22 Rochberg
out the year. This arithmetic scheme is linear because it is characterized
by a difference sequence of fi rst order, that is, the entries in the table
increase and decrease by a constant amount and the values are bounded
by a maximum and a minimum value. The values in the table describe a
so- called linear zigzag function, which is periodic. Much later and in a
more sophisticated form, the zigzag function would still be used in the
astronomy of the Hellenistic period, both in cuneiform mathematical as-
tronomy and all those forms of Greek astronomy that derived from the
Babylonian tradition.^20
Elsewhere in Enu ̄ma Anu Enlil, omen protases refl ect an underlying and
systematic observation of many phenomena, as well as the recognition
of some simple periodicities. The Old Babylonian (ca. 1800 BCE) lunar
eclipse omen protases, for example, identify lunar eclipse days with the
middle of the lunar month, or days 14–16, when lunar eclipses can occur.
Additionally, these protases are constructed with elements such as the
reddish color of the moon during total eclipses, the various times of night
when the eclipse occurs (as well as its duration), and all appropriate phe-
nomena for lunar eclipses. By the seventh century BCE, lunar eclipses in
the omens became more descriptive and detailed, such as in the following
example from Enu ̄ma Anu Enlil Tablet 20:If an eclipse occurs on the 14th day of Tebe ̄tu, and the god (= the moon), in
his eclipse, becomes dark on the east upper part of the disk and clears on the
west lower part; the west wind (rises and the eclipse) begins in the last watch
and does not end (with the watch); his cusps are the same (size), neither one
nor the other is wider or narrower.^21The prediction and exclusion of lunar eclipses was already an estab-
lished practice in the letters and reports from court astrologers, mentioned
above: “(I wrote to the king, my lord) ‘[The moon] will make an eclipse.’
[Now] it will not pass by, it will occur.”^22
Only during the fi fth century BCE was the eighteen- year eclipse pe-
riod, or “Saros,” used for predicting eclipse possibilities, but during the pe-
riod of the Sargonids, letters from scholars attest to the fact that they kept
a regular watch for predicted lunar eclipses^23 and even for anticipated solar
eclipses.^24 The knowledge of astronomical periods during the seventh cen-
tury BCE, however, was characterized by crude intervals between charac-
teristic planetary visibility phenomena (for example, one year between a
fi rst visibility of Jupiter and a last visibility). The interest in prediction was
circumscribed by celestial divination, in which only fi rst visibilities and