The Canadian Mathematical Olympiad 1969-1993 by Michael Doob

By Michael Doob

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Russell, Bertrand. 1937. A critical exposition of the philosophy of Leibniz. New impression with a new preface. 2nd ed. London: George Allen Unwin Ltd. Sasaki, Chikara. 2004. Descartes’s Mathematical Thought. Dordrecht: Kluwer. Serres, Michel. 1968. Le Système de Leibniz et ses modèles mathématiques. F. Leibniz, Philosopher Mathematician and Mathematical Philosopher Philip Beeley Of the numerous constants in Leibniz’s philosophy, stretching from his intellectually formative years in Leipzig and Jena through to the mature writings of the Monadology conceived largely in Hanover and Berlin, few are as remarkable as his conviction that a firm understanding of the concepts of unity and infinity ultimately provide the key to developing sound metaphysics.

Significantly, the characterization of the magnitude of point as being smaller than any magnitude which can be given negates the absolute and thus opens up the possibility of quantitative relations between points themselves. In Theoria motus abstracti, Leibniz defines the phoronomic concept of conatus analogously to the concept of point as the beginning or end of motion. Just as point is ontologically the limit of a line, so conatus is ontologically the limit of a motion. But points fulfilled this function already within the Aristotelian tradition, where they are conceived as being true indivisibles.

Sämtliche Schriften und Briefe, ed. Prussian Academy of Sciences (and successors); now: Berlin-Brandenburg Academy of Sciences and the Academy of Sciences in Göttingen. 8 series, Darmstadt (subsequently: Leipzig); now: Berlin: Otto Reichl (and successors); now: Akademie Verlag. [quoted as A]. Leibniz, Gottfried Wilhelm. 1993. De quadratura arithmetica circuli ellipseos et hyperbolae cujus corollarium est trigonometria sine tabulis, ed. Eberhard Knobloch. Göttingen: Vandenhoeck and Ruprecht. Mahnke, Dietrich.

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