[Analyse mathématique et astronomie physique en Grande-Bretagne et en Irlande (1790–1831): quelques nouveaux éclairages sur les liens français]
The reception by British and Irish mathematicians of late-eighteenth-century French mathematical analysis, and its applications to astronomy, is here re-examined. The main early British participants were John Robison, John Playfair, Robert Woodhouse, John Toplis, John Brinkley, John West, William Spence, John Herapath, James Ivory, William Wallace, and Mary Somerville. Their activities and publications, and those of some others, are outlined. The reviews of John Playfair and Robert Woodhouse, many little-known, are highlighted. Finally, we discuss why, despite the work of these individuals, reform of British mathematics was at first so slow; and why, in contrast, the eventual modernisation of the Cambridge Mathematical Tripos examinations, following the efforts of Charles Babbage, John Herschel, George Peacock and others, led to rapid improvement.
On examine ici la réception à la fin du dix-huitième siècle, parmi des mathématiciens de Grande-Bretagne et d'Irlande, de l'analyse mathématique française et de ses applications à astronomie. Les premières contributions britanniques furent celles de John Robison, John Playfair, Robert Woodhouse, John Toplis, John Brinkley, John West, William Spence, John Herapath, James Ivory, William Wallace, et Mary Somerville. Cet article présente leurs activités et leurs publications, ainsi que quelques autres. Les comptes rendus de John Playfair et Robert Woodhouse sont étudiés de près. On analyse enfin les raisons pour lesquelles, en dépit des travaux de ces individus, la réforme des mathématiques en Grande-Bretagne a d'abord été si lente, et pourquoi la réforme du Cambridge Mathematical Tripos, elle, a finalement débouché sur une amélioration rapide.
Keywords: History of mathematics, history of astronomy, calculus and analysis, celestial mechanics, mathematics and astronomy, mathematics in Britain and France, early nineteenth century, mathematical book reviews.
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author = {Craik, Alex D.D.},
title = {Mathematical analysis and physical astronomy in {Great} {Britain} and {Ireland,} 1790-1831: some new light on the {French} connection},
journal = {Revue d'histoire des math\'ematiques},
pages = {223--294},
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Craik, Alex D.D. Mathematical analysis and physical astronomy in Great Britain and Ireland, 1790-1831: some new light on the French connection. Revue d'histoire des mathématiques, Tome 22 (2016) no. 2, pp. 223-294. doi: 10.24033/rhm.195
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Physical Geography, Murray, London, 1849
On Molecular and Microscopic Science, Murray, London, 1869
Personal Recollections from Early Life to Old Age, of Mary Somerville, with selections from her correspondence, by her daughter Martha Somerville, Murray, London, 1873/1874 (and later editions). 1874 ibid. Boston: Roberts; (also reissued with some additions as Queen of Science: Personal Recollections of Mary Somerville, ed. Dorothy McMillan, Edinburgh: Canongate 2001)
Collected works of Mary Somerville, edited and introduced by James A. Secord, Thoemmes, Bristol, 2004
Some observations on Dr. Taylor's Theorem for the development of the function , Phil. Mag. (1st ser.), Volume 29 (1808), pp. 211-215
An Essay on the Theory of the Various Orders of Logarithmic Transcendents; with an Inquiry into their Applications to the Integral Calculus and the Summation of Series, Murray; Edinburgh: Constable, London, 1809
Outlines of a Theory of Algebraic Equations deduced from the Principles of Harriott, and extended to the Fluxional and Differential Calculus, Davis & Dickson for the author, London, 1814/1817
Mathematical Essays, by the Late William Spence, Esq. Edited by John F.W. Herschel, Esq. with a Brief Memoir of the Author, Moyes, London, 1819 (Some copies are dated 1820.)
The Neptune File. Planet detectives and the discovery of worlds unseen, Allen Lane and Penguin, London, 2000
Some general theorems of considerable use in the higher parts of mathematics, Edinburgh, Sands, 1746
Tracts physical and mathematical, containing an explication of several ... points in physical astronomy; and a new method for ascertaining the sun's distance from the earth, by the theory of gravity, Edinburgh, 1761
Propositiones Geometricæ more veterum demonstratæ, Edinburgh, 1763
Review of Mary Somerville's `On the Connexion of the Physical Sciences', The Athenaeum, Volume 333 (1834), pp. 202-203
An Introduction to the Differential and Integral Calculus with an Appendix, illustrative of the Theory of Curves, Simms & McIntyre etc., Belfast, 1831 (also later editions)
On the Decline of Mathematical Studies, and the Sciences dependent upon them, Philos. Mag., Volume 20 (1805), pp. 25-31
A Treatise upon Analytical Mechanics; being the first book of the Mecanique Celeste of M. le Comte Laplace,... translated and elucidated with Explanatory Notes..., Barnett, Nottingham, 1814
Essays in the History of Mechanics, Springer, New York, 1968
Simson on Porisms: an Annotated Translation of Robert Simson's Posthumous Treatise on Porisms and Other Items on This Subject, Springer, New York, Berlin, Heidelberg, 2000
The Elements of Mathematical Analysis, abridged, For the Use of Students, Edinburgh: Robertson n.d. [1783]. Enlarged in 1798 with additional Notes and 28-page Synopsis of Book V of Euclid's Elements, Bell and Bradfute; London: Wingrave, Edinburgh, 1783/1798
A Complete System of Astronomy, 3 vols, Burges, Cambridge, 1797–1808
A Treatise of Fluxions, Smith, Cambridge, 1818
The Principles of Hydrostatics: designed for the use of students in the University, Smith, Cambridge, 1820
Fluxions, The Edinburgh Encyclopaedia (Brewster, D., ed.), Blackwood, Edinburgh (1815) 18 vols. (1808–1830): 9 (1815), pp. 382–467
Miscellanea analytica de aequationibus algebraicis, et curvarum proprietatibus, Cambridge, 1762
Sir John Herschel at the Cape of Good Hope, Trans. Roy. Soc. of South Africa, Volume 49 (1994), pp. 19-55
Masters of Theory: Cambridge and the Rise of Mathematical Physics, Univ. of Chicago Press, Chicago and London, 2003
Brinkley, John (1766/7–1835), Oxford Dictionary of National Biography, Oxford Univ. Press, Oxford, 2004
Elements of Mathematics, For the Use of Schools, Creech; London: Longman & Cadell, Edinburgh, 1784
Mathematical Treatises, containing I. The Theory of Analytic Functions. II. Spherical Trigonometry, with Practical and Nautical Astronomy... edited (after the author's death) from his mss. by the late Sir John Leslie... accompanied by a memoir of the life and writings of the author by Edward Sang, F.R.S.E, Oliver & Boyd; London: Simpkin, Marshall, Edinburgh, 1838
Thoughts on the Study of Mathematics as a part of a Liberal Education, 2nd edn, Deighton; London: Parker, Cambridge, 1836
Of a Liberal Education in general; and with particular reference to the leading studies of the University of Cambridge, Parker, London, 1845
Early Victorian Cambridge, Cambridge Univ. Press, Cambridge, 1940
Reviews, Monthly Review, or, Literary Journal, New series (1798–1818) (References to some other reviews by Woodhouse of foreign mathematical and astronomical works are given in the Appendix (b))
On the necessary truth of certain conclusions obtained by means of imaginary quantities, Phil. Trans. Roy. Soc. London, Volume 91 (1801), pp. 89-119
On the independence of the analytical and geometrical methods of investigation; and on the advantages to be derived from their separation, Phil. Trans. Roy. Soc. London, Volume 92 (1802), pp. 85-125
The Principles of Analytic Calculation, Cambridge Univ. Press, Cambridge, 1803
A Treatise on Isoperimetrical Problems and the Calculus of Variations, Cambridge Univ. Press, Cambridge, 1810
An Elementary Treatise on Astronomy, 2 vols, Cambridge Univ. Press, Cambridge, 1812/1818
Elementary illustrations of the Celestial Mechanics of Laplace. Part the first, comprehending the first book, John Murray, London, 1821
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