Introduction to Arithmetic

The problems of the Ahmes papyrus on the distribution of loaves of bread among ten people,Eisenlohr, op. cit., pp. 71-74; Peet, op. cit., pp. 78-79. and the problem to which we shall recur on the distribution of 100 loaves of bread according to the terms of an arithmetical series, are certainly suggestive of the type of problems of distribution to which Plato had reference. The following problemEisenlohr, op. cit., pp. 63-65; Peet, op. cit., pp. 70-72. in the Egyptian papyrus is doubtless one of the type dealing with containers (phialite): "I pour (from my container) three times; I add 1/7 and 1/3; I fill it up. What part of the measure have I?" In the Greek anthology are found a series of problems on the distribution of apples and nuts, and problems on the weights of bowls, which involve linear equations in one and two unknown quantities.See Heath, A History of Greek Mathematics, vol. I, pp. 15-16; vol. II, pp. 441-443; Tannery, Diophantine Alexandrian, Complete Works, vol. II (Leipzig, 1895), pp. 43-72.

The intimate connection between Greek logistic and Egyptian arithmetic can hardly be seriously questioned. So far as Greek arithmetica the theory of numbers is concerned, here again we find that the Greeks were inspired by their Oriental predecessors. The available Babylonian and Egyptian documents in the exact sciences are as yet extremely limited; our present information is more or less accidental, and by no means comprehensive. So far as early Egyptian mathematical science is concerned, we are largely dependent upon the Ahmes papyrus. But these few surviving documents give indications of development along many different lines of mathematical thought. Their content is, as we have already partially indicated, quite in harmony with the Greek traditions concerning Egyptian and Babylonian science. In view of this correspondence and of further definite indications of real progress in mathematical thinking among the Egyptians, we are warranted in giving some credence to the Greek traditions concerning Oriental science which are not yet confirmed by indigenous evidence.

Arithmology is closely related to the occult sciences, astrology, alchemy, and magic. While alchemy is undoubtedly a comparatively late development, the Oriental source of its theories is unquestioned.Berthelot, The Origins of Alchemy (Paris, 1885), Chapter III. Between the industrial arts of Egypt and Babylon and the development of theories of alchemy, there is an intimate connection, as Berthelot has shown. Furthermore, this authority even asserts that Thales may have taken from Babylonian myths his theory that water is the material cause of all things.Op. cit., p. 251.