Abstract
The Scottish scientist Colin Maclaurin (1698–1746) is mainly known as a mathematician who focused on pure mathematics. But during his life he was interested in the application of mathematics in all branches of knowledge. This article considers the relationships between theory and practice in Maclaurin's works.
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No potential conflict of interest was reported by the authors.
Correction Statement
This article has been corrected with minor changes. These changes do not impact the academic content of the article.
Notes
1 There are several biographical sources for Colin Maclaurin, for example, (Turnbull Citation1951; Scott Citation1973; Sageng Citation1989; Bruneau Citation2011a). For a study of his work, beyond the sources already quoted, it would be possible to add (Tweedie Citation1916; Guicciardini Citation1989; Grabiner Citation1996, Citation1997, Citation1998, Citation2002, Citation2004; Tweddle Citation2007; Bruneau Citation2010, Citation2011b, Citation2011c, Citation2014).
3 On Maclaurin's role in the founding of this learned society, see (Emerson Citation1979).
4 For a history of the creation of this fund, see (Dunlop Citation1992).
5 This argument was similar to the one given in the famous Scholium Generale which appeared in the second edition of Newton's Principia (Citation1713, 481–484). But the latter was published in June 1713, and it seems unlikely that Maclaurin had this edition when writing his thesis. In the Latin version of Newton's Opticks (Citation1706), published by Samuel Clarke, query 20 touched on this explanation, but without affirming it. The young Maclaurin was more affirmative than both Newton and Clarke.
6 This force was time dependent and could be infinite.
7 Maclaurin used Newtonian notation and fluxional vocabulary.
8 For a study of mathematical arguments used as proof in moral philosophy, see (Bruneau Citation2014).
9 The first method was based on the evolution of given angles around their vertices (Ubi Methodo Universali Linea omnium Ordinum describuntur sola datorum Angulorum & Rectarum Ope). The second one was what we now call pedal curves.
10 The Excise was the British state organization whose role it was to control and set the taxes on products.
11 This paper was first published by Grabiner (Citation1996), followed in 1998 by a commentary (Grabiner Citation1998) on the influence that the memorandum had in Scotland in the 1730s.
12 The barrels were considered as made up of portions of cones, each of which he compared with a cylinder. To evaluate the volume of the barrel, he added the volumes of all the cylinders.
14 See further the paper by Jane Wess in this issue of the BJHM.
15 Ian Tweddle has published an English translation of Maclaurin's text with a commentary (Tweddle Citation2007).
16 To do this he used a development in series.
18 Unlike promoters who took a fixed number of new widows each year, Maclaurin, using Halley's death tables, took a variable rate of new widows that depended on their age.
19 For a history of the mathematization of this problem in the eighteenth century, see the unpublished Master's thesis (Davodeau Citation2012).
20 They considered that the cells had a pyramidal base whose sides were hexagons and whose base was closed by three rhombuses.
21 Already in antiquity it was observed that bee cells had a regular hexagonal shape. Pappus expressed a principle of saving wax and Basil of Caesarea used a description of bee cells in one of his sermons. Kepler compared this structure with that of pomegranate grains. The naturalist Morandi was the first to suggest an approximate solution.
22 This may be why the text was left as a manuscript.
23 It was in the early 1730s that he wrote his Account of Sir Isaac Newton's Philosophical Discoveries (Maclaurin Citation1748a) which contained these relations.
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Davodeau, Guillaume, Le problème de la forme géométrique de la cellule d'abeille : une illustration de la mathématisation de la nature au dix-huitième siècle [the problem of the geometric shape of the bee cell: an illustration of the mathematization of nature in the eighteenth century]. Master thesis, University of Nantes, 2012. Maclaurin, Colin, An account of Sir Isaac Newton's philosophical discoveries in four books, London: Millar & Nourse, 1748a.
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