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Leibniz and the Invention of Mathematical Transcendence

Author: Michel Serfati
Publisher: Stuttgart : Franz Steiner Verlag, 2018.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Serfati, Michel.
Leibniz and the Invention of Mathematical Transcendence.
Stuttgart : Franz Steiner Verlag, ©2018
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Michel Serfati
ISBN: 9783515120838 3515120831
OCLC Number: 1107566279
Notes: A hierarchy in transcendence?
Description: 1 online resource (250 pages)
Contents: Intro; TABLE OF CONTENTS; LEIBNIZ AND THE INVENTION OF MATHEMATICAL TRANSCENDENCE. THE ADVENTURES OF AN IMPOSSIBLE INVENTORY; THE DISCOVERY OF THE TRANSCENDENCE; TRANSCENDENCE AND SYMBOLISM; TRANSCENDENCE AND GEOMETRY; LOOKING FOR AN INVENTORY; SYMBOLICAL INVENTORY?; GEOMETRICAL INVENTORY?; ON HIERARCHIES IN TRANSCENDENCE. EXPLORATIONS BY REPRODUCTION; RECEPTIONS OF THE TRANSCENDENCE; FIRST PART. DISCOVERING TRANSCENDENCE; CHAPTER I. ON THE GERMINATIONS OF THE CONCEPT OF 'TRANSCENDENCE'; 1673: "A TRANSCENDENT CURVE SQUARING THE CIRCLE ... "; 1674: ABOUT 'SECRET' GEOMETRY 1675: THE LETTER TO OLDENBURG1678: THE "PERFECTION OF TRANSCENDENT CALCULUS"; CHAPTER II. SQUARING THE CIRCLE; II-A THE ARITHMETICAL QUADRATURE OF THE CIRCLE (1673), OR THE VERY FIRST MATHEMATICAL GLORY OF LEIBNIZ; The quadrature of the hyperbola in Mercator; Quadratrices and symbolic substitutions: the mathematical ideas of Leibniz; Leibniz on "the exact proportion ... "; Some reflections on the integration of rational fractions; II-B LEIBNIZ AND THE IMPOSSIBILITY OF THE ANALYTICAL QUADRATURE OF THE CIRCLE OF GREGORY; The true quadrature of the circle and hyperbola, by James Gregory The geometric-harmonic mean of GregoryLeibniz and the "convergence" of adjacent sequences (1676); Leibniz's "means by composition"; A mathematical appendix: the geometric-harmonic mean (G-H); CHAPTER III THE POWER OF SYMBOLISM: EXPONENTIALS WITH LETTERS; III-A EPISTOLA PRIOR, OR LEIBNIZ'S DISCOVERY OF SYMBOLIC FORMS WITHOUT A SUBSTANCE (JUNE 1676); Fractional exponents; Symbolism without interpretation?; On the consistency of Newton's exponential; 'Permanence-Ramification'. A scheme; III-B THE EPISTOLA POSTERIOR (OCTOBER 1676); Irrational Exponents; Letters in Exponents III-C DESCARTES, LEIBNIZ AND THE IDEALIZED IMAGE OF THE EXPONENTIALGradus indefinitus; Descartes and Newton transcended by Leibniz; CONCLUSION OF THE FIRST PART: THE TRANSCENDENT IDENTIFIED WITH THE NON-CARTESIAN FIELD; SECOND PART. THE SEARCH FOR AN INVENTORY; CHAPTER IV FROM INFINITELY SMALL ELEMENTS TO THE EXPONENTIAL UTOPIA; IV-A TSCHIRNHAUS AND THE INVENTORIES OF 1679-1684; IV-B DE BEAUNE, DESCARTES, LEIBNIZ, AND THE INFINITELY SMALL ELEMENTS; When a curve is no longer considered as "a set of points" (in modern terminology); Descartes and De Beaune's problem Leibniz and De Beaune's problemIV-C ON EXPONENTIAL SYMBOLISMS; IV-C1 ON THE RESOLUTION OF THE EXPONENTIAL EQUATIONS. THE "ADMIRABLE EXAMPLE"; The admirable example; The impossibility of effective resolutions; IV-C2 EXPONENTIAL EXPRESSIONS AND THE DIALECTICS OF INDETERMINACY --
THE STATUS OF THE LETTER; The symbolism of quantities "arbitrary, but however fixed"; When the unknown enters the exponent; Towards letteralized exponentials; IV-C3 TOWARDS A HIERARCHY IN TRANSCENDENCE: THE INTERSCENDENT EXPONENTIALS; When the degree of the exponential "falls between" two integers

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