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Die Werke von Jakob Bernoulli

Bd. 5: Differentialgeometrie

Autoren: Bernoulli, Jakob

Herausgeber: Speiser, David, Weil, André, Mattmüller, Martin (Eds.)

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Über dieses Buch

This volume contains the work of the great Swiss mathematician on differential geometry, a field marked by some of his greatest achievements. Between 1690 and 1700, Jacob Bernoulli published twelve treatises in the scientific journal Acta Eruditorum on the use of infinitesimal methods to answer geometrical questions. Preparatory notes for most of these papers and on many other themes are found in Bernoulli's scientific diary Meditationes, from which twentynine texts are published here for the first time. Among the curves considered are the isochrones (lines of constant descent), the parabolic spiral, the loxodrome, the cycloid, the tractrix, and the logarithmic spiral (Bernoulli's spira mirabilis, which also adorns his tombstone). The description of these curves by differential equations and by geometrical constructions, their rectification and quadrature, and the determination of their evolutes and caustics offered Bernoulli and his colleagues a range of challenging problems, many of them relevant for mechanical or optical applications. The French mathematician André Weil, who lived in the United States until his recent death, has greatly influenced 20th century mathematics, among other things, as a founding member of the Bourbaki group. For many years he has pursued intensive studies of the history of mathematics, especially number theory and algebraic geometry. Weil's introduction to this volume places Jacob Bernoulli's contribution to differential geometry in a line of development from Descartes, Huygens and Barrow through Newton's und Leibniz's epochal innovations right up to the codification of the subject by Euler. Martin Mattmüller, secretary of the Bernoulli Edition at Basel, edited the source text. His commentaries consider particular topics in differential geometry with reference to their historical context at the end of the 17th century.

Dieses Buch kaufen

Hardcover 210,60 €
Preis für Deutschland (Brutto)
  • ISBN 978-3-7643-5779-5
  • Kostenfreier Versand für Individualkunden weltweit
  • Versandfertig innerhalb von 3 Tagen.

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Bibliografische Information

Bibliographic Information
Buchtitel
Die Werke von Jakob Bernoulli
Buchuntertitel
Bd. 5: Differentialgeometrie
Autoren
Herausgeber
  • David Speiser
  • André Weil
  • Martin Mattmüller
Copyright
1999
Verlag
Birkhäuser Basel
Copyright Inhaber
Birkhäuser Basel
Hardcover ISBN
978-3-7643-5779-5
Auflage
1
Seitenzahl
445
Themen