By E. J. Dijksterhuis
Dijksterhuis E.J., Dikshoorn t.C., with a brand new bibliographic essay Wilbur R. Knorr. Archimedes (PUP, 1987., 5000)(ISBN 0691084211)(600dpi)(T)(460s)
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Yet innumerable "reasons" have been advanced why the Babylonians used the basis 60 for their number system. I shall not make any attempt to discuss here the history of the sexagesimal system in any detail, but a few points must be mentioned because they are of importance for the historical approach to the development of number systems as a whole. First of all, there exists a common misconception as to the gcmerality of the use of the sexagesimal system. The very same tablet which contains hundreds of sexagesimal numbers, column beside column, to compute the dates of the new moons for a given year, might end with a "colophon" containing the name of the owner of the tablet, the name of the scribe, and the date of writing of the text, the year being expressed in the form 2 me 25 "2 hundred 25" where the main text would express the very same date sexagesimally as 3,45.
For an example of an inscription with large number symbols in the alphabetic notation see Inscriptiones Graecae vol. 12,1 (Insularum Maris Aegaei) Berlin 1895, No. 913. , lists the basic numbers of a theory of planetary motion; the author is unknown. For a discussion cr. P. Tannery, Memoires scientifiques vol. 2 p. 487 fl. In the ordinary alphabetic notation the numbers 1000, 2000 etc. are written by means of (x, P. etc. which precede the symbols of lower order. Often accents are added in order to avoid confusion with I, 2.
Indeed, 3" = 2 6. Ordinarily the arrangement of the alphabetic numerals is stricOy from higher to lower numbers. In datings, however, one finds also the inverted order: ct. for examples from Mesopotamia Yale Classical Studies 3 p. 30 fT. (clay bullae from Uruk); Excavations in Dura-Europus, Preliminary Report IX, 1 p. ; Klio 9 p. 353. C. , e. , Tod. The Maeedonian Era; The Annual of the British School at Athens, No. 23 (1918-1919) p. 206-217 and No. 24 (1919-1921) p. 54-67. That the Arabic form for the zero sYmbol (a litOe circle with a bar over it and related forms) is simply taken from Greek astronomical manuscripts was recognized by F.