The Ancient Tradition of Geometric Problems

Knorr, Wilbur Richard

Brossura

ISBN 10: 0486675327 ISBN 13: 9780486675329

Casa editrice: Dover Pubns, 2003

This highly regarded study focuses on attempts by Hippocrates, Archimedes, other ancient Greeks to solve three classical problems: cube duplication, angle trisection, and circle-quadrature. Topics include origins of the study of conics, introduction of special mechanical curves, use of sliding rulers and calculating procedures, and much more. 255 black-and-white illustrations. "Essential reading" —Mathematical Reviews. 1986 edition.

Contenuti:

Preface 1 Sifting History from Legend 2 Beginnings and Early Efforts (I) The Duplication of the Cube (II) The Quadrature of the Circle (III) Problems and Methods 3 The Geometers in Plato's Academy (I) Solutions of the Cube-Duplication (II) Geometric Methods in the Analysis of Problems (III) Efforts toward the Quadrature of the Circle (IV) Geometry and Philosophy in the 4th Century 4 The Generation of Euclid (I) A Locus-Problem in the Aristotelian Corpus (II) Euclid's Analytic Works (III) The Analysis of Conic Problems: Some Reconstructions (IV) "An Angle-Trisection via "Surface-Locus" (V) Euclid's Contribution to the Study of Problems 5 Archimedes?The Perfect Eudoxean Geometer (I) Circle-Quadrature and Spirals (II) Problem-Solving via Conic Sections (III) Problem-Solving via Neuses (IV) An Anonymous Cube-Duplication (V) The Impact of Archimedes' Work 6 The Successors of Archimedes in the 3rd Century (I) Eratosthenes (II) Nicomedes (III) Diocles (IV) "On the Curve called "Cissoid" (V) "Dionysodorus, Perseus and Zenodorus" (VI) In the Shadow of Archimedes 7 Apollonius?Culmination of the Tradition (I) "Apollonius, Archimedes and Heraclides" (II) Apollonius and Nicomedes (III) Apollonius and Euclid (IV) Apollonius and Aristaeus (V) Origins and Motives of the Apollonian Geometry 8 Appraisal of the Analytic Field in Antiquity (I) The Ancient Classifications of Problems (II) "Problems, Theorems and the Method of Analysis" (III) ". . . And many and the greatest sought, but did not find." (IV) Epilogue Bibliography Indices

Product Description:

Book by Knorr Wilbur Richard