III
SYMBOLS IN ARITHMETIC AND ALGEBRA
(ELEMENTARY PART)
100. In ancient Babylonian and Egyptian documents occur certain ideograms and symbols which are not attributable to particular individuals and are omitted here for that reason. Among these signs is (
symbol characters) for square root, occurring in a papyrus found at Kahun and now at University College, London,[1] and a pair of walking legs for squaring in the Moscow papyrus.[2] These symbols and ideograms will be referred to in our “Topical Survey” of notations.
A. GROUPS OF SYMBOLS USED BY INDIVIDUAL WRITERS
GREEK: DIOPHANTUS, THIRD CENTURY A.D.
101. The unknown number in algebra, defined by Diophantus as containing an undefined number of units, is represented by the Greek letter ς with an accent, thus ς′, or in the form ς°′. In plural cases the symbol was doubled by the Byzantines and later writers, with the addition of case endings. Paul Tannery holds that the evidence is against supposing that Diophantus himself duplicated the sign.[3] G. H. F. Nesselmann[4] takes this symbol to be final sigma and remarks that probably its selection was prompted by the fact that it was the only letter in the Greek alphabet which was not used in writing numbers. Heath favors “the assumption that the sign was a mere tachygraphic abbreviation and not an algebraical symbol like our x, though discharging much the same function.”[5] Tannery suggests that the sign is the ancient letter koppa, perhaps slightly modified. Other views on this topic are recorded by Heath.
- ↑ Moritz Cantor, Vorlesungen über Geschichte der Mathematik, Vol. I, 3d ed., Leipzig, p. 94.
- ↑ B. Touraeff, Ancient Egypt (1917), p. 102.
- ↑ Diophanti Alexandrini opera omnia cum Graecis commentariis (Lipsiae, 1895), Vol. II. p. xxxiv–xlii; Sir Thomas L. Heath, Diophantus of Alexandria (2d ed.; Cambridge. 1910), p. 32, 33.
- ↑ Die Algebra der Griechen (Berlin, 1842), p. 290, 291.
- ↑ Op. cit., p, 34–36.
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