Highly regarded study focuses on ancient Greek efforts to solve the three classical problems of cube duplication, angle trisection and circle-quadrature by such famed mathematicians as Hippocrates of Chios, Eudoxus, Archimedes and Apollonius, and spans virtually the entire period of ancient geometry. "Essential reading"-Mathematical Reviews. 1986 edition. Bibliography. 255 black-and-white illustrations.

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