Ebook: Classics in the History of Greek Mathematics

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.

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This volume includes a selection of 19 classic papers on the history of Greek mathematics that were published during the 20th century and affected significantly the state of the art of this field. It is divided into six thematic sections and covers all the major issues of the Greek mathematical production. First, the inclusion in one volume of a considerable number of papers that had been published for the first time in old, and in certain cases hard to find, scientific journals representing turning-points in the history of the field, constitutes a particularly useful aid for all those working on the history of mathematics. Second, by means of the selected papers and the introductory texts of six well-known modern historians of ancient mathematics that accompany them, the reader can follow the ways the historiography of Greek mathematics developed. Finally, the introductory texts that precede each chapter help the reader to approach critically the selected papers and at the same time to get an idea of the issues being further clarified by the new historiographical approaches.

The audience of the book includes scholars from history and philosophy of mathematics and mathematical sciences, scholars from history of science, students in the field of history of mathematics and history of sciences.

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This volume includes a selection of 19 classic papers on the history of Greek mathematics that were published during the 20th century and affected significantly the state of the art of this field. It is divided into six thematic sections and covers all the major issues of the Greek mathematical production. First, the inclusion in one volume of a considerable number of papers that had been published for the first time in old, and in certain cases hard to find, scientific journals representing turning-points in the history of the field, constitutes a particularly useful aid for all those working on the history of mathematics. Second, by means of the selected papers and the introductory texts of six well-known modern historians of ancient mathematics that accompany them, the reader can follow the ways the historiography of Greek mathematics developed. Finally, the introductory texts that precede each chapter help the reader to approach critically the selected papers and at the same time to get an idea of the issues being further clarified by the new historiographical approaches.

The audience of the book includes scholars from history and philosophy of mathematics and mathematical sciences, scholars from history of science, students in the field of history of mathematics and history of sciences.

Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Introduction....Pages 3-18
Die Entdeckung der M?glichkeit von Wissenschaft....Pages 19-44
Wie ist die Mathematik zu Einer Deduktiven Wissenschaft Geworden?....Pages 45-80
On the Early History of Axiomatics: The Interaction of Mathematics and Philosophy in Greek Antiquity....Pages 81-109
Front Matter....Pages 111-111
Introduction....Pages 113-114
Construction as Existence Proof in Ancient Geometry....Pages 115-137
Book II of Euclid’s Elements in the Light of the Theory of Conic Sections....Pages 139-168
The Meno and the Mysteries of Mathematics....Pages 169-183
Front Matter....Pages 185-185
Introduction....Pages 187-190
Eudoxos — Studien I. Eine Voreudoxische Proportionenlehre und Ihre Spuren bei Aristoteles und Euklid....Pages 191-209
The Discovery of Incommensurability by Hippasus of Metapontum....Pages 211-231
Y Avait-Il une Crise des Fondements des Math?matiques Dans L’Antiquit??....Pages 233-241
The Impact of Modern Mathematics on Ancient Mathematics....Pages 243-253
Front Matter....Pages 255-255
Introduction....Pages 257-263
Zur Berechnung der Quadratischen Gleichungen bei den Babyloniern....Pages 265-273
Lost Greek Mathematical Works in Arabic Translation....Pages 275-284
Diophantus’ Methods of Solution....Pages 285-327
Front Matter....Pages 329-329
Introduction....Pages 331-336
Techniques of Fractions in Ancient Egypt and Greece....Pages 337-365
Logistic and Fractions in Early Greek Mathematics: A New Interpretation....Pages 367-380
Front Matter....Pages 381-381
Introduction....Pages 383-384
On the Need to Rewrite the History of Greek Mathematics....Pages 385-431
Defence of a “Shocking” Point of View....Pages 433-445
Who Betrayed Euclid?....Pages 447-449
History of Ancient Mathematics: Some Reflections on the State of the Art....Pages 451-461
Back Matter....Pages 463-474

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This volume includes a selection of 19 classic papers on the history of Greek mathematics that were published during the 20th century and affected significantly the state of the art of this field. It is divided into six thematic sections and covers all the major issues of the Greek mathematical production. First, the inclusion in one volume of a considerable number of papers that had been published for the first time in old, and in certain cases hard to find, scientific journals representing turning-points in the history of the field, constitutes a particularly useful aid for all those working on the history of mathematics. Second, by means of the selected papers and the introductory texts of six well-known modern historians of ancient mathematics that accompany them, the reader can follow the ways the historiography of Greek mathematics developed. Finally, the introductory texts that precede each chapter help the reader to approach critically the selected papers and at the same time to get an idea of the issues being further clarified by the new historiographical approaches.

The audience of the book includes scholars from history and philosophy of mathematics and mathematical sciences, scholars from history of science, students in the field of history of mathematics and history of sciences.

Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Introduction....Pages 3-18
Die Entdeckung der M?glichkeit von Wissenschaft....Pages 19-44
Wie ist die Mathematik zu Einer Deduktiven Wissenschaft Geworden?....Pages 45-80
On the Early History of Axiomatics: The Interaction of Mathematics and Philosophy in Greek Antiquity....Pages 81-109
Front Matter....Pages 111-111
Introduction....Pages 113-114
Construction as Existence Proof in Ancient Geometry....Pages 115-137
Book II of Euclid’s Elements in the Light of the Theory of Conic Sections....Pages 139-168
The Meno and the Mysteries of Mathematics....Pages 169-183
Front Matter....Pages 185-185
Introduction....Pages 187-190
Eudoxos — Studien I. Eine Voreudoxische Proportionenlehre und Ihre Spuren bei Aristoteles und Euklid....Pages 191-209
The Discovery of Incommensurability by Hippasus of Metapontum....Pages 211-231
Y Avait-Il une Crise des Fondements des Math?matiques Dans L’Antiquit??....Pages 233-241
The Impact of Modern Mathematics on Ancient Mathematics....Pages 243-253
Front Matter....Pages 255-255
Introduction....Pages 257-263
Zur Berechnung der Quadratischen Gleichungen bei den Babyloniern....Pages 265-273
Lost Greek Mathematical Works in Arabic Translation....Pages 275-284
Diophantus’ Methods of Solution....Pages 285-327
Front Matter....Pages 329-329
Introduction....Pages 331-336
Techniques of Fractions in Ancient Egypt and Greece....Pages 337-365
Logistic and Fractions in Early Greek Mathematics: A New Interpretation....Pages 367-380
Front Matter....Pages 381-381
Introduction....Pages 383-384
On the Need to Rewrite the History of Greek Mathematics....Pages 385-431
Defence of a “Shocking” Point of View....Pages 433-445
Who Betrayed Euclid?....Pages 447-449
History of Ancient Mathematics: Some Reflections on the State of the Art....Pages 451-461
Back Matter....Pages 463-474
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