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 here1 and discussion about it will be beneath the fold.
Now, let’s take a look at how Ptolemy explains this. He states that it
[consists] of $8$ concentric circles, conceived as lying in the plane of the horizon, to contain the [various] distances and nomenclature for the $7$ climata.
Each of the circles is meant to represent the horizon at each of the $7$ climata which are each called out along the vertical line above the center point.
Then we drew two lines, at right angles to each other, through all the circles: a horizontal one representing the intersection of the planes of the horizon and equator, and another, vertical one representing the intersection of the planes of the horizon and meridian.
In other words, the horizontal line intersects the horizon at east and west while the vertical one is akin to the meridian, intersecting north and south.
On the innermost circle we wrote, at the ends of the horizontal line, ‘equinoctial rising’ and ‘equinoctial setting’, and at the ends of the vertical line ‘north’ and ‘south’.
Since the horizontal line is east/west, Ptolemy substitutes this verbiage with the equinoctial rising/setting since, as we established above, they are equivalent. However, he hasn’t created any fancy terms for the north and south points on the horizon, so he simply labels them north/south2. While Ptolemy doesn’t mention it, we can also note that the symbols for Aries and Libra (the spring and fall equinoxes) are at the end of this line. However, on the interlinear intersections with each of the climata, there are no values. This is because these will be these values are the angle along the horizon between the zodiac point and the ecliptic and for the equinoxes they are zero as described above. Thus, either Ptolemy or Toomer has elected to leave them out.
Similarly, we drew [four] straight lines through all circles at equal inclinations either side of the equator [i.e., the vertical3 line], and wrote along these, in the seven interlinear spaces, the horizon distance of the solstical point from the equator which we found for each latitude (in units where one quadrant contains $90º$). At the ends where these lines meet the innermost circle we wrote, for the southern ones ‘winter rising’ and ‘winter setting’, and for the northern ones, ‘summer rising’ and ‘summer setting’.
This is the lines on either side of the vertical line. The ones toward the top are the rising/setting of the winter solstice (as indicated by the very oddly drawn Capricorn symbol at the end) and the ones toward the bottom are the rising/setting of the summer solstice (as indicated by the more recognizably drawn Cancer symbol). The values on each line are the angular distance, measured along the horizon, between the ecliptic and the respective solstice points at rising (left) and setting (right). Here, we can clearly see the $30º$ on the line for Rhodes which matches the value calculated in II.2.
To indicate the signs in between [equinoxes and solstices] we inserted two more lines in each one of the four segments and [wrote] along these the horizon distance from the equator of [the beginning of] the appropriate zodiacal sign, adding the name of each sign on the outermost circle.
Here, Ptolemy is simply displaying the same calculation for the first points in other signs, taking advantage of the symmetries mentioned above since zodiac signs diametrically opposed along the zodiac4 or the same distance before one equinox as before the other5 will always have the same values. This is why two signs are grouped together at the end of each and also the values reflected on the opposite spoke.
We also wrote, along the meridian line, for [each] parallel, its name, the length [of the longest day] in hours, and the elevation of the pole. In writing in [the data for all of the above], we began with the largest, outermost circle for the northernmost data, [and so on].
Here, Ptolemy is simply telling us where he placed the information about each climata which are readily visible along the vertical line. I believe the last bit, about filling the data in from the largest to the smallest is meant to give some indication as to how this should be read since there could conceivably be some confusion whether you should read it from the inner line or the outer one, but I’m not entirely sure of the intent. However, if you consider how the text is written, since it’s always in an “upright” position, it looks like it’s resting on the second circle in on the top half the diagram and the outermost circle in the bottom half. We can question whether this is how Toomer drew the diagram or Ptolemy, so I may simply be grasping at straws here.
- This diagram is from Toomer’s translation. Neugebauer has a different version of this, owing to his having introduced many topics from a more modern perspective outside the Almagest.
- They’re really squished in there, just inside the first ring, so you may have to enlarge to see them.
- Toomer’s text here says the “horizontal” line, but this appears to be incorrect because the text shortly following says on each of these lines he has written “winter/summer rising/setting” which are clearly on the vertical lines. In addition, it is clear that we find $30º$ along this line for Rhodes which is indeed the horizon distance calculated in the example done in II.2.
- I.e., Sagittarius and Gemini, Leo and Aquarius, Scorpio and Taurus, or Pisces and Virgo.
- I.e., Pisces and Scorpio, Aquarius and Sagittarius, Gemini and Leo, and Taurus and Virgo.