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0;43,10

0;2,22

To determine the maximum solar equation embedded in this table, consider first the daily mean velocity of the Sun derived from the entry for 365 days: 5,59;46,11°/365d = 0;59,8,24,49,18°/d. By inspecting the table, one sees that 0;59,8° is the difference between days 93 (1,29;29,55°) and 94 (1,30;29,3°), and between days 94 (1,30;29,3°) and 95 (1,31;28,11°). Now, computing the position of the mean Sun for days 93, 94, and 95, we obtain 1,31;40,2°, 1,32;39,10°, and 1,33;38,19°, respectively. If we subtract these mean positions from the true positions specified in the table, we obtain 2;10,7°, 2;10,7°, and 2;10,8°, respectively. These are the maximum differences between mean and true positions of the Sun, that is, the maximum solar equation, which we can take confidently as 2;10°. This is indeed the value used in the standard Alfonsine Tables.

As is the case with other tables, Bianchini's text offers an example of its use (Chapter 9). We are asked to find the true position of the Sun in 1446, August 16 at 15;40h. As explained in Chapter 7 (see com ments to Table 8, above), in 1446 the Sun reaches its apogee on June 13 at 8;50h and the position of the solar apogee is 1,30;40,16°. The time since apogee is 64d 6;50h, and therefore 64d is taken as the argument for Table 11. The corresponding entries for 64d are 1,1;10,48° (true motion) and 0;2,25°/h (hourly motion), and the true motion of the Sun that was sought is

2,32;7,36° = 1,30;40,16° + 1,1;10,48° + (6;50h ■ 0;2,25°/h).

This is the value given in the text, but we note that ed. 1526 has 2,32;7,34°.

Table 12. Mean motion of the Moon in collected years

Na, f. 19r: Tabula radicum lune Nu, f. 23v: Tabula radicum lune Va, f. 190v: Tabula radicum lune

Ed. 1495, f. b6r-v: Tabula radicum lune in annis collectis Ed. 1526, f. 14r-v: Tabula radicum [symbol for the Moon] in annis collectis

In this table there are five columns: see Table 12. The first is for the argument: collected years from 40 to 2400 at intervals of 40y (only up to 2000y in Regiomontanus's copy). Thus, all the entries correspond to leap years. The entries in the other columns represent the time (in days, hours, and minutes), the double elongation (in degrees and minutes), the longitude of the Moon (in physical signs, degrees, and minutes), and the argument of lunar latitude (in physical signs, degrees, and minutes). In Regiomontanus's copy the column for the argument of lunar latitude was omitted. The time displayed in column 2 is the excess over an integer number of anomalistic months; hence, the entries in this column do not exceed 27d 13;18,36h, which is the length of the anomalistic month mentioned in Chapter 11 and explicitly given in Table 14, below. We note that the author uses degrees from 0 to 360 for the double elongation, here called centrum and, on the other hand, physical signs of 60° for the lunar longitude and the argument of lunar latitude.

Table 12: Mean motion of the Moon in collected years (excerpt)

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