A “Practique Discipline”? Mathematical Arts in John Blagrave's The Mathematical Jewel (1585)

Blagrave John , “To the Right Honourable Sir William Cycill”, in The mathematical jewel (London, 1585).

See Blagrave , Jewel (ref. 1), Baculum familiare, catholicon sive generale (London, 1590), Astrolabium uranicum generale (London, 1596), Nova orbis terrarium descriptio (London, 1596), An apollogie confirmation explanation and addition to the Uranicall Astrolabe (London, 1597), and The art of dyalling (London, 1609).

Blagrave , Jewel (ref. 1), “The Author to the curteous Reader”.

Blagrave , Baculum familiare (ref. 2) advertises that he may be consulted for advice on the construction of an instrument.

In this essay, I will focus primarily on the sections on the construction of the instrument.

I will rely on an intuitive interpretation of practice and cognate terms in this piece, while recognizing that practices deserve more attention outside the context of this case study, as highlighted by Lynch M. , “Theorizing practice”, Human studies, xx (1997), 335–44, p. 337.

Collins H. M. “The TEA set: Tacit knowledge and scientific networks”, Science studies , iv (1974), 165–85, is particularly clear on this point. There are a wide variety of views on tacit knowledge. See, for instance, Polanyi M. , Personal knowledge: Towards a post-critical philosophy (London, 1958), Polanyi , The tacit dimension (London, 1967), Bloor D. , Knowledge and social imagery (London, 1976), and Lynch M. , Art and artefact in laboratory science: A study of shop work and shop talk in a research laboratory (London, 1985).

See Turner S. , The social theory of practices: Tradition, tacit knowledge and presuppositions (Cambridge, 1994), 43, for one expression of this difficulty. For summary responses to Turner's position see Lynch , “Theorizing practice” (ref. 6), and T. Pinch, “Old habits die hard: Retrieving practices from social theory”, Studies in history and philosophy of science, xxviii (1997), 1997–8.

Turner , Social theory (ref. 8), 105.

Turner , Social theory (ref. 8), 105–7.

Johnston S. , “Making mathematical practice: Gentlemen, practitioners and artisans in Elizabethan England” (unpublished Ph.D. thesis, Cambridge, 1994) emphasizes the importance of printed texts in ‘practical mathematics’.

Personal contact in the workshop is important in Smith's account. See Smith P. , “In a sixteenth-century goldsmith's workshop”, in Roberts L. Schaffer S. Dear P. (eds), The mindful hand: Inquiry and invention from the late Renaissance to early industrialisation (Amsterdam, 2007), 32–57, p. 37.

Blagrave's announcement in Baculum familiare (ref. 2) that he is available for consultation on the construction of an instrument suggests that Blagrave might have been in contact with some readers.

Smith P. , The body of the artisan: Art and experience in the Scientific Revolution (Chicago, 2004), 6.

I will use Blagrave's spelling — ‘theoricke(s)’ — To refer exclusively to those theorics that appear in the Jewel, using ‘theorics’ as a more general term.

Pedersen O. , “The origins of the Theorica planetarum”, Journal for the history of astronomy, xii (1981), 113–23, offers a guide to the content and origins of the Theorica planetarum texts. See ref. 37 for more literature.

Johnston S. , “Theory, theoric, practice: Mathematics and magnetism in Elizabethan England”, Journal de la Renaissance, ii (2004), 53–62.

Bennett J. A. , “The mechanics' philosophy and the mechanical philosophy”, History of science, xxiv (1986), 1–27, p. 15. Bennett , “Presidential address — Knowing and doing in the sixteenth century: What were instruments for?”, The British journal for the history of science, xxxvi (2003), 2003–50, draws a firmer distinction between theorics and philosophical accounts.

Johnston , “Making mathematical practice” (ref. 11), 294–5.

Bennett , “Knowing and doing” (ref. 18), gives some attention to the operation of theorics, although the discussion is framed in relation to the similarities in function between theorics in mathematics and magnetism, rather than in one of the areas for its own sake.

Blagrave , Jewel (ref. 1), 19–20, gives the account of contact with White. Quotations on the design process in the following paragraphs are taken from these pages.

Probably refers to Schöner A. , Gnomonice (Nuremberg, 1562), Stöffler J. , Elucidatio fabricae ususque astrolabii (Oppenheim, 1512), Rojas J. , Commentariorum in astrolabium quod planisphærium vocant (Paris, 1550), and Frisius G. , De astrolabo catholico (Antwerp, 1556), or editions thereof.

This was the case in accounts of both the construction and use of the Jewel, but I will focus here solely on construction. Relating to use, Blagrave gave accounts of his own observational practice, including ad hoc solutions that could be employed at times when the limitations of the instrument were felt. See, for example, Blagrave , Jewel (ref. 1), 18.

Blagrave , Jewel (ref. 1), 2.

See Smith , “Goldsmith's workshop” (ref. 12), 37, for the idea of tools and stencils as “reservoirs of collective cognition and knowledge”.

Blagrave , Jewel (ref. 1), 13.

Blagrave , Jewel (ref. 1), 14.

Blagrave , Jewel (ref. 1), [¶¶iiv].

See, for instance, Recorde R. , The ground of artes (London, 1543), Cunnigham W. , The cosmographical glasse (London, 1559), and Worsop E. , A discoverie of sundrie errours and faults daily committed by lande-meaters (London, 1582).

Blagrave , Jewel (ref. 1), 17.

Ibid.

Blagrave , Jewel (ref. 1), “The Author to the curteous Reader”.

Ash E. H. , Power, knowledge, and expertise in Elizabethan England (Baltimore, 2004).

Worsop , A discoverie of sundrie errours (ref. 29), highlighted the problem of the use of instruments by those who did not understand the mathematical underpinnings of the devices. See Bennett J. A. , “‘Braggers that by showe of their instrument win credit’: The Errours of Edward Worsop”, in Taub L. Willmoth F. (eds), The Whipple Museum of the History of Science: Instruments and interpretations, to celebrate the 60^th Anniversary of R. S. Whipple's gift to the University of Cambridge (Cambridge, 2006), 79–94, for a thorough explication of Worsop's work.

Blagrave , Jewel (ref. 1), 11.

For a summary of the content of works in this category, see Pedersen , “Origins” (ref. 16), 115–18.

This is not to deny the significant and growing minority of astronomers who used theoricae as the basis for causal interpretations. On the complicated issue of interpretations of planetary models see Duhem P. , To save the phenomena: An essay on the idea of physical theory from Plato to Galileo (Chicago, 1969; first publ. 1908), Westman R. S. , “Three responses to Copernican theory: Johannes Praetorius, Tycho Brahe, and Michael Maestlin”, in Westman (ed.), The Copernican achievement (Berkeley, 1975), 285–345, Jardine N. , The birth of history and philosophy of science: Kepler's A defence of Tycho against Ursus with essays on its provenance and significance (Cambridge, 1984), Jardine, “Scepticism in Renaissance astronomy: A preliminary study”, in Popkin R. H. , and Schmitt C. B. (eds), Scepticism from the Renaissance to the Enlightenment (Wiesbaden, 1987), 83–102, and Barker P. Goldstein B. R. , “Realism and instrumentalism in sixteenth century astronomy: A reappraisal”, Perspectives on science, vi (1998), 1998–58. Study of these accounts suggests the need for finer grained divisions than realist versus instrumentalist. Reinhold, for example, held planetary theoricae to construct the true path of planets, but was dismissive of real spheres as causal agents. Such cases demonstrate that the distinction was not as tidy as some accounts attempt to make it. On this point see Jardine , “Scepticism in Renaissance astronomy”, in particular. See Pedersen , “The decline and fall of the Theorica planetarum: Renaissance astronomy and the art of printing”, Studia Copernicana, xvi (1978), 1978–85, for the Theorica planetarum tradition.

Blagrave , Jewel (ref. 1), 11.

Ibid.

Blagrave , Jewel (ref. 1), 18.

This information could be used to determine, for example, the day of the week on which a particular date would fall. For an account of time in almanacs see Chapman A. A. , “Marking time: Astrology, almanacs, and English Protestantism”, Renaissance quarterly, lx (2007), 1257–90, pp. 1269–81.

The idea of applying protocols to extract information from theorics is taken from Bennett , “Knowing and doing” (ref. 18).

Blagrave , Jewel (ref. 1), 95.

Ibid.

Blagrave notes that in practice the instrument would not be sturdy enough to allow accurate dial construction. Ibid.

Blagrave , Jewel (ref. 1), 12.

Ibid.

Cf. Johnston , “Making mathematical practice” (ref. 11), 9, on “theoretical practices”.

That is not to say that causal knowledge was never imparted theorically. See, for example, the cases treated in Johnston , “Theory, theoric, practice” (ref. 17).