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Books by Antoni Malet
"As a general conclusion this dissertation suggests that the mathematical and optical contributio... more "As a general conclusion this dissertation suggests that the mathematical and optical contributions of James Gregorie, Isaac Barrow and Isaac Newton are more closely related to one another than it is usually acknowledged.
The first chapter contains a narrative of Gregorie's life and works. Evidence on Gregorie's life within 17th-century Scottish universities, his involvement in setting up the St Andrews observatory, his activities in the early 1670's as leader of a Scottish network of mathematical virtuosi, and his juvenile astrological concerns is here produced for the first time. Gregorie's correspondence with Newton is studied. It is argued that John Collins, representing the world of practical mathematicians, was a source of motivations for some of Gregorie's mathematical discoveries, and that Gregorie's attempts to publicize his contributions failed because of institutional practices characteristic of the early Royal Society.
The second chapter studies Gregorie's contributions to optics, including a description of a hitherto unpublished manuscript. A major center of interest is the origins of the notion of geometrical optical image, which are shown to have been influenced by the philosophical empiricism. I argue that Gregorie, Barrow, and Newton produced a methodological revolution in geometrical optics. The new optical science sought experimental confirmation for its basic notions and results and thus provided a direct methodological antecedent to Newton's Principia.
The third chapter studies Gregorie's work on "Taylor" expansions and his analytical method of tangents, which has passed unnoticed so far. It appears that Gregorie's work is a substantial counter-example to the standard thesis that geometry and algebra were opposed forces in 17th-century mathematics.
The last chapter studies and translates an unpublished mathematical manuscript featuring results similar to those in section 1 of Newton's Principia. Placing the contributions of Newton and Gregorie in the context of 17th-century discussions on indivisibles, l argue that Gregorie and Newton were idiosyncratic in their rejection of indivisibles.
Research on the manuscripts of James Gregorie and David Gregory shows that David's Geometria practica is actually James's, and that David's optical book heavily borrows from James's optical manuscript."
Papers by Antoni Malet
Historia Mathematica, Jan 1, 2006
Perspectives on Science, 2010
Studies in History and Philosophy of Science, Jan 1, 1990
A. van Helden, S. Dupré, R. van Gent, H. Zuidervaart (eds.) The origins of the telescope
Early Science and Medicine, 2005
This article focuses on some theoretical developments prompted by the use and construction of tel... more This article focuses on some theoretical developments prompted by the use and construction of telescopes in the first half of the seventeenth century.
Studies in History and Philosophy of Science, Jan 1, 2001
This paper deals with Hobbes's theory of optical images, developed in his optical magnum opus, ‘A... more This paper deals with Hobbes's theory of optical images, developed in his optical magnum opus, ‘A Minute or First Draught of the Optiques’ (1646), and published in abridged version in De homine (1658). The paper suggests that Hobbes's theory of vision and images serves him to ground his philosophy of man on his philosophy of body. Furthermore, since this part of Hobbes's work on optics is the most thoroughly geometrical, it reveals a good deal about the role of mathematics in Hobbes's philosophy. The paper points to some difficulties in the thesis of Shapin and Schaffer, who presented geometry as a ‘paradigm’ for Hobbes's natural philosophy. It will be argued here that Hobbes's application of geometry to optics was dictated by his metaphysical and epistemological principles, not by a blind belief in the power of geometry. Geometry supported causal explanation, and assisted reason in making sense of appearances by helping the philosopher understand the relationships between the world outside us and the images it produces in us. Finally the paper broadly suggests how Hobbes's theory of images may have triggered, by negative example, the flourishing of geometrical optics in Restoration England.
Archives Internationales d'Histoire des Sciences, 1990
Journal of the History of Ideas, Jan 1, 1997
D. Garber, S. Roux (eds.) The Mechanization of Natural Philosophy
J. Ferreirós, A. Durán (eds.) Matemáticas y Matemáticos (Sevilla, 2003), p. 57-83.
"As a general conclusion this dissertation suggests that the mathematical and optical contributio... more "As a general conclusion this dissertation suggests that the mathematical and optical contributions of James Gregorie, Isaac Barrow and Isaac Newton are more closely related to one another than it is usually acknowledged.
The first chapter contains a narrative of Gregorie's life and works. Evidence on Gregorie's life within 17th-century Scottish universities, his involvement in setting up the St Andrews observatory, his activities in the early 1670's as leader of a Scottish network of mathematical virtuosi, and his juvenile astrological concerns is here produced for the first time. Gregorie's correspondence with Newton is studied. It is argued that John Collins, representing the world of practical mathematicians, was a source of motivations for some of Gregorie's mathematical discoveries, and that Gregorie's attempts to publicize his contributions failed because of institutional practices characteristic of the early Royal Society.
The second chapter studies Gregorie's contributions to optics, including a description of a hitherto unpublished manuscript. A major center of interest is the origins of the notion of geometrical optical image, which are shown to have been influenced by the philosophical empiricism. I argue that Gregorie, Barrow, and Newton produced a methodological revolution in geometrical optics. The new optical science sought experimental confirmation for its basic notions and results and thus provided a direct methodological antecedent to Newton's Principia.
The third chapter studies Gregorie's work on "Taylor" expansions and his analytical method of tangents, which has passed unnoticed so far. It appears that Gregorie's work is a substantial counter-example to the standard thesis that geometry and algebra were opposed forces in 17th-century mathematics.
The last chapter studies and translates an unpublished mathematical manuscript featuring results similar to those in section 1 of Newton's Principia. Placing the contributions of Newton and Gregorie in the context of 17th-century discussions on indivisibles, l argue that Gregorie and Newton were idiosyncratic in their rejection of indivisibles.
Research on the manuscripts of James Gregorie and David Gregory shows that David's Geometria practica is actually James's, and that David's optical book heavily borrows from James's optical manuscript."
Historia Mathematica, Jan 1, 2006
Perspectives on Science, 2010
Studies in History and Philosophy of Science, Jan 1, 1990
A. van Helden, S. Dupré, R. van Gent, H. Zuidervaart (eds.) The origins of the telescope
Early Science and Medicine, 2005
This article focuses on some theoretical developments prompted by the use and construction of tel... more This article focuses on some theoretical developments prompted by the use and construction of telescopes in the first half of the seventeenth century.
Studies in History and Philosophy of Science, Jan 1, 2001
This paper deals with Hobbes's theory of optical images, developed in his optical magnum opus, ‘A... more This paper deals with Hobbes's theory of optical images, developed in his optical magnum opus, ‘A Minute or First Draught of the Optiques’ (1646), and published in abridged version in De homine (1658). The paper suggests that Hobbes's theory of vision and images serves him to ground his philosophy of man on his philosophy of body. Furthermore, since this part of Hobbes's work on optics is the most thoroughly geometrical, it reveals a good deal about the role of mathematics in Hobbes's philosophy. The paper points to some difficulties in the thesis of Shapin and Schaffer, who presented geometry as a ‘paradigm’ for Hobbes's natural philosophy. It will be argued here that Hobbes's application of geometry to optics was dictated by his metaphysical and epistemological principles, not by a blind belief in the power of geometry. Geometry supported causal explanation, and assisted reason in making sense of appearances by helping the philosopher understand the relationships between the world outside us and the images it produces in us. Finally the paper broadly suggests how Hobbes's theory of images may have triggered, by negative example, the flourishing of geometrical optics in Restoration England.
Archives Internationales d'Histoire des Sciences, 1990
Journal of the History of Ideas, Jan 1, 1997
D. Garber, S. Roux (eds.) The Mechanization of Natural Philosophy
J. Ferreirós, A. Durán (eds.) Matemáticas y Matemáticos (Sevilla, 2003), p. 57-83.
S. Mandelbrote, H. Pulte (eds), The Reception of Isaac Newton in Europe (ch. 6). (London), 2019
Perspectives on Science, Jan 1, 2010
Paula Olmos (ed.) Greek Science in the Long Run: Essays on the Greek Scientific Tradition (4th c. BCE-17th c. CE)
Historia Mathematica, Jan 1, 2006
In the 16th and 17th centuries the classical Greek notions of (discrete) number and (continuous) ... more In the 16th and 17th centuries the classical Greek notions of (discrete) number and (continuous) magnitude (preserved in medieval Latin translations of Euclid's Elements) underwent a major transformation that turned them into continuous but measurable magnitudes. This article studies the changes introduced in the classical notions of number and magnitude by three influential Renaissance editions of Euclid's Elements. Besides providing evidence of earlier discussions preparing notions and arguments eventually introduced in Simon Stevin's Arithmétique of 1585, these editions document the role abacus algebra and Renaissance views on the history of mathematics played in bridging the gulf between discrete numbers and continuous magnitudes.Pendant le seizième et dix-septième siècles, les notions classiques de nombre (toujours sous-entendu discrète) et de grandeur (continue), bien conservées dans les éditions latines médiévales des Éléments d'Euclide, ont connu une transformation majeur au bout de la quelle on trouve les deux notions confondues sous la nouvelle notion de grandeur mesurable ou quantifiée. Cet article étudie les modifications introduites dans les notions classiques de nombre et magnitude par trois éditions des Éléments d'Euclide parues pendant le seizième siècle et largement utilisées. Ces éditions nous montrent comment elles ont amorcé de notions et d'arguments finalement introduits dans l'Arithmétique de Simon Stevin de 1585. Elles nous enseignent aussi le rôle joué par l'algèbre des abacistes et par l'histoire des mathématiques en l'articulation et justification d'un nouveau point de vue sur les grandeurs mathématiques.