| List of Figures | p. x |
| Foreword | p. xv |
| Introduction | p. 3 |
| Astronomical Knowledge of the Ancient Greeks | p. 6 |
| Knowledge of the Sun's, the Moon's, and the Planets' Apparent Motions | p. 6 |
| The Aspects, Stations, and Retrograde Motions of the Planets | p. 8 |
| The Periods of the Planets | p. 9 |
| Apparent Planetary Loops and Zigzags | p. 13 |
| The Elements of a Planetary Orbit | p. 15 |
| Orbit Computation | p. 22 |
| Concepts of Some Early Greek Philosophers | p. 23 |
| Thales of Miletus (c. 624-546 B.C.) | p. 23 |
| Anaximander (c. 611-545 B.C.) | p. 23 |
| Anaximenes of Miletus (c. 585-528 B.C.) | p. 24 |
| Anaxagoras of Clazomenae (c. 500-428 B.C.) | p. 25 |
| Pythagoras of Samos (c. 580-500 B.C.) | p. 25 |
| Philolaus, the Pythagorean (c. 470-400 B.C.) | p. 26 |
| Hicetas of Syracuse (c. 350 B.C.) | p. 26 |
| Ecphantus of Syracuse (c. 325 B.C.) | p. 26 |
| Xenophanes of Colophon (c. 530 B.C.) | p. 27 |
| Heraclitus of Ephesus (c. 500 B.C.) | p. 27 |
| Empedocles of Agrigentum (c. 450 B.C.) | p. 27 |
| Leukippus of Abdera (c. 450 B.C.) | p. 28 |
| Democritus of Abdera (c. 400 B.C.) | p. 29 |
| Metrodorus of Chios (c. 400 B.C.) | p. 29 |
| Plato of Samos (427-347 B.C.) | p. 29 |
| Aristotle of Stagira (384-322 B.C.) | p. 30 |
| Heracleides of Pontus (c. 350 B.C.) | p. 32 |
| Aristarchus of Samos (c. 310-230 B.C.) | p. 32 |
| Eudoxus (408-355 B.C.) | p. 34 |
| Eudoxus's Lunar Theory | p. 35 |
| Eudoxus's Solar Theory | p. 35 |
| Eudoxus's Planetary Theory | p. 37 |
| The Systems of Spheres | p. 40 |
| Hipparchus (fl. 146-126 B.C.) | p. 41 |
| Hipparchus's Main Astronomical Contributions | p. 42 |
| Hipparchus's Solar Theory | p. 42 |
| The Apparent Nonuniform Motion of the Sun in the Ecliptic | p. 42 |
| Hipparchus's Method of Finding the Line of Apsides and the Eccentricity of the Sun's Orbit (Considered as an Eccentric Circle) | p. 45 |
| Hipparchus's Method of Predicting the Sun's Place at Any Instant | p. 47 |
| Equivalence of Epicyclic and Eccentric Motion | p. 49 |
| Hipparchus's Lunar Theory | p. 51 |
| Hipparchus's Method of Finding the Line of Apsides and Eccentricity of the Moon's Orbit | p. 53 |
| Hipparchus's Method of Predicting the Moon's Place at Any Time | p. 56 |
| Hipparchus's (Abortive) Theory of Planetary Motion | p. 60 |
| Hipparchus's Method of Finding the Stationary Points and Arcs of Retrogression of a Planet (a Method Originally Due to Apollonius) | p. 60 |
| Hipparchus's Eclipse Method of Finding the Actual Distances and Diameters of the Sun and Moon | p. 62 |
| Hipparchus's Discovery of the Precession of the Equinoxes | p. 65 |
| Hipparchus's Discussion of Errors | p. 66 |
| Ptolemy (fl. 125-150) | p. 67 |
| Ptolemy's Main Contributions to Astronomy | p. 67 |
| Contents of the Almagest | p. 69 |
| Ptolemy's Solar Theory | p. 72 |
| Ptolemy's Work on the Lunar Orbit | p. 72 |
| Ptolemy's View of the Regression of the Nodes and the Advance of the Apsides of the Lunar Orbit | p. 73 |
| Ptolemy's Preliminary Derivation of the Elements of the Lunar Orbit | p. 73 |
| The Motions in Ptolemy's Lunar Orbit | p. 77 |
| The Effects of Evection | p. 77 |
| Ptolemy's Explanation of the Evection | p. 80 |
| Ptolemy's Determination of the Evection at the Quarters | p. 82 |
| The Prosneusis | p. 82 |
| Ptolemy's Computation of the Prosneusis and an Example of His Prediction of the Moon's True Longitude | p. 84 |
| Approximate Elementary Derivation of the Longitude Correction to the Moon's Position Caused by the Prosneusis | p. 87 |
| Introduction to Ptolemy's Planetary Theory | p. 90 |
| Ptolemy's Planetary Theory | p. 91 |
| Ptolemy's Reason for Introducing an Equant Point in All Planetary Orbits | p. 93 |
| Example of Ptolemy's Prediction of a Superior Planet's Celestial Longitude | p. 93 |
| Ptolemy's Determination of the Equant Point's Position | p. 94 |
| Ptolemy's Theory of the Celestial Latitudes of the Planets | p. 97 |
| The Superior Planets | p. 97 |
| The Inferior Planets | p. 99 |
| Copernicus (1473-1543) | p. 103 |
| Copernicus's Main Astronomical Contributions | p. 109 |
| The Copernican System of the Sun, Moon, and Planets | p. 110 |
| Copernicus's Solar Theory | p. 114 |
| Elementary Considerations | p. 114 |
| Simple Method of Finding the Earth's Orbit | p. 114 |
| Copernicus's (Improved) Method for Finding Eccentricity and Aphelion of the Earth's Orbit | p. 117 |
| Copernicus's Orbit of the Earth | p. 120 |
| Notes on Some Elementary Methods of Finding the Relative Distances in the Planetary System | p. 122 |
| The Precession of the Equinoxes and the Trepidation | p. 127 |
| The Precession of the Equinoxes | p. 127 |
| The Trepidation | p. 128 |
| Copernicus's Treatment of Precession and Trepidation | p. 130 |
| Copernicus's Lunar Theory | p. 133 |
| Copernicus's Orbit of Venus | p. 133 |
| Copernicus's Orbit of Mercury | p. 136 |
| Copernicus's Orbit of a Superior Planet | p. 138 |
| Copernicus's Theory of the Celestial Latitudes of the Superior Planets | p. 141 |
| Copernicus's Obliquation | p. 141 |
| A Mechanical Model of the Obliquation | p. 143 |
| Some Special Observational Facts | p. 143 |
| Copernicus's Theory of the Celestial Latitudes of the Inner Planets, Involving Both Obliquation and Deviation | p. 147 |
| Tycho Brahe (1546-1601) | p. 150 |
| Tycho's Main Astronomical Contributions | p. 152 |
| The Tychonic System | p. 153 |
| Note on Reymers's System | p. 155 |
| Tycho's Solar Theory | p. 156 |
| Tycho's Orbit of Saturn: An Example of an Outer Planet | p. 157 |
| Tycho's Lunar Theory | p. 157 |
| Tycho's Method of Predicting the Moon's Place | p. 163 |
| Modern Development of Tycho's Method into a Series Involving the Mean Anomaly M[subscript 1] and Solar Phase Angle D | p. 166 |
| Change from Tycho's "Mean Solar Time" [tau] to Modern Mean Solar Time t | p. 167 |
| Analytical Comparison between Tycho's Expression and the Modern Expression for the Moon's Longitude | p. 168 |
| Numerical Example of Predicting the Moon's Place at Any Time in Tycho's System | p. 169 |
| Wittich's Formula | p. 171 |
| The Elliptic Terms | p. 171 |
| Kepler (1571-1630) | p. 172 |
| Highlights of Kepler's Most Important Astronomical Books | p. 173 |
| Mysterium Cosmographicum (1596) | p. 173 |
| Astronomia Nova, Based on Celestial Physics with a Commentary on the Motion of Mars (1609) | p. 175 |
| Harmonice Mundi (1619) | p. 175 |
| Astronomiae Copernicanae (In Parts: 1618, 1620, 1621) | p. 175 |
| Tabulae Rudolphinae (1627) | p. 176 |
| Shorter Books and Pamphlets | p. 177 |
| A Brief View of Kepler's Accomlishments | p. 177 |
| A Common Popular (Under) statement of Kepler's Work | p. 177 |
| A More Detailed List of Kepler's Contributions | p. 177 |
| Semipopular Statement of Kepler's Work on Mars's Orbit | p. 178 |
| The Vicarious Hypothesis | p. 180 |
| The First Oval | p. 181 |
| The "Auxiliary Ellipse" | p. 181 |
| The "Orbital Ellipse" | p. 182 |
| Kepler's Work on the Lunar Theory | p. 182 |
| Kepler's Solar Theory | p. 183 |
| Kepler's Determination of the Equant Point of the Earth's Orbit | p. 184 |
| Some Further Determinations of the Equant Position in the Earth's Orbit | p. 188 |
| Kepler's Preliminary Work on the Orbit of Mars | p. 189 |
| Kepler's Vicarious Hypothesis | p. 189 |
| Estimate of the Accuracy of the Vicarious Hypothesis in Longitude | p. 193 |
| Kepler's First Refutation of the Vicarious Hypothesis (from the Latitudes) | p. 196 |
| Estimate of the Accuracy of the Vicarious Hypothesis in Latitude | p. 196 |
| Kepler's Estimate of Mars's Orbital Eccentricity (from the Latitudes) | p. 199 |
| Kepler's Second Refutation of the Vicarious Hypothesis (from the Longitudes) | p. 201 |
| The Bisection of Eccentricity Hypothesis | p. 205 |
| Kepler's Improvement of the Earth's Orbit by Bisecting Its Eccentricity | p. 205 |
| Bisection of the Eccentricity for Mars's Orbit | p. 206 |
| Suspicion of a Law: Estimate of the Accuracy of the Bisection of Eccentricity Hypothesis | p. 206 |
| Direct Determination of the Distances of Mars from the Sun by Tycho's Observations (1602) | p. 207 |
| Three of Kepler's Efforts to Retain an Epicycle and a Deferent: Kepler's "Ovoid" Orbit | p. 208 |
| First Construction of Kepler's Ovoid Orbit | p. 208 |
| Geometrical Estimate of the Sagitta of Kepler's Ovoid Orbit | p. 212 |
| Replacement of the Ovoid by an Epicycle and Deferent | p. 212 |
| Sagitta of the Ovoid Construction | p. 216 |
| Why Kepler Considered the Ovoid Theory to Be a Physical Theory | p. 216 |
| Kepler's First, or Auxiliary, Ellipse: Its Eccentricity and Properties | p. 216 |
| Some of Kepler's Further Attempts with Ovals or Combination Orbits | p. 220 |
| Kepler's Further Experiments with Circular Uniform Motions | p. 222 |
| Kepler's Construction of an Empirical Orbit of Mars Directly from Tycho's Observations | p. 225 |
| Kepler's Check of His Ovoid Theory by 40 of Tycho's Observations | p. 229 |
| Kepler's Rejection of His Ovoid Theory | p. 230 |
| Kepler's Accidental Discovery of His Second, or Final, Ellipse | p. 230 |
| Construction of Kepler's Final Ellipse by Diametral Distances | p. 231 |
| Kepler's Search for a Physical Cause of Elliptic Motion: His First Magnetic Orbit | p. 233 |
| Kepler's Law of Libration for the Magnetic Orbit | p. 235 |
| Kepler's Law of Total Libration for the Magnetic Orbit | p. 236 |
| Kepler's Proof That the Magnetic Orbit Is an Ellipse | p. 236 |
| Kepler's Construction of an Ellipse from Its Total Libration on the Radius of Its Major Auxiliary Circle | p. 238 |
| Kepler's Abandonment of His Epicylic First Magnetic Orbit | p. 240 |
| First Application of the Areal Law to the Final Ellipse | p. 240 |
| Another Attempt with the Areal Law on an Exact Ellipse | p. 240 |
| Astronomy with the Final Ellipse: Kepler's Equation | p. 241 |
| Confirmation of Kepler's Final Elliptic Orbit by Celestial Latitudes of Mars | p. 241 |
| Kepler's Second Magnetic Orbit | p. 243 |
| Comparison between the Shapes of Some of Kepler's Ovals and the True Ellipse | p. 247 |
| Kepler's Correction of His Law of Linear Orbital Velocity | p. 248 |
| Some Curiosities Found in Kepler's Works | p. 252 |
| Kepler's "Proof" of His Third Law | p. 252 |
| Kepler's Views on Stellar Distances | p. 252 |
| Kepler's "Proof" That Mars Has Just Two Moons | p. 253 |
| Concluding Remarks | p. 253 |
| Bibliography | p. 255 |
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