CHAPTER II 



EARLY MATHEMATICAL SCIENCE IN BABYLONIA AND 



EGYPT 



In most sciences one generation tears down what another has built 

 and what one has established another destroys. In Mathematics alone 

 each generation builds a new story to the old structure. Hankel 



A HISTORY of science may be based on some more or less definite 

 logical system of definitions and classifications. As a matter of 

 historical evolution, however, such systems and such points of 

 view belong to relatively recent and mature periods. Science 

 has grown without very much self-consciousness as to how it is 

 itself defined, or any great concern as to the distinction between 

 pure and applied science, or as to the boundaries between the 

 different sciences. Mathematics, for example, has had its roots in 

 the human need of exact statement as to both number and form in 

 all sorts of affairs, and on the other hand in the analytical faculties 

 of the human mind, which have shaped the development of the pure 

 science and given it in course of time its deductive stamp. 



The origin of a science can seldom be precisely determined, and 

 the more ancient the science the more difficult is the attainment 

 of such precision. The periods at which primitive men of different 

 races began to have conscious appreciation of the phenomena of 

 nature, of number, magnitude, and geometric form, can never be 

 known, nor the time at which their elementary notions began to 

 be so classified and associated as to deserve the name of science. 

 Very early in any civilization, however, mathematics must ob- 

 viously have taken its rise in simple processes of counting and 

 adding, of time measurement in primitive astronomy, of the geom- 

 etry and arithmetic involved in land measurement and in archi- 

 tectural design and construction. We can safely sketch certain 

 rough outlines of the prehistoric picture, and we can to some extent 



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