Classics in the History of Greek Mathematics

1. Front Matter

   Pages i-xi

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2. The Beginnings of Greek Mathematics

   1. Front Matter

      Pages 1-1

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   2. Introduction

      • Hans-Joachim Waschkies

      Pages 3-18

   3. Die Entdeckung der Möglichkeit von Wissenschaft

      • Jürgen Mittelstrass

      Pages 19-44

   4. Wie ist die Mathematik zu Einer Deduktiven Wissenschaft Geworden?

      • Á. Szabó

      Pages 45-80

   5. On the Early History of Axiomatics: The Interaction of Mathematics and Philosophy in Greek Antiquity

      • Wilbur Richard Knorr

      Pages 81-109

3. Studies on Greek Geometry

   1. Front Matter

      Pages 111-111

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   2. Introduction

      • Reviel Netz

      Pages 113-114

   3. Construction as Existence Proof in Ancient Geometry

      • Wilbur R. Knorr

      Pages 115-137

   4. Book II of Euclid’s Elements in the Light of the Theory of Conic Sections

      • Ken Saito

      Pages 139-168

   5. The Meno and the Mysteries of Mathematics

      • G. E. R. Lloyd

      Pages 169-183

4. Studies on Proportion Theory and Incommensurability

   1. Front Matter

      Pages 185-185

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   2. Introduction

      • Ken Saito

      Pages 187-190

   3. Eudoxos — Studien I. Eine Voreudoxische Proportionenlehre und Ihre Spuren bei Aristoteles und Euklid

      • Oskar Becker

      Pages 191-209

   4. The Discovery of Incommensurability by Hippasus of Metapontum

      • Kurt von Fritz

      Pages 211-231

   5. Y Avait-Il une Crise des Fondements des Mathématiques Dans L’Antiquité?

      • H. Freudenthal

      Pages 233-241

   6. The Impact of Modern Mathematics on Ancient Mathematics

      • Wilbur R. Knorr

      Pages 243-253

5. Studies on Greek Algebra

   1. Front Matter

      Pages 255-255

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   2. Introduction

      • Jacques Sesiano

      Pages 257-263

   3. Zur Berechnung der Quadratischen Gleichungen bei den Babyloniern

      • Kurt Vogel

      Pages 265-273

The twentieth century is the period during which the history of Greek mathematics reached its greatest acme. Indeed, it is by no means exaggerated to say that Greek mathematics represents the unique field from the wider domain of the general history of science which was included in the research agenda of so many and so distinguished scholars, from so varied scientific communities (historians of science, historians of philosophy, mathematicians, philologists, philosophers of science, archeologists etc. ), while new scholarship of the highest quality continues to be produced. This volume includes 19 classic papers on the history of Greek mathematics that were published during the entire 20th century and affected significantly the state of the art of this field. It is divided into six self-contained sections, each one with its own editor, who had the responsibility for the selection of the papers that are republished in the section, and who wrote the introduction of the section. It constitutes a kind of a Reader book which is today, one century after the first publications of Tannery, Zeuthen, Heath and the other outstanding figures of the end of the 19th and the beg- ning of 20th century, rather timely in many respects.

• Aristotle
• History of Mathematics
• interpret
• issue
• knowledge
• philosophy
• science

From the reviews:

In Classics in the History of Greek Mathematics, Christianidis has provided a very useful collection of papers that encompass many of these changes. Here one can find Unguru's original papers (and the angry responses they elicited), discussions of the supposed "crisis of foundations", papers on the origin of Greek axiomatics, on geometry and "algebra". The papers, alas, are in their original languages (German, French, and English), but anglophone readers can be reassured that most of the articles are in English, especially the more recent ones. In any case, this is an excellent place to go to learn what the historians have been up to, and the give-and-take of debate makes it fascinating. The book is probably too expensive for non-fanatic individual readers, but it is definitely a "must buy" for libraries [Fernando Q. Gouvêa; posted to MAA Reviews 1/11/2006]

"This is a tool for working historian … because it offers a cross-section of the main historiographical currents that represents well the evolution of the field in the last decades. … Essays are reproduced that date back more than 40 years, and written in French or German. This is a very important feature of the book, especially because a large portion of contemporary scholarship appears to resort almost exclusively to the most recent secondary literature and to contributions written in English." (Fabio Acerbi, Aestimatio, Issue 3, 2006)

• University of Athens, Greece

  Jean Christianidis

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