Page:A History of Art in Chaldæa & Assyria Vol 1.djvu/88

 68 A HISTORY OF ART IN CIIALD.KA AND ASSYRIA. person chiefly concerned, the hour in which his star would be in the best quarter of the sky and in the most propitious relations with its neighbours. The phenomena produced in Chaldsea by these studies have been repeated more than once in the history of civilization ; they embody one of those surprises to which humanity owes much of its progress. The final object of all this patient research was never reached, because the relations upon which a belief in its feasibility was based were absolutely chimerical, but as a compensation, the accessory and preliminary knowledge, the mere means to a futile end, have been of incalculable value. Thus, in order to give an imposing and apparently solid basis to their astrological doctrines, the Chaldaans invented such a numeration as would permit really intricate computations to be made. By the aid of this system they sketched out all the great theories of astronomy at a very early age. In the course of a few centuries, they carried that science to a point never reached by the Egyptians. 1 The chief difficulty in the way of a complete explanation of the Chaldsean system of arithmetic lies in the interpretation of the symbols which served it for ciphers, which is all the greater as it would seem that they had several different ways of writing a single number. In some cases the notation varied according to o o the purpose of the calculation. A mathematician used one system for his own studies, and another for documents which had to be read by the public. The doubts attending the question are gradually being resolved, however, by the combined efforts of Assyriologists and mathematicians. At the beginning of their civilization the Chaldseans did as other peoples have done when they have become dissatisfied with that mere rough opposition of unity to plurality which is enough for savage races, and have attempted to establish the series of numbers and to define their properties. " They also began by counting on their fingers, by Jives and tens, or in other words by units of Jive ; later on they adopted a notation by sixes and twelves as an improvement upon 1 This has been clearly shown by LAPLACE in the Precis de I ' Histoire de I' Astronomic, which forms the fifth book of his Exposition du Systeme du Monde (fifth edition). He gives a resume of what he believes to have been the chief results obtained by the Chaldaean astronomers (pp. 12-14 in the separate issue of the Precis 1821, 8vo). It would now, perhaps, be possible, thanks to recent discoveries, to give more precise and circumstantial details than those of Laplace.