Syzygies as Pivots: An Unusual Mid-Fifteenth-Century Working Ephemeris

Neske I. , Die Handschriften der Stadtbibliothek Nürnberg , iv: Die lateinischen mittelalterlichen Handschriften (Wiesbaden, 1997), 169–71.

Zinner E. , Regiomontanus: His life and work (Amsterdam, 1990), 10. The date “about 1468” given by Zinner is obviously a typographical error; it should probably read 1438.

By von Rein Peter , “Crucifer qui fuit commendator Sitauie”. Zittau is a township at the Neisse river.

Kokott W. , “Regiomontans Ephemeriden für die Jahre 1475 bis 1506”, Sterne und Weltraum , xxxvi (1997), 446–51. While the error margin of ±15′ for the syzygies derived in this preliminary paper may not be generalized indiscriminately, it indicates the degree of accuracy that was feasible.

Meeus J. Mucke H. , Canon of lunar eclipses −2002 to +2526 (Vienna, 1979). This catalogue is based upon the corrected elements by Brown E. W. ( USNO improved lunar ephemeris (Washington, 1954)). In Table 1, data from this source are denoted “Canon”. “ARC Dance” refers to the ephemeris programme “Dance of the Planets” from ARC, Englewood, Col., U.S.A.

Lhotsky A. d'Occhieppo Ferrari K. , “Zwei Gutachten Georgs von Peuerbach über Kometen (1456 und 1457)”, Mitteilungen des Instituts für Österreichische Geschichtsforschung , lxviii (1960), 266–90, esp. p. 273 (text), pp. 286–7 (commentary); Kokott W. , “Theorie und Augenschein in Peuerbachs Kometenschrift von 1456”, Die Sterne , lxxii (1996), 210–22, p. 219. It is not clear from the text whether Peurbach actually saw the eclipse, or if he only calculated it from either its saros predecessors or his own Tabulae eclypsium. In the latter case, we could assume that the author of the almanac must have had access to Peurbach's iudicium or another external source for this special case. An eclipse of the Easter full moon, preceding the appearance of Halley's Comet, would have been of some astrological importance, which could have attracted some attention.

For the sake of convenience, eclipse magnitudes are given for Greenwich. Percent figures for other European locations are of course different. Calculations made using “ARC Dance” (ref. 5).

Only for Mercury, this purpose is not fulfilled. The correct period would be 13 years, corresponding to 41 synodic revolutions with a residual error of less than 4 days.

Zinner , op. cit. (ref. 2), finds (for the year 1448) the amount of the average error of planetary longitudes in the ephemeris to be 1.5°, of the same order as in a manuscript ephemeris by Regiomontanus for the same year. He describes, for both authors, the error for Mercury as particularly large. In contrast, he mentions the good accuracy of the Mars and Jupiter values. This is consistent with his 12-year cycle for Jupiter. While the second list shows an improvement in the treatment of Mercury, it is less reliable for Jupiter.

Neske , op. cit. (ref. 1), erroneously attributes this item to Johannes Dank. Layout and handwriting are similar to the copies of Dank's ephemerides for 1340–80 (2r–103r) and 1381–1400 (134r–148r), between which it was placed in binding.

E.g. Nür. Cent. V.94, ff. 41r–109v. A list of copies in Central European libraries is given in Zinner E. , Verzeichnis der astronomischen Handschriften des deutschen Kulturgebietes (Munich, 1925), nos. 6832–6849.

This cycle yields less accurate results than the 33-years alternative selected by the user of the ephemeris. 46 years correspond to 145 synodic revolutions, with an excess of 4 days to be corrected. This error is equivalent to the 13-year cycle (cf. ref. 8). If the author did actually use the Jacobus tables for extrapolation, he probably followed his own judgement at least for Jupiter (cf. ref. 11).

Which is bound preceding it in Cent. VI. 16, cf. ref. 10.

The handwriting seems also to be identical with a few pages substituted for a lost part of the Jacobus ephemeris (ff. 139v–140r), the Jacobus canones (ff. 132v–133r), and the Dank canones (f. 194r-v); these were identified as belonging to the same hand, cf. Neske , op. cit. (ref. 1).