Posted on by VoijaRisa

Almagest Book III: Table of the Mean Motion of the Sun

To help us determine where the sun is on a given date, Ptolemy sets out a table to allow us to more quickly look this up instead of needing to calculate how far around the ecliptic the sun has moved. This table is very similar to another set of tables Ptolemy would produce later: The Handy Tables. However, there are some notable differences between this table and the Handy Tables.

The first is that Ptolemy starts this table in 1 Nabonassar. It contains 45 rows in the 18-year table which means it spans 810 years. But Nabonassar began, by the Julian calendar, in 747 BCE. Thus, 810 years later is only 63 CE which doesn’t even cover the period up to Ptolemy’s own time. So although Ptolemy presents these tables, they’re really only good for things in his own past. The footnote in Toomer states,

By the time he came to compose the Handy Tables, he had reaslized the inconvenience of this arrangement, and switched to 25-yea periods and an epoch closer to his own time (Era Phillip, 323 BCE Nov. 12).

Regardless of the impracticality of these tables over longer time periods, here are the tables. I’ve rearranged the order in descending period whereas Ptolemy presented them in a fashion that fit them all onto two pages.

Distance [in Anomaly] from the Sun’s Apogee in Gemini 5;30º to its Mean
Longitude in the 1st Year of Nabonassar, Pisces 0;45º : 265;15º
18-year period º ‘ ” ”’ ”” ””’ ”””
18 355 37 25 36 20 34 30
36 352 14 51 12 41 9 0
54 346 52 16 49 1 43 30
82 342 29 42 25 22 18 0
90 338 7 8 1 42 52 30
108 333 44 33 38 3 27 0
126 329 21 59 14 24 1 30
144 324 59 24 50 44 36 0
162 320 36 50 27 5 10 30
180 316 14 16 3 25 45 0
198 311 51 41 39 46 19 30
216 307 29 7 16 6 54 0
234 303 6 32 52 27 28 30
252 298 43 58 28 48 3 0
270 294 21 24 5 8 37 30
288 289 58 49 41 29 12 0
306 285 36 15 17 49 46 30
324 281 13 40 54 10 21 0
342 276 51 6 30 30 55 30
360 272 28 32 6 51 30 0
378 268 5 57 43 12 4 30
396 263 43 23 19 32 39 0
414 259 20 48 55 53 13 30
432 254 58 14 32 13 48 0
450 250 35 40 8 34 22 30
468 246 13 5 44 54 57 0
486 241 50 31 21 15 31 30
504 237 27 56 57 36 6 0
522 233 5 22 33 56 40 30
540 228 42 48 10 17 15 0
558 224 20 13 46 37 49 30
576 219 57 39 22 58 24 0
594 215 35 4 59 18 58 30
612 211 12 30 35 39 33 0
630 206 49 56 12 0 7 30
648 202 27 21 48 20 42 0
666 198 4 47 24 41 16 30
684 193 42 13 1 1 51 0
702 189 19 38 37 22 25 30
720 184 57 4 13 43 0 0
738 180 34 29 50 3 34 30
756 176 11 55 26 24 9 0
774 171 49 21 2 44 43 30
792 167 26 46 39 5 18 0
810 163 4 12 15 25 52 30

 

Single Years º ‘ ” ”’ ”” ””’ ”””
1 359 45 24 45 21 8 35
2 359 30 49 30 42 17 10
3 359 16 14 16 3 25 45
4 359 1 39 1 24 34 20
5 358 47 3 46 45 42 55
6 358 32 28 32 6 51 30
7 358 17 53 17 28 0 5
8 358 3 18 2 49 8 40
9 357 48 42 48 10 17 15
10 357 34 7 33 31 25 50
11 357 19 35 18 52 34 25
12 357 4 57 4 13 43 0
13 356 50 21 49 34 51 35
14 356 35 46 34 56 0 10
15 356 21 11 20 17 8 45
16 356 6 36 5 38 17 20
17 355 52 0 50 59 25 55
18 355 37 25 36 20 34 30

 

Days

(by Month)

 º ‘ ” ”’ ”” ””’ ”””
30 29 34 8 36 36 15 30
60 59 8 17 13 12 31 0
90 88 42 25 49 48 46 30
120 118 16 34 26 25 2 0
150 147 50 43 3 1 17 30
180 117 24 51 39 37 33 0
210 206 59 0 16 13 48 30
240 236 33 8 52 50 4 0
270 266 7 17 29 26 19 30
300 295 41 26 6 2 35 0
330 325 15 34 42 38 50 30
360 354 49 43 19 15 6 0

 

Days º ‘ ” ”’ ”” ””’ ”””
1 0 59 8 17 13 12 31
2 1 58 16 34 26 25 2
3 2 57 24 51 39 37 33
4 3 56 33 8 52 50 4
5 4 55 41 26 6 2 35
6 5 54 49 43 19 15 6
7 6 53 58 0 32 27 37
8 7 53 6 17 48 40 8
9 8 52 14 34 58 52 39
10 9 51 22 52 12 5 10
11 10 50 31 9 25 17 41
12 11 49 36 26 38 30 12
13 12 48 47 43 51 42 43
14 143 47 56 1 4 55 14
15 14 47 4 18 18 7 45
16 15 46 12 35 31 20 16
17 16 45 20 52 44 32 47
18 17 44 29 9 57 45 18
19 18 43 37 27 10 57 49
20 19 42 45 44 24 10 20
21 20 41 54 1 37 22 51
22 21 41 2 18 50 35 22
23 22 40 10 36 3 47 53
24 23 39 18 53 17 0 24
25 24 38 27 10 30 12 55
26 25 37 35 27 43 25 26
27 26 36 43 44 56 37 57
28 27 35 52 2 9 50 28
29 28 35 0 19 23 2 59
30 29 34 8 36 36 15 30

 

Hours º ‘ ” ”’ ”” ””’ ”””
1 0 2 27 50 43 3 1
2 0 4 55 41 26 6 2
3 0 7 23 32 9 9 3
4 0 9 51 22 52 12 5
5 0 12 19 13 35 15 6
6 0 14 47 4 18 18 7
7 0 17 14 55 1 21 9
8 0 19 42 45 44 14 10
9 0 22 10 36 27 17 11
10 0 24 38 27 10 30 12
11 0 27 6 17 53 33 14
12 0 29 34 8 36 36 15
13 0 32 1 59 19 39 16
14 0 34 29 50 2 42 18
15 0 36 57 40 45 45 19
16 0 39 25 31 28 48 20
17 0 41 53 22 11 51 21
18 0 44 21 12 54 54 23
19 0 46 49 3 37 57 24
20 0 49 16 54 21 0 25
21 0 51 44 45 4 3 27
22 0 54 12 35 47 6 28
23 0 56 40 26 30 9 29
24 0 59 8 17 13 12 31