The Study of Thomas Harriot's Manuscripts

Expectations were raised notably, and in succession, by Artis analyticae Praxis … Tractatus e posthumis Thomae Harriott … schediatismi … descriptus (London, 1631) 180; Birch Th. , The history of the Royal Society (London, 1756) 120; von Zach X. , “Anzeige von den in England aufgefundenen Harriotschen Manuscripten” … London 26 Nov. 1784 in Bode's J. E. Berliner astronomisches Jahrbuch … (Berlin, 1785) 153; Hutton Ch. , A mathematical and philosophical dictionary, i (London, 1795) 584; Stevens H. (posth.), Thomas Harriot, the mathematician, the philosopher, the scholar developed chiefly from dormant materials (London, privately printed, 1900) 187; Quinn D. B. , The Roanoke voyages I (London, Hakluyt Soc., 1952) 3.

Guildhall Library, London, MS 9052, box V (1618–1623), and MS 9051, vol. vi, resp. (Archdeaconry of London Court Records). The Will is reproduced in the appendix to Tanner R. H. C. , “Thomas Harriot as mathematician—a legacy of hearsay; part i”, Physis, ix (1967), 235–247.

Stevens , op. cit., n. 1. For biographical details on Stevens, see the Preface by his son, and Boase F. (ed.), Modern English biography iii (1965) 739.

Clerke A. M. (1842–1907), author of the popular History of astronomy during the 19th century (London, 1885), contributed a number of excellent articles to the Dictionary of National Biography (London, 1885–1900) and is herself the subject of one in the new edition (1908).

Rigaud S. J. , Stephen Peter Rigaud, a memoir (Oxford, privately printed, 1883) 39.

Bodleian Library, Oxford, MSS Rigaud 1–62, esp. MS 35. (Nos 26203–26261 in Summary catalogue of western manuscripts.) Presented in 1874 to the Savile Library, Oxford, by two sons, John and Gibbes Rigaud, and passed to the Bodleian in 1884.

Historical MSS Commission Leconfield 241, Petworth bundle vii, Letters from S. P. Rigaud to Rev. T. Sockett, 23 July 1831; 25 July and 25 Aug. 1932.

Information on wills has been taken principally from B. G. Bouwen, revised by Camp A. G. , Wills and their whereabouts (1963) iii, ix; and Montague F. C. , Law reform 1800–1885, 543 in Trail H. D. Mann J. S. (ed.). Social England, vi (London, 1904). Also relevant is Burn R. , Ecclesiastical law, 4th ed., iv (London, 1731), art. “Wills”, esp. 179, 180, 206, 208.

Parliamentary papers, vol. xix, Session 5 Febr.–23 July 1830, pp. 47 sqq.

Bodleian Library MS Rigaud 35, f. 179 (f. 68 in Rigaud's numbering of a batch on “Thomas Harriot and Sir William Lower”), Oct. 1835.

Ibid. f. 220 in “Particulars respecting Harriot in addition to the Accounts which have been published of him” (ff. 214–235, undated).

Moore P. C. , Registrar, Doctor's Commons 29 Jan. 1830 in op. cit. n. 9, 88, 89.

Recollections of Mr James Lenox of New York and the formation of his library (1886), quoted in Dictionary of American Biography, xvii (1935), art. “Henry Stevens”, 611–612.

Public & General Acts 20 & 21 Vict. c. 77, 710, III, IV.

Ibid. 716, xxvi.

Needham R. Webster A. , Somerset House, past and present (London, 1905) 245, 259. Public & General Acts 36 & 37 Vict. c. 66, esp. 45, 92, “Transfer of books and papers to supreme court”.

Stevens , op. cit. n. 1, 166 and 203.

Ibid. 166–167.

Information kindly communicated by the Librarian, The Guildhall, London, by letter 20 October 1967, and quoted with permission.

Shirley J. W. , “The scientific experiments of Sir Walter Ralegh, the Wizard Earl and the three Magi in the Tower 1603–1617”, Ambix, iv (1949–51) 59, n. 34.

Information kindly communicated by the Librarian, The Guildhall, London, by letter 23 November 1967. The Public & General Acts 1958 (HMSO, 1959) 486–502, esp. 298 (n).

Rigaud's source was Aubrey's Letters and lives of eminent men, ii (1813) 578 (Bodleian Library MS Rigaud 35, f. 218). The later selection by A. Clark (Brief lives, 1898) gives the passage in the article “Walter Warner” (ii, 291).

Rigaud S. P. , The correspondence of scientific men in the seventeenth century, i (Oxford, 1841) 153 (posthumous, but already in print in Rigaud's lifetime; see op. cit. n. 5, 11).

Bodleian Library, Rigaud MS 35, f. 218. William Camden (1551–1623) made notes for the reign of James I, as a continuation of his Annales of the reign of Elizabeth (1615 sqq.), which Thomas Smith appended to his edition of Camden's Epistolae (1691). They run chronologically from 1603 to 1623, and Anno 1621 starts at p. 65. On p. 72 the entry for June 16, between items on peers of the realm, reads: Th. Hariotus, Mathematicus insignis, moritur: Bona legavit Vicecomiti Insulae et Thomae Ailsburio.

von Zach , op. cit. i, 153; Rigaud S. P. , “On Harriot's papers”. Journal of the Royal Institution, ii (1831) 268.

Birch , op. cit. n. 1, 126.

Ibid. 309.

Lee Sidney , “Henry Percy, 9th Earl of Northumberland (1564–1632)”, D.N.B., xliv (1895) 413.

Confused accounts of the circumstances are current. The search was instigated by the Earl of Egremont's stepfather, Count von Brühl, amateur astronomer and envoy of Saxony in London, and achieved by his protégé, Xaver von Zach (1754–1832), who was, however, side-tracked by the commission to build and supervise the Observatory at Seeberg near Gotha (now in East Germany). For fuller details, see Allgememeine deutsche Biographie, xliv (Leipzig, 1898) 613; Armitage A. , “Baron von Zach and his astronomical correspondence”, Popular astronomy, lvii (1949) 326–333; and von Zach's own report, op. cit. n. 1, 145–147 and 152–153.

Birch , op. cit. 1, 410.

Bodleian Library MS Rigaud 35, f. 219.

Hariot Th. , A Briefe and True Report of the New Found Land of Virginia …, Imprinted in London 1588, 4°.

Torporley's main work, Diclides caelometricae (London, 1602) is a didactic treatise on spherical trigonometry (prefaced by an astrological disquisition of no interest to us), which Cantor briefly analyses in Vorlesungen über Geschichte der Mathematik, ii (2nd ed., Leipzig, 1913) 701, following the detailed account by Kästner A. G. (1719–1800), Geschichte der Mathematik, iii (Göttingen, 1796–1800) 101–107, which treats as rather a joke Torporley's verbal and pictorial inventions.

Bodleian Library MS Rigaud 9, ff. 18, 21, 22.

Pepper Jon V. , “A letter from Nathaniel Torporley to Thomas Harriot”, British journal for the history of science, iii (1967) 285–290.

Cf. Jacquot Jean , “Thomas Harriot's reputation for impiety”, Notes and records of the Royal Society of London, ix (1952) 168, 180.

Warner Walter (?1560–1643)—the year of death being certified by the burial entry for 28 March 1643 in the Memorials of St Margaret's Church, Westminster in the Guildhall Library (and tallying with mentions of him in letters of Pell and Mersenne in 1642)—was already in the Earl's service in 1591: Shirley , Ambix, iv (1949–51) 56–57.

Robert Hughes or Hues (1553–1632)—these years being certified by the memorial to him in the Cathedral of Christ Church, Oxford—entered the Earl's household only in 1615: ibid. 59, 60.

The dates of Torporley's ecclesiastical appointments have been confirmed from the church records at Lyddington and Salwarpe, which provide no further information on him, as their Rectors have very kindly informed me by letters on 3 and 6 June 1967 from Lyddington Rectory, and 21 October 1967 from Salwarpe.

Read Alexander (Rhead, Reid; 1586–1641), The chirurgicall lectures of tumors and ulcers (London, 1635) 307. See Tanner-Young R. C. H. , “La place de Thomas Harriot dans l'histoire de la médecine et de l'astronomie”, Gesnerus, xxiv (1967) 75–77 and (shortened version) Actes de la Société helvétique des sciences naturelles (1966) 172–173.

Shirley , op. cit. n. 20, 59.

Examination of Nathaniel Topherley, 27 Nov. 1605, Heading G : Cal. SP Dom. James I 1603–1611, 14/216 [Gunpowder plot book No 122]: Reference from autograph notes kindly supplied by Dr Shirley.

Batho G. R. , Household papers of Henry Percy (London, 1962) 163.

Pearce E. H. , Sion College and library (Cambridge, 1913) 234.

Somerset House, Prerogative Court of Canterbury, Original Wills Box 506, N. Torperley, 1 June 1632; Register Copy, Audley 65, f. 8 v. (5th from end of volume): Listed in PCC Probates 1630–1634; Probate Record, P.A. 1632 (mid-volume).

Brit. Mus. MS Add. 6789, ff. 448–450. The endorsement on the back with the names of Torporley and Protheroe was so deep in the binding at the spine that a microfilm, taken before the rebinding effected in 1967, does not show it.

Bodleian Library MS Rigaud 35, f. 123. See also Rigaud S. P. , Miscellaneous works of James Bradley (Oxford, 1832–1833), Supplement: An account of Harriot's astronomical papers, 42, note y.

Bodleian Library MS Rigaud 35, f. 219.

Stevens , op. cit., n. 1, 171.

Torporley , op. cit., n. 33, preface (unpaginated) sig. A₂v; quoted by Stevens , op. cit., n. 1, 101, with translation 102. The document is reproduced and discussed in R. H. C. Tanner, “Nathaniel Torporley and the Harriot manuscripts”, Annals of science (in press).

Wallis John (1616–1703), A treatise on algebra (1876, printed 1885) 125–208, was interpreting, in the light of this reputation, the attempt made at publication on Harriot's behalf; by bringing in the name of Descartes, he introduced a polemical element on which quotations tend to fasten.

Praxis (op. cit., n. 1), preface, third p., line 7 ab infr.

Bodleian Library MS Rigaud 35, ff. 183, 184, extract dated 27/4 38. It is followed by one more dated 11/12 39, a slip of pen for 38. Rigaud died on 16 March 1839.

Brit. Mus. MS Add.4395 (formerly 4408), Warner's Mathematical collection, vol. ii, f. 92.

Torporley , Corrector analyticus, Sion College MS L 40.2/E 10.

Sion College now stands on Victoria Embankment near Blackfriars, beside the City of London School. The combined frontage was originally allocated to the School. The land had been reclaimed from the River by the Thames Act of 1862. See Douglas-Smith A. E. , The City of London School, 2nd ed. (Oxford, 1965) 217, 244. Both buildings date from the early 1880's.

Halliwell J. O. (1820–1889), A Collection of letters illustrative of the progress of science in England from the reign of Queen Elizabeth to that of Charles the Second (1841), usually quoted as Letters on scientific subjects, Appendix, 109–116.

Rigaud , op. cit., n. 47, 520 and plate 5.

Robert Recorde (1510–1558), The whetstone of witte (London, 1557) leaf Ff lv., unpaginated.

Lohne J. , “Thomas Harriot als Mathematiker”, Centaurus xi (1965) 42, where they have been printed as modern cancelled inequality signs, and “Dokumente zur Revalidierung von Thomas Harriot als Algebraiker”, Archive for the history of the exact sciences, iii (1966) 204, footnote, which reproduces the stylised form of Harriot's inequality sign found, e.g., in his pupil William Lower's letter to him on 3 April 1611 (Brit. Mus. MS Add.6789, f. 431), reprinted with modernised symbols by Halliwell , op. cit. n. 57, 41, where < appears both for ‘angle’ and for ‘less than’. A facsimile reproduction of Harriot's sign is given in Tanner R. H. C. , op. cit., n. 2.

E.g., Brit. Mus. MS Add.6782, f. 232.

They are the classical inequalities between geometric and arithmetic means and their analogues between geometrico-arithmetic means of successive degrees: Praxis (op. cit. n. 1) 78 (misprinted 72)–86, lemmata 1–6.

Brit. Mus. MS Harl. 6083, f. 147. It seems significant that John Pell (1611–1685) invented a series of very pertinent mathematical symbols, exhibited in the transcription of his algebraic instruction to J. R. Rahn (Rhonius, 1622–1676), Teutsche algebra (Zurich, 1659), almost the only writer to adopt the inequality signs of the Praxis (though without naming it) in print until relatively recent times. A precocious and lifelong friend of Warner, neglectful of his own interests, Pell was taking his B.A. at Cambridge and corresponding with Briggs in 1628, and in 1631 he was incorporated at Oxford.

Mrs Muriel Seltman has undertaken a study of the Praxis for the M.Sc. at University College, London.

That Walter Warner brought out the Praxis seems to have been common knowledge: Wallis , op. cit. n. 51, Preface, 4th page; Halliwell , op. cit. n. 57, 71, corrected in Stevens , op. cit. n. 1, 189 (Aylesbury, 5 July 1632, Brit. Mus. MS Add.4396, f. 90).

Stevens , op. cit. n. 1, 172, 174, 176.

Jacquot , op. cit. n. 36. The later account by Kargon R. H. , Atomism in England from Harriot to Newton (Oxford, 1966), as regards Harriot and Torporley, adds nothing but errors.

Cf. Wallis to Collins, Oxford, 12 April 1673, in Rigaud , op. cit. n. 23, ii, 573.

Verbally, by Beardsworth T. I. M. , 10 Nov. 1967.

Wallis , op. cit. n. 51, “To the Reader”, 20 Nov. 1684, long passage winding up with “For it many times happens, that a man lights on a good notion; which he hath not the happiness to express so intelligibly, as perhaps another may do for him. …”.

As witness, e.g., Rigaud's detailed investigations on Harriot's associates in Bodleian Library MS Rigaud 35, ff. 106 seq. and 314 seq.

On Harriot's last illness, further research is needed. Contradictions in the reports were noted already by Rigaud, Bodleian Library MS Rigaud 9, f. 1; cf. also op. cit. n. 40.