Springer | 2004 | 463 páginas | pdf | 4 Mb
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.
TABLE OF CONTENTS
Permissions ix
Preface xi
PART 1. THE BEGINNINGS OF GREEK MATHEMATICS
Texts selected and introduced by Hans-Joachim Waschkies
HANS-JOACHIM WASCHKIES / Introduction 3
JÜRGEN MITTELSTRASS / Die Entdeckung der Möglichkeit von Wissenchaft
Archive for History of Exact Sciences 2 (1962-66), 410-435 19
ÁRPÁD SZABÓ / Wie ist die Mathematik zu einer deduktiven Wissenschaft geworden?
Acta Antiqua Academiae Scientiarum Hungaricae IV (1956), 109-151 45
WILBUR RICHARD KNORR / On the early history of axiomatics.
The interaction of mathematics and philosophy in Greek antiquity.
Theory change, ancient axiomatics, and Galileo’s methodology.
J. Hintikka, D. Gruender, E. Agazzi (Eds), Dordrecht/Boston/London, 1981, 145-186 81
PART 2. STUDIES ON GREEK GEOMETRY
Texts selected and introduced by Reviel Netz
REVIEL NETZ / Introduction 113
WILBUR RICHARD KNORR / Construction as Existence Proof in Ancient Geometry
Ancient Philosophy 3 (1983), 125-148 115
KEN SAITO / Book II of Euclid’s Elements in the Light of the Theory of Conic Sections
Historia Scientiarum 28 (1985), 31-60 139
G.E.R. LLOYD / The Meno and the Mysteries of Mathematics
Phronesis 37 (1992), 166-183 169
PART 3. STUDIES ON PROPORTION THEORY AND INCOMMENSURABILITY
Texts selected and introduced by Ken Saito
KEN SAITO / Introduction 187
Proportionenlehre und ihre Spuren bei Aristoteles und Euklid
Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik B.II (1933), 311-330 191
KURT VON FRITZ / The Discovery of Incommensurability by Hippasus of Metapontum
Annals of Mathematics 46 (1954), 242-264 211
HANS FREUDENTHAL / Y avait-il une crise des fondements des mathématiques dans l’antiquité?
Bulletin de la Société mathématique de Belgique 18 (1966), 43-55 233
WILBUR RICHARD KNORR / The Impact of Modern Mathematics on Ancient Mathematics
Revue d’histoire des mathématiques 7 (2001), 121-135 243
PART 4. STUDIES ON GREEK ALGEBRA
Texts selected and introduced by Jacques Sesiano
JACQUES SESIANO / Introduction 257
KURT VOGEL / Zur Berechnung der quadratischen
Unterrichtsblätter für Mathematik und Naturwissenschaften 39 (1933), 76-81 265
G.J. TOOMER / Lost Greek mathematical works in Arabic translation
Mathematical Intelligencer 6.2 (1984), 32-38 275
THOMAS L. HEATH / Diophantus’ methods of solution
Fourth chapter (pp. 54-98) of Heath’s book Diophantus of Alexandria. A study in the history of Greek algebra. New York, 1964 285
PART 5. DID THE GREEKS HAVE THE NOTION OF COMMON FRACTION? DID THEY USE IT?
Texts selected and introduced by Jean Christianidis
JEAN CHRISTIANIDIS / Introduction 331
WILBUR RICHARD KNORR / Techniques of fractions in Ancient Egypt and Greece.
Historia Mathematica 9 (1982), 133-171 337
DAVID H. FOWLER / Logistic and fractions in early Greek mathematics: a new interpretation.
Histoire des fractions, fraction d’histoire. P. Benoit, K. Chemla, J. Ritter (Eds), Basel/Boston/Berlin, 1992, 133-147 367
PART 6. METHODOLOGICAL ISSUES IN THE HISTORIOGRAPHY OF GREEK MATHEMATICS
Texts selected and introduced by Sabetai Unguru
SABETAI UNGURU / Introduction 383
SABETAI UNGURU / On the Need to Rewrite the History of Greek Mathematics.
Archive for History of Exact Sciences 15 (1975), 67-114 385
B.L. VAN DER WAERDEN / Defence of a ‘Shocking’ Point of View.
Archive for History of Exact Sciences 15 (1976), 199-210 433
ANDRÉ WEIL / Who Betrayed Euclid? (Extract from a letter to the Editor)
Archive for History of Exact Sciences 19 (1978), 91-93 447
SABETAI UNGURU / History of Ancient Mathematics: Some Reflections on the State of the Art
Isis 70 (1979), 555-565 451
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