Apollonius of Perga's Conica: Text, Context, SubtextBRILL, 2001 - 499 sider 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. |
Innhold
Geometrical Algebra | 17 |
The Influence of Geometrical Algebra in | 38 |
Figures | 44 |
The Elements of Conic Sections in the Framework | 56 |
The Definitions of the Conic Sections and | 74 |
A Second Look at the Algebraic Interpretation | 90 |
The Locus Problem | 97 |
The Place of Diameters | 103 |
Book V of | 146 |
Book VI of the Conica | 221 |
Elementary | 364 |
Some Circumscribed Reflections on | 390 |
English Translation of Book IV | 413 |
| 487 | |
| 495 | |
Figures | 109 |
Andre utgaver - Vis alle
Apollonius of Perga's Conica: Text, Context, Subtext Michael Fried,Sabetai Unguru Begrenset visning - 2017 |
Apollonius of Perga's Conica: Text, Context, Subtext Michael N. Fried,Sabetai Unguru Ingen forhåndsvisning tilgjengelig - 2001 |
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analogy ancient angle contained Apollonius Conics Books Apollonius of Perga Apollonius says Apollonius's Archimedes asymptotes axes axial triangle axis bisected Book VII chapter circle coincide cone or circumference conic sec conic sections conic surface conjugate diameters constructed curve cut the section definition Descartes diagram diam Diocles diorismic theorems draw ellipse emphasis added equality and similarity equation Euclid Euclid's Elements Eudemus Eutocius example figure follows geometrical algebra given greater Greek mathematics half the latus Halley's Heath homologue hyperbola Ibid joined Knorr latera latera recta latus rectum line cut lines drawn maximum means meet minimum line neusis opposite sections ordinates ordinatewise Pappus parabola parallelogram perpendicular point of contact possible problem Proclus proof propositions in Book proved ratio rectangle contained refers right cone segments square straight line symptomata tangent things tion Toomer touch the section translation transverse diameter upright side vertex Zeuthen