Apollonius of Perga's Conica : text, context, subtext
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
Early works
xii, 499 pages : illustrations ; 25 cm
9789004119772, 9004119779
47056365
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
Includes English translation of Conica Book IV