Dot-Age: Newton’s Mathematical Legacy in Eighteenth Century


  • Niccolò Guicciardini Universidad de Siena



Isaac Newton, uxions, history of mathematics, mathematics, Colin Maclaurin


According to the received view, eighteenth-century British mathematicians were responsible for a decline of mathematics in the country of Newton; a decline attributed to chauvinism and a preference for geometrical thinking. This paper challenges this view by first describing the complexity of Newton’s mathematical heritage and its reception in the early decades of the eighteenth century. A section devoted to Maclaurin’s monumental Treatise of Fluxions (1742) describes its attempt to reach a synthesis of the different strands of Newton’s mathematical legacy, and compares it with contemporary Continental work. It is shown that in the middle of the eighteenth century academic Continental mathematicians such as Euler and Lagrange were driven by local cultural assumptions in directions which sensibly diverged from the ones followed by Maclaurin and his fellow countrymen.

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Author Biography

Niccolò Guicciardini, Universidad de Siena

Universidad de Siena


Ackerberg-Hastings, Amy. “Analysis and Synthesis in John Playfair’s Elements of Geometry”, en: British Journal for the History of Science, 35, 2002, pp. 43-72.

Barrow-Green, June. “‘A Correction to the Spirit of Too Exclusively Pure Mathematics’: Robert Smith (1689-1768) and his Prizes at Cambridge University”, en: Annals of Science, 56, 1999, pp. 271-316.

Becher, Harvey. “Radicals, Whigs, and Conservatives: The Middle and Lower Classes in the Analytical Revolution at Cambridge in the Age of Aristocracy”, en: British Journal for the History of Science 28, 1995, pp. 405-426.

Blay, Michel. La naissance de la mécanique analytique: la science du mouvement au tournant des XVIIe et XVIIIe siècles. París, 1992.

Bos, Henk J. M. Rede ning Geometrical Exactness: Descartes’ Transformation of the Early Modern Concept of Construction. NewYork, Berlín, Heidelberg, 2001.

Brian,E. La mesure del’état: administrateurs et géomètres au XVIII e siècle. París, 1994.

Cajori, Florian. A History of the Conceptions of Limits and Fluxions in Great Britain from Newton to Woodhouse. Chicago y Londres, 1919.

Cohen, I. Bernard. “The Case of the Missing Author: the Title Page of Newton’s Opticks (1704), with Notes on the Title Page of Huygens’s Traité de la lumière”, en: Buchwald, J. Z. y Cohen, I. B. (eds.). Isaac Newton’s Natural Philosophy. Cambridge (Mass), Londres, 2001, pp. 15-45.

Cotes, Roger. “Logometria”, en: Philosophical Transactions, 39, 1714, pp. 5-45.

Charles Babbage. Passages from the Life of a Philosopher. Londres, 1864.

Chasles, Michel. Aperçu historique sur l’origine et le développement des méthodes en géométrie, particulièrement de celles qui se rapportent à la géométrie moderne. París, 1837.

Davie, George E. The Democratic Intellect: Scotland and Her Universities in the Nineteenth Century. Edimburgo, 1964.

Demidov, S. S. “The Study of Partial Differential Equations of the First Order in the 18th and 19th Centuries”, en: Archive for the History of the Exact Sciences, 26, 1982, pp. 325-350.

Descartes, René. Geometria a Renato Descartes. 2da edición Latina. Frans van Schooten (trad). Ámsterdam, 1659-1661.

____________. The Geometry of René Descartes with a Facsimile of the First Edition, ed. D. E. Smith and M. L. Latham. New York, 1954.

Emerson, William. The Doctrine of Fluxions: Not Only Explaining the Elements Thereof, But Also Its Application and Use in the Several Parts of Mathematics and Natural Philosophy. Londres, 1743.

Engelsman, S. B. Families of Curves and the Origins of Partial Differentiation. Ámsterdam, 1984.

Enros, Philip C. “The Analytical Society (1812-1813): Precursor of the Renewal of Cambridge Mathematics”, en: Historia Mathematica 10, 1983, pp. 24-47.

Euler, Leonhard. Opera omnia. Lausanne, 1954. Feingold, Mordechai. “Mathematicians and Naturalists: Sir Isaac Newton and the Royal Society”, en: Buchwald, J. Z. y Cohen, I. B. (eds.). Isaac Newton’s Natural Philosophy. Cambridge (Mass), Londres, 2001, pp. 77-102.

Fraser, Craig. “D’Alembert’s Principle: the Original Formulation and Application in Jean d’Alembert’s Traité de dynamique (1743)”, en: Centaurus, 28, 1985, pp. 31-61, pp. 145-159.

____________. “J. L. Lagrange’s Changing Approach to the Calculus of Variations”, en: Archive for the History of the Exact Sciences, 32, 1985, pp. 151-191.

____________. “The Calculus as Algebraic Analysis: Some Observations on Mathematical Analysis in the 18th Century”, en: Archive for the History of the Exact Sciences, 39, 1989, pp. 317-335.

Gascoigne, John. “Mathematics and Meritocracy: The Emergence of the Cambridge Mathematical Tripos”. Social Studies of Science, 14, 1984, pp. 547-584. Reimpreso como el capítulo 5 de John Gascoigne, Science, Politics, and Universities in Europe, 1600-1800. Ashgate, 1998.

____________. Cambridge in the Age of Enlightenment: Science, Religion, and Politics from the Restoration to the French Revolution. Cambridge, 1992.

____________. Joseph Banks and the English Enlightenment: Useful Knowledge and Polite Culture. Cambridge, 1994.

Goldstine, H. H. A History of the Calculus of Variations from the 17th Through the 19th Century. New York, 1980.

Grabiner, Judith V. “Was Newton’s Calculus a Dead End? The Continental Influence of Maclaurin’s Treatise of Fluxions”, en: American Mathematical Monthly, 104, 1997, pp. 393-410.

____________. “Maclaurin and Newton: the Newtonian Style and the Authority of Mathematics”, en: Withers, C. W. J. and Wood, P. (eds.). Science and Medicine in the Scottish Enlightenment. Londres, 2002, pp. 143-171.

Grattan-Guinness, Ivor. “The Varieties of Mechanics by 1800”, en: Historia Mathematica, 17, 1990, pp. 313-338.

Greenberg, J. L. “Alexis Fontaine’s Integration of Ordinary Differential Equations and the Origins of the Calculus of Several Variables”, en: Annals of Science, 39, 1982, pp. 1-36.

Gregory, David. Exercitatio geometrica de dimensione gurarum. Edimburgo, 1684.

Guicciardini, Niccolò. “Isaac Newton and the Publication of His Mathematical Manuscripts”, en: Studies in the History and Philosophy of Science, 35, 2004, pp. 455-470.

____________. Reading the Principia: the Debate on Newton’s Mathematical Methods for Natural Philosophy from 1687 to 1730. Cambridge, 1999.

Hall, A. Rupert. “Correcting the Principia”, en: Osiris 13, 1958, pp. 291-326.

____________. Philosophers at War: the Quarrel between Newton and Leibniz. Cambridge, 1980.

Heilbron, John L. “A Mathematicians’ Mutiny, with Morals”, en: Horwich, P. (ed.).World Changes: Thomas Kuhn and the Nature of Science. Cambridge (Mass)/Londres, 1993, pp. 81-129.

Hermann, Jacob. Phoronomia, sive de viribus et motibus corporum solidorum et uidorum libri duo. Amsterdam, 1716. Mazzone

Hiscock, W. G. David Gregory, Isaac Newton and Their Circle: Extracts from David Gregory’s Memoranda, 1677-1708. Oxford, 1937.

Howson, Albert. A History of Mathematics Education in England. Cambridge, 1982.

Jesseph, Douglas M. Berkeley’s Philosophy of Mathematics. Chicago, 1993.

Kitcher, Philip. The Nature of Mathematical Knowledge. New York y Oxford, 1983. Kline, Morris. Mathematical Thought from Ancient to Modern Times. New York, 1972.

Kuhn, Thomas. “Mathematical versus Experimental Traditions in the Development of Physical Science”, en: The Essential Tension: Selected Readings in Scientific Tradition and Change, Chicago, 1977, pp. 31-65.

Maclaurin, Colin. A Treatise of Fluxions, in Two Books (Edimburgo, 1742), 2da ed. (Londres, 1801).

Machin, John. “De motu nodorum lunae”, en: Isaac Newton, Philosophiæ Naturalis Principia Mathematica, 3ra ed. Londres, 1726, pp. 451-454.

Maglo, Kof. “The Reception of Newton’s Gravitational Theory by Huygens, Varignon, and Maupertuis: How Normal Science May Be Revolutionary”, en: Perspectives on Science, 11, 2003, pp. 135-169.

Mandelbrote, Scott. “Newton and Eighteenth-Century Christianity”, en: Cohen I. Bernard y Smith, George E. (eds.). The Cambridge Companion to Newton. Cambridge, Cambridge University Press, 2002, pp. 409-430.

Mazzone, Silvia y Roero, Clara S. Jacob Hermann and the Diffusion of the Leibnizian Calculus in Italy. Florence, 1997.

Murdoch, Patrick. Neutoni genesis curvarum per umbras, seu perspectivae universalis elementa; exemplis coni sectionum et linearum tertii ordinis illustrata. Londres, 1746.

Newton, Isaac. Analysis per quantitatum series, fluxiones, ac differentias: cum enumeratione linearum tertii ordinis. Londres, 1711.

____________. Opticks or, a Treatise of the Reflexions, Refractions, In exions and Colours of Light. Also two Treatises of the Species and Magnitude of Curvilinear Figures. Londres, 1704.

____________. The Mathematical Papers of Isaac Newton. D. T. Whiteside (ed.). 8 vols. Cambridge, Cambridge University Press, 1967-1981.

____________. The Principia, Mathematical Principles of Natural Philosophy: a New Translation by I. Bernard Cohen and Anne Whitman, Assisted by Julia Budenz, Preceded by a Guide to Newton’s Principia by I. Bernard Cohen. Berkeley, Los Angeles, Londres, 1999.

Panteki, Maria. “William Wallace and the Introduction of Continental Calculus to Britain: a Letter to George Peacock”, en: Historia Mathematica 14, 1987, pp. 119-132.

Playfair, John. “Traité de Mechanique Celeste”, The Edinburgh Review, 22, 1808, pp. 249-284.

Pycior, Helena M. Symbols, Impossible Numbers, and Geometric Entanglements: British Algebra through the Commentaries on Newton’s Universal Arithmetick. Cambridge, 1997.

Schofield, Robert E. “An Evolutionary Taxonomy of Eighteenth-Century Newtonianisms”, en: Studies in Eighteenth Century Culture 7, 1978, pp. 175-92.

Shank, J. B. “‘There was no such Thing as the ‘Newtonian Revolution’, and the French Initiated it.’ Eighteenth-Century Mechanics in France Before Maupertuis”, en: Early Science and Medicine, 9 (3), pp. 257-292.

Shapiro, Alan E. Fits, Passions, and Paroxysms: Physics, Method, and Chemistry and Newton’s Theories of Colored Bodies and Fits of Easy Reflection. Cambridge, 1993.

Schaffer. Simon. “Newtonianism”, en: Olby, R. C. et al. (eds.). Companion to the History of Modern Science. Londres, 1990, pp. 610-626.

Simpson, Thomas. The Doctrine and Application of Fluxions. Containing (Beside What is Common on the Subject) a Number of New Improvements in the Theory. And the Solution of a Variety of New, and Very Interesting, Problems in Different Branches of the Mathematicks, 2 vols. Londres, 1750.

Simson, Robert. “Pappi Alexandrini propositiones duæ generales”, en : Philosophical Transactions, 32, 1723, pp. 330-40.

____________. Opera quaedam reliqua. Glasgow, 1776.

Smith, George E. “The Newtonian Style in Book II of the Principia”, en: Buchwald, J. Z. y Cohen, I. B. (eds.). Isaac Newton’s Natural Philosophy. Cambridge Mass., Londres, 2001, pp. 249-298.

Stewart, Matthew. “Pappi Alexandrini collectionum mathematicarum libri quarti propositio quarta generalior facta, cui propositiones aliquot eodem spectantes adjicuntur”, en: Essays and Observations Physical and Literary, Read before a Society in Edinburgh, and Published by Them, 2 vols. Edimburgo, 1754.

____________. Propositiones geometricae, more veterum demonstratae, ad geometriam antiquam illustrandam et promovendam idoneae. Edimburgo, 1763.

Terrall, Mary. “Metaphysics, Mathematics, and the Gendering of Science in Eighteenth-Century France”, en: W. Clark, J. Golinski and S. Schaffer (eds.). The Sciences in Enlightened Europe. Chicago y

Londres, 1999, pp. 246-271.

Tweddle, Ian. James Stirling’s Methodus Differentialis. An Annotated Translation of Stirling’s Text. Londres, 2003.

____________. Simson on Porisms: an Annotated Translation of Robert Simson’s Posthumous Treatise on Porisms and Other Items on This Subject. New York, Berlin, Heidelberg, 2000.

Wallis, John. A Treatise of Algebra: both Historical and Practical. Londres, 1685.

____________. Opera mathematica, 3 vols. Oxford, 1693-1699.

Wallis, Meter y Wallis, Ruth. Newton and Newtoniana 1672-1975: A Bibliography. Londres, 1977.

Warwick, Andrew. Masters of Theory: Cambridge and the Rise of Mathematical Physics. Chicago y Londres, 2003.

Westfall, Richard S. Never at Rest: a Biography of Isaac Newton. Cambridge, 1980.

Whewell, William. History of the Inductive Sciences, Cambridge. University Press, 1837.



How to Cite

Guicciardini, N. (2007). Dot-Age: Newton’s Mathematical Legacy in Eighteenth Century. Estudios De Filosofía, (35), 67–109.



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