HINDU, ARABIAN AND MOORISH SCIENCE 159 



in his first book, includes weights and measures, decimal numera- 

 tion, fundamental operations, addition etc., square and cube root, 

 fractions, equations of the first and second degrees, rule of three, 

 progressions, approximate value of TT, volumes. Applications are 

 made to interest, discount, partnership, and the time of filling 

 a cistern by several fountains. While there is reason to believe 

 that the decimal system was known as early as the time of Brahma- 

 gupta, this work contains the first systematic discussion of it, 

 including the so-called Arabic numerals and zero. 



As an intermediate stage between the earlier use of entire words 

 and our modern employment of single letters, he employs abbre- 

 viations, but multiplication, equality and inequality have still 

 to be written out. The divisor is written under the dividend 

 without a line, one member of an equation under the other with 

 verbal context to insure clearness. Polynomials are arranged in 

 powers, though without our exponents, coefficients follow the un- 

 known quantities. In his "rules of cipher" he even gives the 

 equivalent of a = a, O 2 = 0, V(j = 0, a -v- = oo. 



In comparison with Greek mathematics, power and freedom 

 are gained at the cost of some sacrifice of logical rigor. Among 

 the Greeks, only the greatest appreciated the possibility and the 

 importance of an unending series of numbers; but the Hindu 

 imagination tended naturally in this direction. A notable achieve- 

 ment of the Hindus was the introduction of the idea of negative 

 numbers and the illustration of positive and negative by assets 

 and debts, etc. 



On the whole, the Hindus, having received a part of their 

 mathematics originally from the Greeks, made great contributions 

 on the arithmetical and algebraic side, their influence on Euro- 

 pean science with which they had little or no direct contact being 

 exerted mainly through the Arabs. 



The Hindu mathematicians had no interest in what is termed 

 mathematical method. They gave no definitions; preserved little 

 logical order; they did not care whether the rules they used were 

 properly established or not and were generally indifferent to funda- 

 mental principles. They never exalted mathematics as a subject 



