American Mathematical SocietyLondon Mathematical Society

S O U R C E S

Volume 29

A Translation and Study of a Hellenistic Treatise in Spherical Astronomy

J. L. BerggrenR. S. D. Thomas

Euclid’s Phaenomena

https://doi.org/10.1090/hmath/029

Editorial Board

American Mathematical SocietyJoseph W. DaubenPeter DurenKaren Parshall, ChairMichael I. Rosen

London Mathematical SocietyAlex D. D. CraikJeremy J. GrayPeter NeumannRobin Wilson, Chair

2000 Mathematics Subject Classification. Primary 01A20; Secondary 01A75.

For additional information and updates on this book, visitwww.ams.org/bookpages/hmath-29

The Library of Congress has cataloged an earlier hardcover edition as follows:

Euclid.[Phaenomena. English]Euclid’s Phaenomena : a translation and study of a hellenistic treatise in spherical astronomy /

J. L. Berggren and R. S. D. Thomas.p. cm. — (History of mathematics, ISSN 0899-2428 ; v. 29)

Includes bibliographical references and indexes.ISBN 0-8153-0493-5 (acid-free paper)1. Euclid. Phaenomena. 2. Spherical astronomy—Early works to 1800. 3. Astronomy, Greek.

I. Berggren, J. L. II. Thomas, Robert S. D. III. Title. IV. Series: Sources and studies in thehistory and philosophy of classical science ; 4.

QB144 .E9313 1996523′.7—dc20 95051133

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The book contains a translation and study of Euclid’s Phaenomena, a work which once formed part of the math-ematical 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.