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The book contains a translation and study of Euclid’s Phaenomena, a work which once formed part of the mathematical training of astronomers from Central Asia to Western Europe. Included is an introduction that sets Euclid’s geometry of the celestial sphere, and its application to the astronomy of his day, into its historical context for readers not already familiar with it. So no knowledge of astronomy or advanced mathematics is necessary for an understanding of the work. The book shows mathematical astronomy shortly before the invention of trigonometry, which allowed the calculation of exact results and the subsequent composition of Ptolemy’s Almagest.
The Phaenomena itself begins with an introduction (possibly not by Euclid) followed by eighteen propositions set out in geometrical style about how arcs of the zodiacal circle move across the sky. The astronomical application is to the small arc of that circle occupied by the Sun, but the Sun is not mentioned. This work and the (roughly) contemporaneous treatises of Autolycus and Aristarchos form a corpus of the oldest extant works on mathematical astronomy. Together with Euclid’s Optics one has the beginnings of the history of science as an application of mathematics.
Preface to Second Printing
Preface
Introduction
The purpose and strategy of the Phaenomena
Pre-Euclidean works on the subject of the Phaenomena
The integrity and authenticity of the Phaenomena
History of the text
Euclid's Presuppositions
Mathematical presuppositions
Astronomical presuppositions
Geographical presuppositions
Notes on the Translation
The Greek text
Other translations
General remarks
Technical remarks
The figures
Sigla
Euclid's Phaenomena
English glossary of selected technical terms and phrases
Greek glossary of selected technical terms and phrases
Bibliography
Index of Names
Index of Subjects
Index of Subjects (Greek)