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13 17;51

204; 17

3,17;28

1, 0;30

As noted previously, Regiomontanus omitted the column for the argument of lunar latitude, but he added the radix for Vienna (Incarnation): 15d 4,14h. In ed. 1526 three rows were added for years 1480, 1500, and 1508.

The entry 15d 4;10h for the Incarnation has to be understood as meaning that 15d 4;10h before the Incarnation the mean lunar anomaly was 0°. According to the Parisian Alfonsine Tables, the lunar anomaly for the Incarnation and the longitude of Ferrara was 3,18;14,31°.8 The time taken by the Moon to cover this distance, at the mean motion of anomaly used in Alfonsine astronomy (13;3,54°/d) is precisely 15d 4;10h (= 3,18;14,31/13;3,54), in agreement with the entry given in Table 15.

The entries for the double elongation, the lunar longitude, and the argument of lunar latitude given for the Incarnation are the values of these quantities at the time when the anomaly was 0° (that is, Incarnation - 15d 4;10h), and can also be computed from the tables of radices in the Parisian Alfonsine Tables. Thus, for double elongation, at the Incarnation for the geographical longitude of Ferrara, the longitude of the Sun was 4,38;17,34° (see Table 5) and that of the Moon 2,2;0,43° = 122;0,43°;9 hence, the double elongation was 407;26,18° = 47;26,18°. Now, in 15d 4;10h the increment in double elongation amounts to 369;57,29° = 2- (15d 4;10° ■ 12;11,27°/d). Subtracting one quantity from the other we obtain 37;29° (= 407;26,18° - 369;57,29°), in full agreement with the given entry.

The procedure is analogous for the other two quantities: in 15d 4;10h the Moon progresses in longitude 199;56,0° at the standard mean motion of 13;10,35°/d. As the longitude of the Moon for Ferrara at the Incarnation was 2,2;0,43°, 15d 4;10h earlier it was 4,42;5° (= 122;0,43° - 199;56,0°), in agreement with the entry in Table 12. Similarly, for the argument of lunar latitude, in 15d 4;10h the Moon progresses 200;44,18° at the standard mean motion of 13;13,46°/d. The argument of lunar latitude for Ferrara at the Incarnation was 3,33;42,24° = 213;42,24°;10 hence, 15d 4;10h earlier it was 12;58° (= 213;42,24° - 200;44,18°). This result differs from the entry in Table 15 by 0;14°, but we note that the entry for the radix of the argument of lunar latitude at conjunction (5,52;52°: see Table 58) also differs by 0;14° from the recomputed value, indicating that the two radices for the argument of lunar latitude are consistent with each other.

As was the case for the radices of the Sun and the lunar node, the entries for the radices in 1400 and 1440 in Table 15 are obtained by adding those for the Incarnation to those corresponding to 1400

8 See Ratdolt, Tabule astronomice Alfontij, dlv; see also Poulle, Les tables alphon-sines, 128.

9 See Ratdolt, Tabule astronomice Alfontij, dlv; see also Poulle, Les tables alphon-sines, 127.

10 See Ratdolt, Tabule astronomice Alfontij, dlv; see also Poulle, Les tables alphon-sines, 128.

and 1440 years in the tables of the mean motions. Thus, for 1400 we obtain:

7d 15;51h = 15d 4;10h (Incarn.) + 20d 1;0h (1400y) - 27d 13;19h (1 anom. month),

178;56° = 37;29° (Incarn.) + 189;38° (1400y) + 311;49° (1 anom. month),

10;30° = 4,42;5° (Incarn.) + 1,25;21° (1400y) + 3;4° (1 anom. month), 3,0;12° = 13;12° (incarn.) + 2,42;28° (1400y) + 4;32° (1 anom. month), in agreement with the tabulated values.

Table 16. Monthly mean motion of the Moon

Na, f. 19r: Menses non bisextiles and Menses bisextiles Nu, f. 23v: Menses non bisextiles and Menses bisextiles Va, f. 190v: Menses non bisextiles and Menses bisextiles Ed. 1495, f. b8r: Tabula mensium non bisextilium and Tabula mensium bisextilium

Ed. 1526, f. 16r: Tabula mensium non bisextilium and Tabula mensium bisextilium

This table has two sub-tables, one for a common year and another for a leap year, both beginning in January: see Table 16. The layout of this table is the same as that of Table 12, but here the first column lists the names of the 12 months. As was the case in previous tables, Regiomon-tanus omitted the column for the argument of lunar latitude.

Table 16: Monthly mean motion of the Moon for a common year (excerpt)
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