P3 pk pk d

where d, the maximum of the third component of latitude for the inner planets (deviation), is 0;10° for Venus and -0;45° for Mercury. Had he followed them, he would have found for Venus P3 = 0;5,9° ■ 0;30,52 = 0;2,39°, and the final result would have been P = 0;50,53°. Analogously, for Mercury he would have computed P3 = -0;44° ■ 0;59,12 = -0;44°, and in this case his final result would have been the same.

In sum, all the entries in Bianchini's latitudes tables ultimately derive from Almagest XIII.5, but Bianchini presented them differently. In particular, he introduced one column for Venus (col. 6) and two columns for Mercury (cols. 5 and 6) which are not found in Almagest XIII.5.

Table 75. Lunar equation

Na, f. 122r: Tabula equationis lune Rc, f. 75v: Tabula equationis lune Va, f. 259v: Tabula equacionis lune

Ed. 1526, ff. 345r-347v: Tabula equationis [symbol for the Moon]

Although the lunar equation is already embedded in Table 17, we are given another table with explicit entries for the lunar equation. This is the same table that appears in the editio princeps of the Alfonsine Tables.23

Planetary equations: Tables 76 (Saturn), 77 (Jupiter), 78 (Mars), 79 (Venus), and 80 (Mercury)

Na, f. 122v (Saturn: Tabula equationis Saturni); f. 123r ( Jupiter); f. 123v

(Mars); f. 124r (Venus); and f. 124v (Mercury) Rc, f. 74v: (Saturn: Tabula equationis Saturni); ff. 74v-75r ( Jupiter);

f. 75r (Mars); ff. 75v-76r (Venus); and f. 76r (Mercury) Va, f. 260r: (Saturn: Tabula equacionis Saturni); f. 260v ( Jupiter); f. 261r (Mars); f. 261v (Venus); and f. 262r (Mercury)

23 Ratdolt, Tabule astronomice Alfontij, e4r-e6v.

Ed. 1526, ff. 348r-350v (Saturn: Tabula equationis [symbol for Saturn]); ff. 351r-353v ( Jupiter); ff. 354r-356v (Mars); ff. 357r-359v (Venus); and ff. 360r-362v (Mercury)

Although the planetary equations are already embedded in Tables 27, 34, 41, 48, and 56, we are given another set of tables with explicit entries for the planetary equations. These are the same tables that appear in the editio princeps of the Alfonsine Tables.24

Table 81. Stations

Na, f. 125r: Tabula stationum 5 planetarum

Rc, f. 78v: Tabula stationum 5 planetarum

Va, f. 262v: Tabula stationum quinque planetarum

Ed. 1526, ff. 363r-365v: Tabula stationum quinque planetarum

This table has 6 columns. The first lists the arguments at intervals of 1°, from 1° to 3,0°. There is one column for the first stations of each of the first stations of the five planets. According to the headings in ed. 1526, the units are degrees and minutes, but this is a mistake for physical signs and degrees. This table is an expanded version of those for the same purpose in Almagest XII.8 and the zij of al-Battani25 where the entries are given with a higher precision (to minutes), but at intervals of 6° of the argument. We note that no such table appears in the editio princeps of the Alfonsine Tables.

Table 82. Equation of time

Na, f. 108r-v: Tabula horarum meridiei et equationis dierum ad meridi-

anum ferarrie et bononie Rc, f. 48r-v: Tabula horarum meridiei ad meridianum ferarrie et bononie et equationis dierum Va, ff. 258v-259r: Tabula horarum meridiei et equationis dierum ad meridianum ferarrie et bononie Ed. 1526, f. 366r-v: Tabula equationis dierum

24 Ratdolt, Tabule astronomice Alfontij, e7r-g5v.

25 Nallino, Al-Battani, 2:138-39.

In the manuscript tradition26 the equation of time is presented together with the length of daylight (Table 83), and this is indeed the case in Na, Rc, and Va. We shall treat the two items separately.

The entries in this table are given in minutes and seconds of time, whereas in most tables of this kind the units are degrees and minutes: see Table 82. To transform the entries of a table for the equation of time from units of arc to units of time, one has to multiply the value by 4, for 360 time-degrees = 24 hours or 1 time-degree = 0;4 hours. This explains why all entries in Table 82 are multiples of 4. The extremal values in this table are:

max = 22;12 min (Tau 28° - Gem 5°) min = 12;16 min (Leo 1° - 9°) Max = 31;36 min (Sco 8° - 9°) Min = 0;0 min (Aqu 18° - 19°).

This table is a variant of the table for the equation of time associated with the Toledan Tables,27 with a maximum of 7;54°, and yielding a maximum value, expressed in time, of 31;36 min (= 7;54 • 4). In the manuscripts containing the Toledan Tables, the equation of time is usually combined with right ascensions in a single table, and this is also the case in the zij of al-Battanl, where the same table is found.28 Toomer and Pedersen located copies of this table with only the equation of time, expressed in minutes of an hour.29 In the editio princeps of the Alfonsine Tables, the equation of time (in degrees) was combined with right ascensions in a single table.30

Table 82: Equation of time (excerpt)

Arg. (°)

Ari

Tau

Gem

Cnc

Leo

Vir

(min)

(min)

(min)

(min)

(min)

(min)

0 0

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