**History of Mathematics**

Volume: 29;
2006;
132 pp;
Softcover

MSC: Primary 01;

Print ISBN: 978-0-8218-4072-6

Product Code: HMATH/29

List Price: $32.00

Individual Member Price: $25.60

**Electronic ISBN: 978-1-4704-1809-0
Product Code: HMATH/29.E**

List Price: $32.00

Individual Member Price: $25.60

#### Supplemental Materials

# Euclid’s Phaenomena: A Translation and Study of a Hellenistic Treatise in Spherical Astronomy

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*J. L. Berggren; R. S. D. Thomas*

A co-publication of the AMS and the London Mathematical Society

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.

This volume is one of an informal sequence of works within the
History of Mathematics series. Volumes in this subset,
“Sources”, are classical mathematical works that served as
cornerstones for modern mathematical thought.

#### Readership

Undergraduates, graduate students, and research mathematicians interested in the history of mathematics and astronomical applications of geometry.

#### Table of Contents

# Table of Contents

## Euclid's Phaenomena: A Translation and Study of a Hellenistic Treatise in Spherical Astronomy

- Cover Cover11
- Title page i2
- Dedication iii4
- Contents v6
- Preface to second printing vii8
- Preface ix10
- Quote by Plato xi12
- Introduction 114
- Euclid’s presuppositions 1932
- Notes on the translation 3346
- Sigla 3952
- Euclid’s Phaenomena translated with commentary 4154
- Euclid’s Phaenomena 4356
- English glossary of selected technical terms and phrases 115128
- Greek glossary of selected technical terms and phrases 120133
- Bibliography 122135
- Index of names 126139
- Index of subjects 128141
- Index of subjects (Greek) 132145
- Back Cover Back Cover1146