Abstract
In the two reading selections included in this chapter, taken from Books I andV of the Almagest, Ptolemy describes the design and use of three astronomical instruments which may be used to measure the angular distance between heavenly bodies. The first two instruments are very similar; they can both be used to measure the 42 altitude of the sun above the horizon at any time during the day. Since for a particular observer the altitude of the sun at local noon varies over the course of the year (in the northern latitudes the sun is much closer to the horizon at noon during the winter than during the summer), these types of instruments were employed to measure the length of the year itself. This, in turn, played a significant role in the development of the calendar.5 The third instrument, which Ptolemy refers to as an “astrolabe,” is today called a spherical astrolabe or an armillary sphere. It is depicted in Fig. 7.2. The spherical astrolabe consists of a network of adjustable intersecting rings which can be oriented so as to measure the celestial coordinates of heavenly bodies, such as the sun and the moon.
We were led to this understanding and belief—both from the passages of the moon observed and recorded by Hipparchus, and from the things we ourselves have received through an instrument we constructed.
—Claudius Ptolemy
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Notes
- 1.
This is done in Chap. 3 of Book III of the Almagest, which has been omitted from the present volume.
- 2.
Figure 6.1 accompanies Ex. 6.2 in the previous chapter of this volume.
- 3.
The eccentric and the epicyclic models were both employed by Hipparchus of Nicaea (d. 127 B.C.), but were probably known to Apollonius of Perga (d. 190 B.C.). See the careful discussion of Ptolemy’s skillful use of these models in Pedersen, O., A Survey of the Almagest, revised ed., Springer, New York, 2010.
- 4.
We will come to Copernicus’ Revolutions of the Heavenly Spheres in Chap. 11 of the present volume.
- 5.
See Ex. 6.1 in the previous chapter of this volume.
- 6.
Figure
- 7.
In other words, the so-called meridian circle [4] represents the solsticial colure, which is a great circle intersecting both the poles of the equator and the poles of the ecliptic.—[{K.K.]
- 8.
i.e. minutes, seconds, thirds, etc.—[{K.K.]
- 9.
So the arc de is made identical to the (previously) measured angle of the ecliptic (with respect to the equator), which is about 24° according to Ptolemy.—[K.K.]
- 10.
Ptolemy is here referring to the instrument described in Book I, Chap. 12, which he used to determine the inclination of the ecliptic by measuring the altitude of the sun above the horizon during the solstices.—[{K.K.]
- 11.
In other words, the meridian circles [6, 7] are aligned in the north-south direction. The inner circle [6] is then rotated within the outer circle [7] until the axis [d, d] is aligned with the North Star. Thus, the angle between the axis [\(d, d\)] and the zenith is determined by the latitude at which the instrument is located.—[{K.K.]
- 12.
The inside circles [1–5], all being attached to the meridian circle [6], can be rotated together around an axis [\(d, d\)] which is aligned with the axis of the celestial sphere.—[{K.K.]
- 13.
For example, during the month of October, the outer circle [5] is spun around until it is in front of the constellation Libra on the ecliptic circle [3].—[{K.K.]
- 14.
The circle representing the solsticial colure [4] is rotated about the poles of the equator [\(d, d\)] until a line connecting the two intersections of the ecliptic circle [3] and the one through its poles [5] is pointed at sun. Proper orientation is identified by noting when the sunward half of the ecliptic circle [3] casts a shadow on its back half, and the sunward half of the other circle [5] casts a shadow on its back half.—[{K.K.]
- 15.
The angular separation of the moon and the sun along the ecliptic is determined by measuring the angular separation of the inner [2] and outer [5] circles.—[{K.K.]
- 16.
The angular separation of the moon and the sun perpendicular to the ecliptic is determined by measuring the angular separation of a line through the sights [\(b, b\)] and the ecliptic circle [3].—[{K.K.].
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Kuehn, K. (2015). Geometrical Tools. In: A Student's Guide Through the Great Physics Texts. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1360-2_7
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DOI: https://doi.org/10.1007/978-1-4939-1360-2_7
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