Abstract
The mathematics and the spherical astronomy of the first two Books of the Almagest contained what Ptolemy considered the preliminaries necessary to the study of planetary theory, which is the main subject of the whole work, and that part of astronomy in which Ptolemy asserts his own originality in the most convincing way.
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Notes
- 1.
There are many earlier expositions of the theory of the motion of the Sun among which we may mention the writings of Delambre (II, pp. 99 ff.), Herz (1887,1), Tannery (1893, pp. 142–178), Dreyer (1906, pp. 148 ff.), Rome (1937–38 and 1943), StumpfT(I, 15 ff.) and Petersen and Schmidt (1967).
- 2.
This has been proved by Petersen and Schmidt (1967); see in particular the section On Ptolemy’s Use of the Egyptian Calendar, pp. 91 ff.
- 3.
Nabonassar reigned 747-735 B.C. His name means Nebu Protector, Nebu being the Assyrian name of the old Babylonian god of writing and learning. For this reason the name was common in Mesopotamia, and temples were dedicated to Nebu in astronomical centres like Babylon and Borsippa.
- 4.
For this section see Tannery (1893, pp. 142–160) and Rome (1937 and 1938). 9 A Survey of the Almagest
- 5.
Because Ptolemy assumed a constant rate of precession (see page 248) his tropical year became an astronomical constant and there was no inconvenience in referring stellar positions to the vernal equinox. Later Arabic astronomers called the Ptolemaic theory of precession in question and advocated the sidereal or the anomalistic year as the fundamental, astronomical unit of time. An early example of this criticism is the treatise De motu Solis by the 9th century Baghdad astronomer Thabit ben Qurra (ed. Carmody, 1960, pp. 63–79); a late instance is Copernicus’ use of the fixed stars as a frame of reference instead of the vernal equinox {De Rev., II, 14), and his discussion of the sidereal year (De Rev., Ill, 13).
- 6.
The Julian dates of these observations are taken from Manitius’ translation of the Almagest. More recent calculations haveVesulted in a number of corrections to which references are given in Appendix A.
- 7.
The only instrument for this purpose described by Ptolemy [III, 1; Hei 1, 195] is a ring of bronze with a diameter of 2 cubits and placed in the plane of the equator. At the time of an equinox the shadow of one half of the ring falls exactly upon the other half (cf. Dicks 1954, p. 79). The instrument was still used by Theon of Alexandria (see Rome 1926, p. 11). – Theon (ed. Rome, p. 817) assumed that both Hipparchus and Ptolemy had found equinoxes and solstices by the meridian instrument mentioned by Ptolemy [I, 12; Hei 1, 64] in connection with the obliquity of the ecliptic and described in great detail by Proclus (Hyp. III, 1). This view is supported by Rome (1937, p. 218 f.) but it seems impossible that solstices were determined in this way because of the slow variation at the declination of the Sun just before the maximum (or minimum). Also the fact that the time of the summer solstice S15 is given as two hours after midnight reveals that it was the result of some kind of calculation, based perhaps on measurements of corresponding altitudes.
- 8.
The originally extremely confused Latin terminology of Mediaeval astronomers became more settled during the 13th century. In a recent paper (Pedersen 1973) I have published a 15th century glossary of the most widely used terms, found in a MS in St. John’s College, Cambridge. This glossary is derived from the anonymous Theorica Planetarum which from about the middle of the 13th century spread a standard terminology in all European universities (see Pedersen 1962).
- 9.
In his Epitome Astronomiae Copernicanae (V, 2, 3, ed. Caspar p. 386) Kepler explains that although, properly speaking, anomaly - irregularity - is a change in the movement of the planet, nevertheless astronomers employ this word for the very motion in which the irregularity is present. In the Almagest the word anomaly is used in so many different meanings that one cannot but sympathise with Rome (1943, p. 142) when he says that one never ought to use this ambiguous term in connection with ancient astronomy. One of the principal achievements of Mediaeval Latin astronomy was to create a more precise terminology with different terms for different concepts.
- 10.
Almost all histories of astronomy have ascribed the discovery of the proper motion of the apogee of the Sun to the 9th century Muslim astronomer al-Battam; but it seems that the first who clearly distinguished this motion from precession was al-BIruni (ca. A.D. 1000), while the Toledo astronomer al-Zarqālī (ca. 1050) was the first to assign a definite value to it. - See Hartner and Schramm (1963), and Toomer (1969).
- 11.
11) Although a general theory of errors was unknown to Antiquity there are many testimonies to the fact that Hellenistic astronomers were aware both of several types of observational errors and of their influence on calculations. Ptolemy mentions unsatisfactory construction or mounting of instruments and quotes Hipparchus for an evaluation of the ensuing errors [III, 1; Hei 1, 194 f.]. Theon of Alexandria (ed. Rome, pp. 819 if.) gives an example in which he assumes the graduated ring of a meridian instrument to be correctly placed in the plane of the meridian, but so that there is an error of 6 minutes of arc in the measured zenith distances. He then determines the resulting error of the declination and longitude of the Sun, and of the equinox. This is a rare example, and many speculations on.Ptolemy’s good or bad faith could have been avoided if he had given a little more information on such questions. - See also Rome (1937, pp. 227 ff.).
- 12.
It is worth noticing that the Almagest shows no trace of any considerations of what might be called the initial conditions of the universe. Since Ptolemy believed in the eternity of celestial motions [1,1; Hei 1, 6] such questions could not arise. Later both Muslim and Christian astrologers - believing the world to be created in time, or together with time - were much interested in determining the date of ’great conjunction’ of all the planets marking the event of the creation. This was an influence of older, Persian ideas of a cyclic life of the universe. - See Kennedy (1962).
- 13.
We notice that the Almagest gives only a procedure for finding the true longitude or argument of the Sun by the tables of mean motions and equations. There is no procedure for the inverse problem of finding the mean from the true position (cf. Kepler’s problem), but this question turns up later in the theory of latitudes (see page 367).
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Pedersen, O. (2011). The Motion of the Sun. In: Jones, A. (eds) A Survey of the Almagest. Sources and Studies in the History of Mathematics and Physical Sciences. Springer, New York, NY. https://doi.org/10.1007/978-0-387-84826-6_5
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