Tag: Almagest

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Almagest Book VII: On the Rate of Precession from Hipparchus’ Observations

In the last post, Ptolemy concluded that the motion of the fixed stars over time, known as precession, happens about the poles of the ecliptic. He determined this by stating that the longitude of stars with relation to the ecliptic remained consistent over a long interval of time but varied with respect to the celestial equator. That post concluded with Ptolemy’s promise that we would be able to determine rate of that precession using the same data he presented previously.

It is particularly [easy to demonstrate] from the differences in declination found for those stars near the equinoctial points.

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Almagest Book VII: On the Poles of Precession

From the above, it has become clear to us that the sphere of the fixed stars, too, performs a rearward motion along the ecliptic, of approximately the amount indicated. Our next task is to determine the type of this motion, that is to say, whether it takes place about the poles of the equator or about the poles of the inclined circle of the ecliptic.

Now that Ptolemy has determined that precession does indeed happen at a rate that agrees with Hipparchus, he now asks whether that precession is happening in the same direction as the ecliptic or the celestial equator.

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Almagest Book VII: On Precession

At the beginning of the last chapter, Ptolemy noted that the celestial sphere appears to have a rearward motion of its own known as precession of the equinoxes. This motion means that the position of the sun in the zodiacal signs slowly increase in advance as time passes. In particular, the sun was at the beginning of Aries in Ptolemy’s time, but since then has advanced such that today it lies near the beginning of Pisces.

We can see this mainly from the fact that the same stars do not maintain the same distance with respect to the solstical and equinocital points in our times as they had in former times: rather, the distance [of a given star] towards the rear with respect to [one of] the same points is found to be greater in proportion as time [of observation] is later.

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Almagest Book VII: Hipparchus’ Star Alignments

Ptolemy lays out the arrangements described by Hipparchus by going through stars in various constellations:

Stars in Cancer. [Hipparchus] records that the star in the southern claw of Cancer [α Cnc], the bright star which is in advance of the latter and of the head of Hydra [β Cnc], and the bright star in Procyon [α CMi] lie almost on a straight line. For the one in the middle lies $1 \frac{1}{2}$ digits to the north and east of the straight line joining the two end ones, and the distances [from it to each of them] are equal.

First, we should discuss the identification of the stars. The designations of the stars in the brackets are the modern Bayer designations first created in $1603$. For Ptolemy’s part, he described the positions of the stars based on how they should appear in the representation of the constellation. For example, we see him here describing α Cnc as the “southern claw of Cancer”. However, because the depiction of the figures in constellations is somewhat subjective, this leads to some ambiguity in which stars are which, making assessing the validity of Ptolemy’s statements somewhat difficult. Continue reading “Almagest Book VII: Hipparchus’ Star Alignments”

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Almagest Book VII: On the Relative Positions of the Stars

Now, to deal with the next part of the theory, we shall begin discussing the stars, and first, in accordance with the logical order, the so-called fixed stars.

To introduce the next book of the Almagest, Ptolemy informs the reader that we will be taking some time to understand the fixed stars. There are two important things to note about this sentence. The first is that Ptolemy is taking extra care to make sure the reader knows we are discussing the fixed stars. This is because the Greek concept of “stars” could include the planets. Continue reading “Almagest Book VII: On the Relative Positions of the Stars”

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Almagest Book VI: Determining the Inclinations

And here we are. Final chapter of Book VI. Here, we’ll finish out Ptolemy’s discussion of the inclinations of eclipses. In the previous post, we discussed a few things we’ll need to determine that1, but we really haven’t discussed is what the “inclination” means. So I’ll begin by doing that as Ptolemy doesn’t really do a clear job of doing so. Continue reading “Almagest Book VI: Determining the Inclinations”

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Almagest Book VI: Horizon Diagram

In the previous chapter, we mentioned that one of the things we’ll need for Ptolemy’s weather prediction is the angle between the ecliptic and celestial equator as measured along the horizon. This is something we calculated back in II.2 and only now are we getting around to displaying a diagram to summarize it. So I’ll display the diagram here2 and discussion about it will be beneath the fold.

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