Works of archimedes : the two books on the sphere and the cylinder.
This is Volume 1 of the first authoritative translation of Archimedes' works into English. Also provided are a scientific edition of the diagrams, a translation of the ancient commentator Eutocius and a commentary, where attention is paid to the cognitive and aesthetic nature of Archimedes'...
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge :
Cambridge Univ Press,
2004
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| Subjects: | |
| Local Note: | ProQuest Ebook Central |
Table of Contents:
- COVER; HALF-TITLE; TITLE; COPYRIGHT; DEDICATION; CONTENTS; ACKNOWLEDGMENTS; INTRODUCTION; 1 goal of the translation; 2 preliminary notes: conventions; 2.1 Some special conventions of Greek mathematics; 2.2 Special conventions adopted in this translation; 2.3 Purpose and practices of the critical edition of diagrams; 3 preliminary notes: archimedes ́works; 3.1 Archimedes and his works; 3.2 The text of Archimedes; 3.3 The two books On the Sphere and the Cylinder; TRANSLATION AND COMMENTARY; ON THE SPHERE AND THE CYLINDER, BOOK I; /Introduction: general/; textual comments; general comments.
- Introduction: the genreArchimedes' audience: conon and dositheus; /"Axiomatic" introduction/; /Definitions/; /Postulates/; textual comments; general comments; Definitions 1-4; Postulates 1-2: about what?; Unpacking Postulate 2; Unpacking Postulate 3; The overall structure of Definitions 1-4, Postulates 1-4; Postulate 5; /1/; textual comments; general comments; The use of the diagram; The use of the axiomatic introduction; Generality of the proof; /2/; textual comments; general comments; Existence and realism; Shortcuts used in exposition.
- Schematic nature and the intended generality of the diagram/3/; textual comments; general comments; The scholiast's regress; /4/; textual comments; general comments; Repetition of text, and virtual mathematical actions; /5/; textual comments; general comments; Impatience revealed in exposition; /6/; textual comments; general comments; Lack of pedagogic concerns; Meta-mathematical interests displayed in the text; /7/; textual comments; general comments; Equality and identity; The "grounds" for a claim; /8/; textual comments; general comments.
- The significance of different ways of naming objectsGenerality and the use of letters referring to the diagram; /9/; textual comments; general comments; Bifurcating structure of proof; Ambiguities and their implication for the author/audience attitude; /10/; textual comments; general comments; What is the sequence of actions inside a construction?; The role of the axiomatic discussion; /11/; textual comments; general comments; The significance of different ways of using letters; Operations on phrases as a tool for argumentation; /12/; textual comments; general comments.
- The extent to which words are allowed to shiftThe operation of "imagination"; A tendency to abbreviate; /Sequel to sequence 9-12/; textual and general comments; /13/; textual comments; general comments; Equalities and inequalities; Arguments based on division of logical space; Relations between parts of text; Some notes on operations with ratios; /14/; textual comments; general comments; Different layers of imagination; /15/; textual comments; general comments; Reference to Proposition 14; /16/; textual comments; general comments; The phenomenon of arguments that are left implicit.
