Abstract
In this chapter we shall give a brief survey of the number systems and the number notations in the principal cultural periods, and of the related arithmetical techniques. We shall see that these notations and these techniques are of very great importance for the development of mathematics; not, of course, in the sense that a good number system leads automatically to a high development in mathematics, but rather that a good notation and a convenient manipulation of the four fundamental operations are necessary conditions for the development of mathematics. Without mastery of these fundamental operations, mathematics can not get beyond a certain low level.
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References
For Babylonian cultural history see, in the first place B. Meissner, Babylonien und Assyrien, I and II (Heidelberg 1921–25). Next E Chiera, They wrote on clay, Chicago, 1938. For cuneiform script, see Ch. Fossey, Manuel d’ Assyriologie I, Paris, 1904, and B. Meissner, Die Keilschrift (Sammlung Göschen), 1922. For the chronology, see B. L. v. d. Waerden, Jaarboek, Ex Oriente Lux 10 (1948), p. 414 and the literature cited there.
O. Neugebauer, Abhandlunyen, Gesellschaft der Wtssenschaften, Gottingen. 13 (1927), p. 1.
F. Thureau—Dangin, Esquisse d’une histoire du system sexagesimal, Paris, 1932, p. 11.
O. Neugebauer. Quellen und Studien, A 3, Berlin, 1935.
YBC stands for Yale Babylonian Collection. The text is reproduced in O. Neugebauer and A. Sachs. Mathematical Cuneiform Texts, New Haven, Conn., 1945, p. 16.
See the examples of Pappus in Vogel, Sitzungsber. Miinchen? 1936, p. 393.
VAT stands for Vorder—Asiatische Textsammlung Berliner Museum. For this text see F. Thureau—Dangin, Textes math, babyl, Leiden, 1938, p. 123.
O. Becker, Quellen und Studten, B 4, p. 181.
Neugebauer—Sachs, Mathematical Cuneiform Texts, New Haven, 1945, p. 43. See Plate 8b.
See the example of Pappus in Vogal, Sitzungsber. München 1936, p. 393.
J. Baillet, Le Papyrus Mathematique d’ akhmim, memoires de la Mission archéologique francaise au Caire 9, fasc. 1, Paris 1892.
H. Gerstinger und K. Vogel, Eine stereometrische Aufgabensammlunfi im Papyrus Vindobon. 19996, Mitteilungen Papyrussammlung Erzherzog Rainer, Neue Serie, 1. Folge, Wien 1932, p. 11.
A Rome, CommenUnra de Pappus et de Theon d’Alexandrie sur I’Almageste, Tome 2, Roma 1936.
See, e.g. Datta and Singh, History of Hindu mathematics I.
G. R. Kaye, Notes on Indian mathematics, Journal of the Asiatic Society of Bengal, 1907, III, p. 482.
A translation with excellent commentary is given by Burgess and Whitney, Journal of the American Oriental Society 6(1860), p. 141.
Pargiter, Journal Royal Asittic Society, 1902, p. 254.
See W. E. Clark, the Aryabhatiya of Aryabhata, Chicago, 1950.
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Van Der Waerden, B.L. (1975). Number Systems, Digits and the Art of Computing. In: Science Awakening I. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1379-0_2
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