The Sun in the Summer and Winter Skies. 23 Modern Explanation for the Appearance of

Retrograde Motion of a Planet. 25

Retrograde Motion from Concentric Spheres. 26

Eccentric and Epicycle Hypotheses. 32

Eccentric Solar Orbit. 33

Change of Distance in the Epicycle Hypothesis. 33

Retrograde Motion in the Epicycle Hypothesis. 35 Ptolemy's Geometrical Demonstration of the

Solar Eccentricity and Apogee. 48

Ptolemy's Lunar Theory. 54—55

Opposition for Inferior Planets. 57 Motion at Perigee and Apogee in the Eccentric and

Epicycle Hypotheses. 59

Equant Point. 60

Straight Line Motion from Circular Motion. 79

A page from al-Tusi's Al-Tadhkira. 80

Rotating Circles to Rectilinear Oscillations. 81 Ptolemy and Regiomontanus are seated beneath an armillary sphere. 88 Spherical Scheme of the Universe from Petrus Apianus,

Cosmographicus Liber, 1540. 90

Portrait of Copernicus. 100 Copernicus's Heliocentric Planetary Spheres,

De revolutionibus, 1543. 103 Orbit of an Inferior Planet in the Ptolemaic and

Copernican Systems. 104

Figure 14.4.

Figure 14.5 Figure 15.1. Figure 15.2.

Figure 15.3. Figure 15.4. Figure 15.5. Figure 15.6. Figure 15.7. Figure 15.8. Figure 15.9. Figure 16.1. Figure 16.2. Figure 16.3. Figure 16.4. Figure 16.5.

Figure 16.6. Figure 16.7. Figure 16.8. Figure 16.9.

Figure 16.10. Figure 16.11. Figure 16.12. Figure 16.13. Figure 16.14.

Figure 17.1.

Figure 17.2. Figure 17.3. Figure 17.4.

Distances from the Earth of a Superior Planet at Conjunction and Opposition in the Ptolemaic and

Copernican Systems. 105

Parallax, Stellar Parallax, Distance. 106

Leonard Digges, A prognostication everlasting, 1556. 112 Thomas Digges, A Perfit Description of the

Caelestial Orbes, 1576. 112

Frontispiece, Galileo Galilei, Sidereus nuncius, 1610. 115

Galileo's drawing of the Moon, 1610. 116

Galileo's Discovery of Four Satellites of Jupiter. 117 Phases of Venus in Ptolemaic and Copernican Models. 120

Sunspot Drawing by Galileo, summer 1612. 120

Frontispiece, Portrait of Galileo, The Assayer, 1623. 122

Frontispiece, Dialogo di Galileo Galilei. 123

The Great Quadrant at Augsburg. 133

Tycho Brahe's Nova Stella or New Star of 1572. 133

Tycho Brahe's Great Mural Quadrant at Uraniborg. 134

The Tychonic World System. 135 The Tychonic, Copernican, and Ptolemaic Systems

Compared. 136

Portrait of Tycho Brahe. 137

Basic Polygons between Circular Orbits. 138

The Five Regular Solids. 139 Kepler's Model of the Solar System;

Close-up of the Model. 140

Stars. Engraving by M. C. Escher. 141

Ellipse. 143

Kepler's Law of Equal Areas. 144

Kepler's Music of the Spheres. 146 Log—Log Plot of Orbital Period versus Distance from the Sun. 147 Whirlpools of Matter. Descartes,

Principia philosophiae, 1644. 150

Shooting cannon balls on the Earth. 153

The Moon in orbit around the Earth. 153

Title page from the Principia, 1687. 154

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