Suchergebnisse

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 OLDENBURG -- 1678: 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 Gregory -- Leibniz 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.