Apollonius of Perga's Conica : text, context, subtext. By Michael N. Fried, Sabetai Unguru

Fried, Michael N.; Unguru, Sabetai (ed.); Apollonius Pergaeus, A. of Perga (auth.)

ISBN 10: 9004119779 / ISBN 13: 9789004119772

Published by Brill Academic Publishers, Leiden, Boston, 2001., 2001

About this Item

Large octavo (245 x 165 mm), publisher's illustrated hardcover, XII, 499 (+1) pp., with numerous schematic b/w-illustrations in the text, previous owner's stamp to front fly leaf (Exlibris H. S. Versnel), a well preserved copy. [MnS - Mnemosyne Supplements; 222]. - ISBN: 9004119779. - Contents/Inhalt : I. Geometrical Algebra -- A. Its Formulation -- B.1. Its Origins -- B.2. Strength and Weakness of Geometrical Algebra -- C. The Influence of "Geometrical Algebra" in the Interpretation of the Conica -- II. The Elements of Conic Sections in the Framework of Books I-III -- Apollonius's Introduction and the General Nature of "Elements" -- The Initial Definitions -- The Definitions of the Conic Sections and the Symptomata -- A Second Look at the Algebraic Interpretation of The Elements of Conics -- Symptomata and Equations -- The Locus Problem -- Intentiones Primae and Intentiones Secundae -- The Place of Diameters -- III. Book IV of the Elements of Conic Sections: How Conic Sections Meet in the Plane -- The Investigation of Opposite Sections -- How Conic Sections Meet in a Plane -- Digression: Descartes' Treatment of Cutting and Touching in La Geometrie -- The Possibility of Different Conic Sections in One Plane -- IV. Maximum and Minimum Lines: Book V of the Conica -- The Conventional View: Normals as Maxima and Minima -- The Importance of Normals -- The Evolute -- Maximum and Minimum Lines as Longest and Shortest Lines -- Neusis-like Constructions -- V. Equality and Similarity: Book VI of the Conica -- Equality -- Similarity -- Equality and Similarity -- The Constructions -- VI. Diorismic Theorems and the Use of Analogy: Book VII of the Conica -- Diorismoi and Diorismic Theorems -- A Glance at Halley's Book VIII -- The Diorismic Theorems of Book VII -- Images of Diameters and Latera Recta -- VII. Once Again, the use of Analogy in Apollonius: Conics and Circles -- The Tangent and the Asymptote: An "Internal" Analogy in the Conica -- Circles and Conic Sections -- VIII. The Conica as an Integral Whole: Elementary and Non-Elementary Books -- Was the Conica Written as One book? -- Elementary and Advanced Books: The Basic Division in the Conica -- IX. Some Circumscribed Reflections on the Historiography of Hellenistic Mathematics -- App. English Translation of Book IV. Appendix: p. [413]-485.; Includes bibliographical references (p. [487]-494) and index. ||| Apollonius, of Perga. Conics; Mathematics, Greek; Conic sections Early works to 1800 - Apollonius von Perge. Konische; Mathematik, Griechisch; Konische Abschnitte Frühe Werke bis 1800 - [00B | SOD | oR ] 1010 g.

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Bibliographic Details

• Title: Apollonius of Perga's Conica : text, context, subtext. By Michael N. Fried, Sabetai Unguru
• Publisher: Brill Academic Publishers, Leiden, Boston, 2001.
• Publication Date: 2001
• Language: English
• ISBN 10: 9004119779
• ISBN 13: 9789004119772
• Binding: Hardcover
• Weight: 1010 grams
• Seller catalogs:
  • ANTIKE - Classical Antiquity - Mnemosyne Supple...

About this title

Synopsis

This volume takes a new look at one of the greatest works of Hellenistic mathematics, Apollonius of Perga's Conica. It provides a long overdue alternative to H.G. Zeuthen's Die Lehre von den Kegelschnitten im Altertum.
The central part of the volume contains a historically sensitive analysis and interpretation of the entire Conica, both from the standpoint of its individual books and of the text as a whole. Particular attention is given to Books V-VII, which have had scant treatment until now. Two chapters in the volume concern histioriographic issues connected with the Conica in paricular and Greek mathematics in general.
Although the volume is intended primarily for historians of ancient mathematics, its approach is fresh and engaging enough to be of interest also to historians, philosophers, linguists, and open-minded mathematicians.

About the Author

Michael N. Fried, Ph.D. (1998) in History of Science, Tel-Aviv University, a graduate of St.John's College, is Researcher at Ben Gurion University of the Negev, Center for Science and Technology Education.
Sabetai Unguru, Ph.D. (1970) in History of Science, University of Wisconsin, Madison, is Professor Emeritus at Tel-Aviv University. His publications are in the fields of the history of Greek mathematics and medieval optics.