Leibniz and the Invention of Mathematical Transcendence:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Stuttgart :
Franz Steiner Verlag,
2018.
|
| Schriftenreihe: | Studia Leibnitiana. Sonderheft ;
53. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | A hierarchy in transcendence? |
| Beschreibung: | 1 online resource (250 pages) |
| Bibliographie: | Includes bibliographical references (pages 217-225). |
| ISBN: | 3515120831 9783515120838 |
Internformat
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| 490 | 1 | |a Studia Leibnitiana. Sonderhefte ; |v 53 | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 500 | |a A hierarchy in transcendence? | ||
| 504 | |a Includes bibliographical references (pages 217-225). | ||
| 600 | 1 | 0 | |a Leibniz, Gottfried Wilhelm, |c Freiherr von, |d 1646-1716. |0 http://id.loc.gov/authorities/names/n79081493 |
| 600 | 1 | 7 | |a Leibniz, Gottfried Wilhelm, |c Freiherr von, |d 1646-1716 |2 fast |1 https://id.oclc.org/worldcat/entity/E39PBJxCxx9XjP7GxJkTmvXrv3 |
| 650 | 0 | |a Mathematics |x Philosophy. |0 http://id.loc.gov/authorities/subjects/sh85082153 | |
| 650 | 0 | |a Transcendence (Philosophy) |0 http://id.loc.gov/authorities/subjects/sh85136881 | |
| 650 | 0 | |a Transcendental numbers. |0 http://id.loc.gov/authorities/subjects/sh85093223 | |
| 650 | 6 | |a Mathématiques |x Philosophie. | |
| 650 | 6 | |a Transcendance (Philosophie) | |
| 650 | 6 | |a Nombres transcendants. | |
| 650 | 7 | |a Mathematics |x Philosophy |2 fast | |
| 650 | 7 | |a Transcendence (Philosophy) |2 fast | |
| 650 | 7 | |a Transcendental numbers |2 fast | |
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| 776 | 0 | 8 | |i Print version: |a Serfati, Michel. |t Leibniz and the Invention of Mathematical Transcendence. |d Stuttgart : Franz Steiner Verlag, ©2018 |
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| _version_ | 1816882495605440512 |
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| author | Serfati, Michel |
| author_GND | http://id.loc.gov/authorities/names/no2004112329 |
| author_facet | Serfati, Michel |
| author_role | |
| author_sort | Serfati, Michel |
| author_variant | m s ms |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
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| 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 |
| ctrlnum | (OCoLC)1107566279 |
| dewey-full | 510.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.1 |
| dewey-search | 510.1 |
| dewey-sort | 3510.1 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-on1107566279 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:29:31Z |
| institution | BVB |
| isbn | 3515120831 9783515120838 |
| language | English |
| oclc_num | 1107566279 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (250 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | Franz Steiner Verlag, |
| record_format | marc |
| series | Studia Leibnitiana. Sonderheft ; |
| series2 | Studia Leibnitiana. Sonderhefte ; |
| spelling | Serfati, Michel. http://id.loc.gov/authorities/names/no2004112329 Leibniz and the Invention of Mathematical Transcendence Stuttgart : Franz Steiner Verlag, 2018. 1 online resource (250 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Studia Leibnitiana. Sonderhefte ; 53 Print version record. 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 A hierarchy in transcendence? Includes bibliographical references (pages 217-225). Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716. http://id.loc.gov/authorities/names/n79081493 Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716 fast https://id.oclc.org/worldcat/entity/E39PBJxCxx9XjP7GxJkTmvXrv3 Mathematics Philosophy. http://id.loc.gov/authorities/subjects/sh85082153 Transcendence (Philosophy) http://id.loc.gov/authorities/subjects/sh85136881 Transcendental numbers. http://id.loc.gov/authorities/subjects/sh85093223 Mathématiques Philosophie. Transcendance (Philosophie) Nombres transcendants. Mathematics Philosophy fast Transcendence (Philosophy) fast Transcendental numbers fast has work: Leibnitz and the invention of mathematical transcendence (Text) https://id.oclc.org/worldcat/entity/E39PCGG8jmv4dtvxRqcVQtKXtX https://id.oclc.org/worldcat/ontology/hasWork Print version: Serfati, Michel. Leibniz and the Invention of Mathematical Transcendence. Stuttgart : Franz Steiner Verlag, ©2018 Studia Leibnitiana. Sonderheft ; 53. http://id.loc.gov/authorities/names/n42033148 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=2478774 Volltext |
| spellingShingle | Serfati, Michel Leibniz and the Invention of Mathematical Transcendence Studia Leibnitiana. Sonderheft ; 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 Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716. http://id.loc.gov/authorities/names/n79081493 Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716 fast https://id.oclc.org/worldcat/entity/E39PBJxCxx9XjP7GxJkTmvXrv3 Mathematics Philosophy. http://id.loc.gov/authorities/subjects/sh85082153 Transcendence (Philosophy) http://id.loc.gov/authorities/subjects/sh85136881 Transcendental numbers. http://id.loc.gov/authorities/subjects/sh85093223 Mathématiques Philosophie. Transcendance (Philosophie) Nombres transcendants. Mathematics Philosophy fast Transcendence (Philosophy) fast Transcendental numbers fast |
| subject_GND | http://id.loc.gov/authorities/names/n79081493 http://id.loc.gov/authorities/subjects/sh85082153 http://id.loc.gov/authorities/subjects/sh85136881 http://id.loc.gov/authorities/subjects/sh85093223 |
| title | Leibniz and the Invention of Mathematical Transcendence |
| title_auth | Leibniz and the Invention of Mathematical Transcendence |
| title_exact_search | Leibniz and the Invention of Mathematical Transcendence |
| title_full | Leibniz and the Invention of Mathematical Transcendence |
| title_fullStr | Leibniz and the Invention of Mathematical Transcendence |
| title_full_unstemmed | Leibniz and the Invention of Mathematical Transcendence |
| title_short | Leibniz and the Invention of Mathematical Transcendence |
| title_sort | leibniz and the invention of mathematical transcendence |
| topic | Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716. http://id.loc.gov/authorities/names/n79081493 Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716 fast https://id.oclc.org/worldcat/entity/E39PBJxCxx9XjP7GxJkTmvXrv3 Mathematics Philosophy. http://id.loc.gov/authorities/subjects/sh85082153 Transcendence (Philosophy) http://id.loc.gov/authorities/subjects/sh85136881 Transcendental numbers. http://id.loc.gov/authorities/subjects/sh85093223 Mathématiques Philosophie. Transcendance (Philosophie) Nombres transcendants. Mathematics Philosophy fast Transcendence (Philosophy) fast Transcendental numbers fast |
| topic_facet | Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716. Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716 Mathematics Philosophy. Transcendence (Philosophy) Transcendental numbers. Mathématiques Philosophie. Transcendance (Philosophie) Nombres transcendants. Mathematics Philosophy Transcendental numbers |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=2478774 |
| work_keys_str_mv | AT serfatimichel leibnizandtheinventionofmathematicaltranscendence |