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The ancient tradition of geometric problems

Author: Wilbur Richard Knorr
Publisher: Cambridge, MA : Birkhäuser Boston, 1985-
Edition/Format:   Print book : EnglishView all editions and formats
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Genre/Form: History
Document Type: Book
All Authors / Contributors: Wilbur Richard Knorr
ISBN: 0817631488 9780817631482
OCLC Number: 9646780
Description: ix, 411 pages : illustrations (some color) ; 25 cm
Contents: Sifting history from legend --
Beginnings and early efforts --
The geometers in Plato's academy --
The generation of Euclid --
Archimedes--the perfect Eudoxean geometer --
The successors of Archimedes in the 3rd century --
Apollonius--culmination of the tradition --
Appraisal of the analytic field in antiquity.
Responsibility: Wilbur Knorr.

Table of Contents:

by drozdek (WorldCat user on 2008-04-22)

Preface vii 1 Sifting History from Legend 1 2 Beginnings and Early Efforts 15 (i) The Duplication of the Cube 17 (ii) The Quadrature of the Circle 25 (iii) Problems and Methods 39 3 The Geometers in Plato's Academy 49 (i) Solutions of the Cube-Duplication 50 (ii) Geometric Methods in the Analysis of Problems 66 (iii) Efforts toward the Quadrature of the Circle 76 (iv) Geometry and Philosophy in the 4th Century 86 4 The Generation of Euclid 101 (i) A Locus-Problem in the Aristotelian Corpus 102 (ii) Euclid's Analytic Works 108 (iii) The Analysis of Conic Problems: Some Reconstructions 120 (iv) An Angle-Trisection via "Surface-Locus" 128 (v) Euclid's Contribution to the Study of Problems 137 5 Archimedes—The Perfect Eudoxean Geometer 151 (i) Circle-Quadrature and Spirals 153 (ii) Problem-Solving via Conic Sections 170 (iii) Problem-Solving via Neuses 178 (iv) An Anonymous Cube-Duplication 188 (v) The Impact of Archimedes' Work 194 6 The Successors of Archimedes in the 3rd Century 209 (i) Eratosthenes 210 (ii) Nicomedes 219 (iii) Diodes 233 (iv) On the Curve called "Cissoid" 246 (v) Dionysodorus, Perseus and Zenodorus 263 (vi) In the Shadow of Archimedes 274 7 Apollonius—Culmination of the Tradition 293 (i) Apollonius, Archimedes and Heraclides 294 (ii) Apollonius and Nicomedes 303 (iii) Apollonius and Euclid 313 (iv) Apollonius and Aristaeus 321 (v) Origins and Motives of the Apollonian Geometry 328 8 Appraisal of the Analytic Field in Antiquity 339 (i) The Ancient Classifications of Problems 341 (ii) Problems, Theorems and the Method of Analysis 348 (iii) "... and many and the greatest sought, but did not find." 361 (iv) Epilogue 367 Bibliography 382 Indices 393

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