Use of the Normal Star reference
system is more characteristic of the earlier horoscopes, in which case the
evidence argues somewhat more forcibly for the first method, that is,
excerpting the desired lunar position with respect to a Normal Star from the
appropriate diary text. We have the following excerpt from a third-century B.C.
horoscope (BH rev. 1-3, dated 258 B.C.): “night of the 8th, beginning of night,
the moon was ½ cubits below (the bright star of the Ribbon of) the Fishes, the
moon passed ½ cubit to the east.” Similarly, from another third-century example
(BH 13:2—4, dated 224 B.C.), we have “night of the 4th, beginning of night, the
moon was below the bright star of the Furrow by 15/, cubits, the moon passed
1/, cubit to the east.”3* This horoscope also gives the zodiacal sign of the
moon”: “In his hour (of birth), the moon was in Libra” (BH13:5).
. . .
The Normal Stars provided a
positional system in which distance with respect to a certain Normal Star was
noted in cubits (Kùš = ammatu)
and fingers (šu.sI = ubānu).
The equivalence between the finger and the degree is 12 fingers = 1°. Because
some astronomical texts seem to be at variance where the cubit is concerned,
some measuring this unit apparently as 30 fingers, others as 24 fingers, it has
been assumed that the Babylonian cubit was reckoned variously as 2° or 21/2°.13
The 21/2° cubit, however, does not accord with the distances from Normal Stars
as determined from the diary texts directly, in which the size of the cubit seems
to be something just a little more than 2°.
. . .
Calculations of astronomical
phenomena in Greek, Arabic, and Indian astronomy are carried out in the
Babylonian sexagesimal (base-60) system, the origins of which may be traced to
Sumerian bookkeeping of the third millennium, preserved in the archaic texts of
Uruk. Units of measure for time and arc in the Babylonian system give us the
360° circle, as the day was measured as 12 DANNA units, each subdivided into 30
Uš: 12 x 30 = 360 uš. Because the day is the equivalent
of one rotation of the heavens from sunrise to sunrise (or sunset to sunset),
the circle was thereby divided into 360 uš
units, or "degrees." This convention, along with the use of
sexagesimal notation, is attested in Greek astronomy by the mid- second century
B.C., associated with Hipparchus and Hypsicles (ca. 200 B.C.). The cubit (Kùš = ammatu), with its
subdivision the finger or digit (ŠU.SI = ubānu), was a unit of distance
in Babylonian metrology with an astronomical application for measuring
distances in the heavens between, for example, fixed stars and the meridian, or
between planets and ecliptical stars, and also for measuring eclipse magnitude.
The equivalence I cubit = 30 fingers = 2 ½ uš,
gives us 1 finger = 0.5° and 1° = 12 fingers. The cubit is used in two of the
earliest observations (of the planet Mercury) recorded in the Almagest,
from 245 and 237 B.C. (Almagest IX, 7). Ptolemy cites Babylonian eclipse
reports, giving the time the eclipse begins, statement of totality, time of
mid-eclipse, and direction and magnitude of greatest obscuration in digits, in
the manner of cuneiform eclipse reports.5 Ptolemy (Almagest IX, 7) also
cites distance in cubits from ecliptical norming stars (Normal Stars) at dawn
for Mercury, the dates for which are given in the Babylonian calendric system
of lunar months (translated into Macedonian month names) and Seleucid Era
years, and he also cites the distance of Saturn in digits from a Normal Sar in
the evening (Almagest XI, 7). These observational reports attest to Greek
awareness of the Babylonian astronomical diaries and related observational and
predictive texts. The Babylonian cubit is also used by Strabo in his Geography
(2, I, 18). (Francesca Rochberg, The Heavenly Writing: Divination,
Horoscopy, and Astronomy in Mesopotamian Culture [Cambridge: Cambridge
University Press, 2004], 106, 125, 238-39)
