386 Christine proust
in Akkadian. Sachs has shown that these instructions refer to calculations
found in the numeric tablet CBS 1215. 6 Th us, we have both a numeric text
and a verbal text related to the same algorithm. Th ese two texts both refer to
the reciprocal algorithm in widely diff erent manners. Th ey neither employ
the same means of expression, nor do they deliver exactly the same type of
information. Th us there is a shift between the diff erent texts and the prac-
tices of calculation to which they refer.
In addition, some properties of the tablet CBS 1215, notably those
which concern spatial arrangement and reciprocity, are likewise mani-
fested in calculations of square roots. Such is notably the case for the tablet
UET 6/2 222, which is an Old Babylonian school exercise from Ur (see
Table 12.1 ). Also, in the case of the square root algorithm just as for the
reciprocal algorithm, both numeric and verbal texts are attested. In fact, J.
Friberg has shown that tablet IM 54472, composed in Akkadian, contains
instructions which relate to calculations found in the numeric tablet UET
6/2 222. 7
In order to facilitate the reading of the following sections, which alter-
nate between diff erent tablets, I have designated the tablets by the letters A
to D. Th e concordance between these letters, their museum numbers and
provenance is presented in Table 12.1. 8
In addition, many other parallels to Tablet A exist. In some cases, entire
sections of the text are identically reproduced. Such reproductions and cita-
tions occur principally in the texts from the scribal schools which operated(^6) Sachs 1947.
(^7) Friberg 2000 : 108–12.
(^8) Th e tablets of Table 12.1 have been published in the following articles and works. A = CBS 1215
in Sachs 1947 for the transliteration and interpretation; Robson 2000 : 14, 23–4 for the hand
copy and several joins ; B = VAT 6505 in Neugebauer 1935 –7: i 270, ii pl. 14, 43; C = UET 6/2
222 in Gadd and Kramer 1966 : 248; D = IM 54472 in Bruins 1954. Other than the tablet from
Ur, the tablets come from illicit excavations. VAT 6505 may come from the north because of its
orthographic and grammatical properties (H2002: 331, n. 383); according to Friberg 2000 : 106,
159–60, it may come from Sippar. IM 54472 likewise may come from the north, perhaps from
Shaduppum (Friberg 2000 : 110).
Table 12.1 Principal texts studied here
Museum number Provenance Contents Style
A CBS 1215 Unknown Reciprocal Numeric
B VAT 6505 Unknown Reciprocal Verbal
C UET 6/2 222 Ur Square Root Numeric
D IM 54472 Unknown Square Root Verbal