The Almagest: Introduction to the Mathematics of the Heavens

by Claudius Ptolemy, Bruce M. Perry (Translator), William H. Donahue (Editor)

Overview

The Almagest is by far the greatest work in astronomy in ancient times. In a massive series of thirteen books, Ptolemy shows how every detail of the motions of the sun, moon, planets, and stars can be expressed using geometrical models that can be used to compute celestial positions with remarkable accuracy
The present selection covers all the essential features of Ptolemy’s treatment of the heavens, omitting only more difficult and abstruse matters such as the moon’s motion and the calculation of eclipses. In the interest of conciseness, development of planetary theories is restricted to two planets, one inferior (Venus) and one superior (Mars).
Ptolemy’s text is accompanied by extensive notes and introductions that are aimed at making the book accessible to students encountering Ptolemy for the first time. This edition is designed to provide everything needed for a one-semester course, or it can be a component of a more general course on planetary theory or history of astronomy.

Product Details

ISBN-13:	9781888009439
Publisher:	Green Lion Press
Publication date:	12/07/2014
Pages:	264
Product dimensions:	6.90(w) x 9.90(h) x 0.90(d)

Table of Contents

The Green Lion's Preface xi

Translator's Preface xv

Preliminaries to The Almagest

Appearances of the Fixed Stars 1

Appearances of the Sun 4

Observing Instruments 8

The Sexagesimal System 9

Chronology 11

Epitome of the Ptolemaic System

Layout of the World 15

The Horizon 17

Meridian 18

The Right Sphere and the Oblique Sphere 19

Right Ascension and Longitude 20

The Almagest - Book I

Chapter 1 Introduction 23

Chapter 2 On the Order of the Theorems 26

Chapter 3 That the Heavens are Spherical and Move as a Sphere 27

Chapter 4 That the Earth Also Is Sensibly Spherical as a Whole 29

Chapter 5 That the Earth Is in the Middle of the Heavens 30

Chapter 6 That the Earth Has the Ratio of a Point to the Heavens 32

Chapter 7 That the Earth Does Not Move at All 32

Chapter 8 That There Are Two Different Kinds of Primary Motions in the Heavens 34

Chapter 9 On the Particular Conceptions 37

Proposition 1.1 38

Chapter 10 On the Magnitude of Chords in a Circle 38

Proposition 1.2 40

Lemma 1.1 40

Proposition 1.3 41

Proposition 1.4 42

Proposition 1.5 42

Lemma 1.2 43

Chapter 11 Table of Chords in a Circle 46

Chapter 12 On the Arc Between the Tropics 56

Chapter 13 Preliminaries to the Spherical Proofs 59

Lemma 1.3 59

Lemma 1.4 60

Lemma 1.5 60

Lemma 1.6 61

Lemma 1.7 61

Lemma 1.8 62

Proposition 1.6 62

Proposition 1.7 64

Proposition 1.8 64

Chapter 14 On the Arcs Between the Equatorial the Oblique Circle 64

Chapter 15 Table of Obliquity 66

Proposition 1.9 68

Chapter 16 On Ascensions in the Right Sphere 68

The Almagest - Book II

Chapter 1 On the General Position of the Zone Inhabited by Us 71

Proposition 2.1 72

Chapter 2 Arcs of the Horizon 72

Proposition 2.2 73

Proposition 2.3 74

Proposition 2.4 74

Chapter 3 Elevation of the Pole 74

Proposition 2.5 75

Proposition 2.6 75

Proposition 2.7 76

Preliminaries to Book III

Precession of the Equinoxes 77

Mean Sun and Apparent Sun 78

Dates of Equinoxes and Solstices 80

Greatest, Mean, and Least Motion 80

The Almagest - Book III

(Introduction) 81

Chapter 1 On the Magnitude of the Annual Period 81

Chapter 2 Table of the Uniform Motion of the Sun 90

Chapter 3 On the Hypotheses as to Uniform, Circular Motion 94

Proposition 3.1 95

Proposition 3.2 96

Proposition 3.3 96

Proposition 3.4 96

Proposition 3.5 97

Proposition 3.5, A.1 98

Proposition 3.5, A.2 99

Proposition 3.5, A.3 99

Proposition 3.5, A.4 100

Proposition 3.5, B.1 100

Proposition 3.5, B.2 101

Proposition 3.5, C.1 101

Proposition 3.5, D.1 102

Proposition 3.5, D.2 103

Chapter 4 On the Apparent Anomalistic Motion of the Sun 104

Chapter 5 Particular Segments of Anomalistic Motion 109

Chapter 6 Table of the Sun's Anomalistic Motion 116

Chapter 7 On the Epoch for the Mean Passage of the Sun 118

Chapter 8 On the Calculation of the Sun 120

Chapter 9 On the Inequality of Days and Nights 120

The Almagest - Book VII

Chapter 1 That the Fixed Stars Always Preserve the Same Position Relative to One Another 125

Chapter 2 That the Sphere of the Fixed Stars Also Makes a Certain Motion Eastwards Through the Mid-zodiac Circle 126

Chapter 3 That the Eastward Motion of the Sphere of the Fixed Stars is Also Produced Around the Poles of the Mid-zodiac Circle 129

Preliminaries to Book IX

Mercury and Venus 131

Mars, Jupiter, and Saturn 132

Planetary Anomalies 133

The Planets and the Mean Sun 139

The Almagest - Book IX

Chapter 1 On the Order of the Spheres of the Sun, Moon, and Five Planets 141

Chapter 2 On the Aim of the Hypotheses of the Planets 142

Chapter 3 On the Periodic Returns of the Five Planets 145

Chapter 5 Preliminaries to the Hypotheses of the Five Planets 149

Chapter 6 On the Mode and Difference of the Hypotheses 151

Proposition 9.1 151

Proposition 9.3 153

Preliminaries to Book X

Apogee and Perigee 155

Eccentricity and the Equant 156

Zodiacal Anomaly and the Two Eccentricities 157

The Epicycle of Mars, At Last 160

The Almagest - Book X

Chapter 1 Demonstration of the Apogee of the Star Venus 161

Chapter 2 On the Size of Its Epicycle 162

Proposition 10.1 163

Proposition 10.2 163

Chapter 3 On the Ratios of the Eccentricity of the Star 164

Proposition 10.3 165

Chapter 4 On the Correction of the Periodic Motions of the Star 167

Chapter 5 On the Epoch of its Periodic Motions 171

Chapter 6 Preliminaries to the Demonstrations Concerning the Remaining Stars 172

Proposition 10.6 173

Proposition 10.7 174

Chapter 7 Demonstration of the Eccentricity and the Apogee of Mars 175

Proposition 10.8 Part A 176

Proposition 10.8 Part B 178

Proposition 10.8 Part C 178

Proposition 10.8 Part D 179

Proposition 10.8 Part E 179

Proposition 10.9 Part A 180

Proposition 10.9 Part B 181

Proposition 10.10 182

Proposition 10.11 183

Proposition 10.12 184

Proposition 10.13 184

Proposition 10.14 185

Proposition 10.15 186

Proposition 10.16 187

Proposition 10.17 188

Proposition 10.18 189

Proposition 10.19 190

Chapter 8 Demonstration of the Size of the Epicycle of the Star Mars 191

Proposition 10.20 Part A 192

Proposition 10.20 Part B 192

Proposition 10.20 Part C 193

Chapter 9 On the Correction of the Periodic Motions of the Star Mars 193

Proposition 10.21 194

Chapter 10 On the Epoch of its Periodic Motions 196

Preliminaries to Book XI

Computation of Planetary Positions 199

How the Tables are Constructed 200

How to Use the Tables 202

The Almagest - Book XI

Chapter 9 How Precise Passages are Obtained from Periodic Motions 203

Chapter 10 Treatment of Table-Construction of the Anomalies 204

Chapter 11 Tables of the Longitudinal Adjustment of the Five Planets 209

Chapter 12 On the Longitudinal Calculation of the Five Planets 214

Preliminaries to Book XII

Alternative Hypotheses 217

The Station Criterion 219

The Almagest - Book XII

Chapter 1 On the Preliminaries to the Retrogradations 221

Proposition 12.1 221

Proposition 12.2 222

Proposition 12.3 222

Proposition 12.4 223

Lemma 12.1 224

Proposition 12.5 225

Proposition 12.6 226

Proposition 12.7 227

Proposition 12.8 227

Preliminaries to Book XIII

Context of the Selection 229

The Almagest - Book XIII

Chapter 2 On the Mode of the Motion of the Hypothetical Inclinations and Obliquities 231

Appendix 1 The Trigonometric Functions 233

Appendix 2 Days of the Year 237

Appendix 3 The Menelaus Theorems 239

Select Bibliography 241

Index 243

About the Author, the Translator, and the Editor 247