On the Revolutions of the Celestial Spheres

6. Confirmation of those things which were set forth concerning the uniform motions of the Moon in longitude and anomaly. In astronomy, "anomaly" refers to the angular distance of a planet or the moon from its furthest point from Earth.
7. On the positions of Lunar longitude and anomaly.
8. On the second lunar inequality, and the ratio of the first epicycle to the second. An epicycle is a small circle whose center moves around the circumference of a larger one; it was used to explain the complex loops in planetary and lunar motion.
9. On the remaining inequality, by which the Moon is seen to move nonuniformly from the highest apse of the epicycle. The "highest apse" is the point in an orbit furthest from the center of motion, also known as the apogee.
10. How the apparent lunar motion is demonstrated from given uniform motions.
11. Canonical exposition of the prosthaphaereses, or lunar equations. Prosthaphaeresis is a Greek-derived term for the mathematical corrections added to or subtracted from a mean (average) position to find the "true" or apparent position.
12. On the calculation of the lunar course.
13. How the motion of lunar latitude is examined and demonstrated.
14. On the positions of the anomaly of the Moon's latitude.
15. Construction of the parallactic instrument. Also known as a triquetrum, this was a tool used by pre-telescopic astronomers to measure the zenith distance of celestial bodies.
16. On the parallaxes of the Moon. Parallax is the change in the apparent position of an object when viewed from two different locations, such as from the Earth's surface versus its center.
17. A demonstration of the Moon's distance from the Earth, and the ratio it has in parts—of which the distance from the center of the Earth to the surface is one.
18. On the diameter of the Moon and of the Earth's shadow at the place of the Moon’s transit.
19. How the distance of the Sun and Moon from the Earth, their diameters, and the shadow at the place of the Moon’s transit, as well as the axis of the shadow, are demonstrated simultaneously.
20. On the magnitude of these three stars—the Sun, Moon, and Earth—and in comparison with each other.
21. On the apparent diameter of the Sun and its parallaxes.
22. On the unequal apparent diameter of the Moon and its parallaxes.
23. What the ratio of the variation of the Earth's shadow may be.
24. Canonical exposition of the particular parallaxes of the Sun and Moon in the circle which passes through the poles of the horizon.
25. On the calculation of the parallax of the Sun and Moon.
26. How the parallaxes of longitude and latitude are distinguished.
27. Confirmation of those things which were set forth regarding the parallaxes of the Moon.
28. On the mean conjunctions and oppositions of the Sun and Moon. Mean conjunctions and oppositions refer to the average timing of new moons and full moons.
29. On investigating the true conjunctions and oppositions of the Sun and Moon.
30. How the ecliptic conjunctions and oppositions of the Sun and Moon are distinguished from others. Ecliptic conjunctions/oppositions are those that result in an eclipse because the bodies are aligned with the Earth's orbital plane.
31. How great the eclipse of the Sun and Moon might be.
32. For predicting how long an eclipse will last.

B O O K F I V E.

1. On their revolutions and mean motions. This book shifts focus to the "wandering stars," or planets.
2. A demonstration of the uniformity and appearance of these stars according to the opinion of the ancients.
3. A general demonstration of the apparent inequality caused by the motion of the Earth.
4. In what ways the proper motions of the wanderers appear unequal.
5. Demonstrations of the motion of Saturn.
6. On three other acronychal positions of Saturn recently observed. An acronychal position refers to a planet being in opposition to the sun, rising exactly at sunset; these were crucial for measuring planetary distances.
7. On the examination of Saturn’s motion.
8. On establishing the positions of Saturn.
9. On the parallaxes of Saturn which proceed from the annual orbit of the Earth, and how great its distance is.
10. Demonstrations of the motion of Jupiter.