late’. The rise of Isaac Newton’s early Scottish circle

Abstract

This paper traces the rise of three Scottish mathematicians – Colin Campbell, John Craig, and David Gregory – to become key figures in the dissemination and promotion of Newton’s mathematical ideas and natural philosophy in the 1680s. Two medical men – Archibald Pitcairne and his former student George Cheyne – both likewise captivated by the Principia, played minor roles in the story of Newton’s mathematics, while at the same time promoting the concept of mathematical medicine derived from his philosophical thought. Drawing on contemporary correspondence and previously unpublished papers, it considers how these men contributed to the scholarly perception of Newton and how, conversely, Newton used his increasing influence in order to encourage their work, most notably obtaining for Gregory the vacant chair in astronomy at Oxford in 1691.

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No potential conflict of interest was reported by the author.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Notes

1 Between James Gregory’s death and David Gregory’s appointment to the Edinburgh professorship the teaching duties of the professor of mathematics had been carried out by John Young.

2 ‘Invenienda itaque erat methodis istis seriebus producendis apta, quam etiam illustravimus elegantioribus aliquot exemplis figurarum quarum, apud Geometras frequentior et celebrior est contemplatio, quamque ingenuis candidorum Geometrarum et benevolis studiis hic exponimus’ (Gregory 1684, 4). After James Gregory’s death, his mathematical books and papers passed to his nephew.

3 Friesen (2003) argues that the receptivity of Scottish Episcopalians to new philosophical ideas of Cartesianism or Newtonianism was considerably greater than that of their English High-Church counterparts. Elsewhere, Friesen (2008) has explored the particular role that Christ Church, Oxford played in the promotion of Newtonianism.

4 Arbuthnot’s first (1692) publication appears to have come about through his studies under Gregory: see (Shuttleton 1995, 49).

5 See for example David Gregory to Colin Campbell, 16/[26] December 1687 and David Gregory to Colin Campbell, 11/[21] May 1689; Edinburgh University Library MS 3099.11, No. 10 and No. 15.

6 David Gregory to Colin Campbell, 5/[15] March 1685; University of Edinburgh Library MS 3099.11, No. 14.

7 ‘Ac quod proinde (per annot. 5) omnium aequationum, omnes possibiles expressiones Analyticas Radicum, hac Methodo exhibere possim, prout suo loco diffusius explicabo’ (von Tschirnhaus 1683, 207).

8 David Gregory to Colin Campbell, 12/[22] May 1685; Edinburgh University Library MS 3099.11, No. 13.

9 David Gregory to Colin Campbell, 25 February/[7 March] 1686; Edinburgh University Library MS 3099.11, No, 17.

10 David Gregory to Colin Campbell, 11/[21] February 1687; Edinburgh University Library MS 3099.11, No. 19.

11 ‘The not printing my new methode of quadratures is not I assure you ane effect of lazines, nor yet of further improvement of it, but of ane absolute impossibilitie to apply my selfe for want of time which the colledge is sitting. Besides, I would gladly see Newtons methode which I am certainly informed will be published in that Astronomie, of which I have hade no further account, but expects it shortly.’ David Gregory to Colin Campbell, 11/[21] February 1687; Edinburgh University Library MS 3099.11, No. 19.

12 The Tractatus de quadratura curvarum was the second of two additional tracts, the first being the Enumeratio linearum tertii ordinis.

13 Gregory’s publication was hosted by his friend Pitcairne in his (1688, 9–10); on this episode see (Hearne 1885, 90): ‘[…] and that some Scotch men. (who would make a great Figure in Mathematical Learning) got access to them [sc. Newton’s lectures], & transcrib’d abundance of things out of them, which afterwards they publish’d as their own Inventions, getting Credit and Repuatation in the World by stealing another man’s Works, without any manner of Acknowledgment.’

14 David Gregory to Colin Campbell, 25 January/[4 February] 1686; Edinburgh University Library MS 3099.11, No. 11.

15 David Gregory to Colin Campbell, 25 February/[7 March] 1686; Edinburgh University Library MS 3099.11, No. 17.

16 See also his letter to Colin Campbell, dated 4/[14] October 1686; Edinburgh University Library MS 3099.11, No. 18:

Mr Newton in Cambridge hath just now published a book of Astronomie. it will containe many miscellanea. I shall give you ane account of it by the first occasion, for I recieved yours but this morning and am by the bearer limited to nine aclock.

17 David Gregory to Colin Campbell, 11/[21] February 1687; Edinburgh University Library MS 3099.11, No. 19. The publication to which Gregory evidently referred was (Clüver 1686); see (Mancosu 1996, 156–159).

18 Keill was appointed Savilian professor of astronomy at Oxford following the death of John Caswell in 1712. He had already followed Gregory in migrating from Balliol to Christ Church in 1703. See (Westfall 1980, 697; Guerrini 1986, 305–308; Friesen 2008, 42).

19 Gregory’s original manuscript is now Royal Society MS 210. Other transcripts are at Oxford, Christ Church Library MS B.13.cxxxi; Edinburgh University Library MS DC.4.35, and University of Aberdeen Library MS 465. See (Guicciardini 1999, 179–184).

20 At the May meetings Newton communicated to Gregory many of his ideas on a Prisca philosophia, leading him to assert that Newton’s revised third hypothesis in Book III of the Principia, that is, ‘Corpus omne in alterius cujuscunque generis corpus transformari posse, & qualitatum gradus omnes intermedios successive induere’, would show ‘that the most ancient philosophy is in agreement with this hypothesis’. See (Newton 1959–77, vol 3, p 384 (David Gregory, Memorandum, c. July 1694); Friesen 2008, 50).

21 David Gregory to Colin Campbell, 16/[26] December 1687; Edinburgh University Library MS 3099.11 No. 10: ‘I beleeve Newton will take you up the first month you have him’.

22 See David Gregory to Colin Campbell, 4/[14] October 1686; University of Edinburgh Library MS 3099.11, No. 18.

23 David Gregory to Colin Campbell, 29 January/[8 February] 1689; Edinburgh University Library MS 3099.11, No. 12: ‘I am sorry that the smallness of its volume should make it obscure, but I hope that after 2 or 3 letters enterchanged it shall be plain enough.’

24 ‘Sed et Craigius vester annis abhinc sex diutius apod nos commoratus, MSS mea inspexit (ut ipse in libro suo tunc edito fatetur) qua tempestate quadraturam meam curvae illius ad vos transmisit de qua cum disputatio epistolaris suborta esset quadraturam curvarum denuo aggressus es et in seriem meam vidisse confirmaret cum ipse nec litem ea de re ab illo motam esse nec te seriem invenisse prius didiceras. Sed ut postulato tuo jam satisfaciam describenda sunt verba epistolae. Et quoniam ea quae de quadratura cur[v]arum aliquando fortean communicabo pendent a methodo quadam analytica quam subo[b]scure illic attingebam. Describam quoque quae ad hanc methodum spectant. Methodi hujus initia excogitavit Fermatius et Slusius promovit. De quodam igitur tractatu quem annis abhinc viginti de seriebus infinitis et methodo fluentium quantitatum conscripseram, sed ob ingruentes quasdam de luce et coloribus disputationes imperfectum reliqueram verba faciens et methodum illam cum Slusiana quoad Curvarum tangentes ducendas coincidere praeterquam quod mea ad quantitates surdas non haereret. Eandem quoque a me auctam fuisse sic commemorabam.’

25 ‘Hanc ille Seriem tum soli mihi notam putabat, at paullo post rescivit Seriem eandem prius notam fuisse summon illi Philosopho & Geometrae D. Isaaco Newtono, qui ad eam diversa methodo ante, ut opinor, pervenerat. Profecto reipublicae literariae interest, ne Methodus illa diutius premature, sed potius ut edition matura non minus innotescat Methodus Newtoniana, quam hactenus innotuit nostra’: p 380.

26 ‘The president gave leave to Mr. Gregory, a nephew of Mr. Gregory the professor of mathematics at Glasgow, to be present at this meeting’: (Birch 1756–7, vol 4, p 84).

27 Shuttleton (1995, 52) points out that Gregory’s legally skilled friend Pitcairne played an important role in defending him aginst these charges.

28 As Bernard was able to point out at the time, Oxford had thrown its weight behind Caswell, but the intentions of Gilbert Burnet and others in London were unclear. See Edward Bernard to Thomas Smith, 17/[27] July 1691; Oxford, Bodleian Library MS Smith 47, pp 103–4: ‘This place is inclin’d to Mr Caswell for the Astronomy lecture & accordingly hath recommended him to the Electors: what the Bishop of Sarum & others do for their countryman Mr Gregory, is better known at London.’ See also his letter to Smith, 30 June/[10 July] 1691; MS Smith 47, pp 179–80:

[…] the Lord Bishop touching the irreligion & even blasphemous discourses of Mr Haley, otherwise a most able astronomer, will not easily be granted. So the place is left for Mr Caswell a sober, pious & skilfull person to try his interest in competition with Mr David Gregory, who is also a good mathematician.

29 See Thomas Smith to Edward Bernard, 11/[21] July 1691; Oxford, Bodleian Library MS Smith 57, pp 219–20:

I am very sorry, that Mr Haly his Skepticall and Atheisticall discourse has rendred himselfe so obnoxious for the just censure of the world: & I beeleive there is such a deep prejudice against him, that it will put him wholly by his pretensions of succeeding you: for which otherwise by reason of his excellent skill in Astronomy and other Mathematical learning hee is so highly qualified.

30 The Oxford mathematician Stephen Jordan Rigaud found little evidence to support the accusation against Halley. See (Rigaud 1844).

31 Edward Bernard to Thomas Smith, 30 June/[10 July] 1691; Oxford, Bodleian Library MS Smith 47, pp 179–80.

32 Arthur Charlett to Humfrey Wanley, 30 December 1702/[9 January 1703]; London, British Library Add. MS 70477 (Loan MS 29/253), not foliated.

33 See Edward Bernard to Thomas Smith, 17/[27] December 1691; Oxford, Bodleian Library MS Smith 47, pp 199–200: ‘Mr Caswell desists, so that my place lyes between Mr Gregory & Mr Haley. The latter hath written me a letter this weeke to recommend him againe to the Electors, but his name is not in the highest order’.

34 Arthur Charlett to Humfrey Wanley, 30 December 1702/[9 January 1703]; London, British Library Add. MS. 70477 (Loan MS 29/253), not foliated.

35 ‘Et quod Omnes Oculati vident Ratio qua Scientia phisica in Culmen hic perducta sit, exteris invidiosum’.

36 ‘Atque hujusce unius problematis confectionem tanti habuerunt exteri, ut post illud ante quatuor annos hic editum, Magni Nominis Geometra Gothofredus Leibnitius ejus pro modulo suo constructionem ediderit non absque paralogismi labe.’

37 Archibald Pitcairne for David Gregory, 15/[25] October 1695; Edinburgh University Library Dk.1.2¹, Quarto A, f. 94.

38 Archibald Pitcairne to Colin Campbell, 1/[11] October 1703; Edinburgh University Library MS 3099.18, Colin Campbell Collection; (Pitcairne 1979, 38–39).

39 David Gregory to Colin Campbell, 25 October/[4 November] 1703; Edinburgh University Library MS 3099.11, No. 22. The article to which he referred was (Craig 1703).

40 Archibald Pitcairne to Colin Campbell, 1/[11] October 1703; Edinburgh University Library 3099.18.

41 Archibald Pitcairne to Colin Campbell, 1/[11] October 1703; Edinburgh University Library 3099.18. On the concerns of Newton’s Scottish circle see (Friesen 2008, 52–53). As Friesen points out, Keill in particular felt that Leibniz’s philosophy could serve as a medium for introducing materialist or pantheistic conceptions of nature.