REEDITION OF A DIVISION TABLE PRESERVED ON TABLEWARE

REEDITION OF A DIVISION

The ostracon is an inscribed fragment of the rim of an open bowl. 1 It contains one line of writing on the exterior side and four partially preserved lines on the interior. It was fi rst published in O.Sarga under no. 27, and then later republished with virtually no change to the ed.pr. in MPER N.S. 18.325 as tables of fractions, also known as division tables, for 1 /25, 1 /49, and 1 /7. These divisions also feature in David Fowler's lists of division tables for 7' , 25' , and 49' (as conventional, n' = 1 /n). 2 For one familiar with such tables, the previous publications arouse suspicion because of the strange assemblage of calculations, which have been interpreted as divisions of 11 by 25, 7 by 49, and part of a series of divisions by 7. Nowhere else does one fi nd partial selections of tables involving disparate divisors. Thus, one naturally wonders if there is a simpler way to interpret the preserved fractions.

The ed.pr. and MPER N.S. 18.325 both offer the following text:

Not only the combination of divisions is surprising, but also the quotient of the division on the 'recto' is incredible. The result of the division of 11 by 25 can be easily expressed as 1 /3 1 /15 1 /25. The current interpretation, although formally correct, entails a complex and implausible calculation, and it requires supplementing of the last two fi gures [ρ̅ν ̅ σ ̅ι̅ ], which do not survive on the ostracon. There is a simpler explanation that presents itself if one looks fi rst at col. 2 on the side designated 'verso'. It preserves part of a standard series of divisions in 7 with consecutively increasing dividends (here preserved are 7, 8, and 9) and the same divisor. The next dividend must have been 10, and the division of 10 by 7 is exactly what is written on the other side of the sherd, not the division of 11 by 25. To see this, the numerals simply need to be articulated slightly differently than in the previous editions and nothing should be restored to the right of the last preserved fraction: † τῶν ϊ α γʹ ιδ/ μ ̅ β̣ ̅ ( 1 /7) of 10 is 1 1 /3 1 /14 1 /42 * This publication originated in the Collaborative Research Centre 933 "Material Text Cultures. Materiality and Presence of Writing in Non-Typographic Societies" (subproject A09 "Writing on Ostraca in the Inner and Outer Mediterranean"). The CRC 933 is funded by the German Research Foundation (DFG). I am grateful to Elisabeth O'Connell of the British Museum for providing information on the ostraca from Wadi Sarga discussed here.

1 More precisely, it is "the rim of a fi ne buff-coloured pottery bowl with fl aring sides and turned rim, both interior and exterior covered with an orange-red burnished slip", cf. the description of the object on the British Museum Collection site, https://research.britishmuseum.org/research/collection_online/collection_object_details.aspx?objectId=121316&partId=1&-searchText=55842&page=1.

2 D. Fowler , Tables of Parts, ZPE 53 (1983) Having seen what is going on with the 'recto', we should account for the division of 7 in 49 postulated to the left of the column featuring 1 /7 on the interior side. All that survives there is ]νζζ/. This happens to be the end of the quotient of 6,000 divided by 7, as 6,000 ÷ 7 = 857 1 /7, which was written as ωνζζ/. This division served as the heading of the table for 1 /7. What exact form this header took, whether τὸ ζ ἐν ἀριθμῶ(ν) ωνζζ/, τὸ ζ ἐν ψήφω(ν) ωνζζ/, or some abbreviated version of either of these, is probably indeterminable. 3 Under it, the dividends from 1 to 6 must have been inscribed, likely in two columns, now all lost. 4 The surviving three divisions in what now is col. 2 would originally have constituted col. 3, while the division of 10 was placed on the other, exterior side of the sherd, perhaps because there was not enough room left for it on the interior side. Interestingly, it was introduced with a staurogram, which could have led previous editors to think that it was unrelated to the text on the interior side. The whole series would have been recorded thus:

Interior side (concave) 5 [ † ?τὸ ζ ἐν ἀριθμῶ ( One wonders if the interpretations of previous editors were at least partly due to the presumption that the convex side, usually viewed as 'recto', had to be inscribed before the concave or 'verso' side. While this is true in general, there are exceptions, particularly in the case of late antique ostraca that derive from fi ne tableware such as bowls or plates. 7 Because these sherds tend to have little curvature and similar fi nishing on both sides, it is perhaps more accurate to refer to their sides as 'interior' and 'exterior' rather than 'convex' and 'concave'; not infrequently, both sides of such fragments are inscribed, and it is not always possible to determine the sequence of writing. In some cases, however, the interior side was clearly inscribed fi rst. For example, O.Frange 791, a piece of tableware, has a Greek liturgical text that starts on the interior and continues on the exterior surface. 8 And a large sherd from a plate inscribed with a peculiar assemblage of texts, which include a hymn to Mary, biblical quotations, and a diagram explaining a Coptic cryptograph-