HINDU, ARABIAN AND MOORISH SCIENCE 157 



through Italy from Constantinople. Before following the direct 

 Latin-Italian line a brief sketch of Hindu and Arabic science is 

 desirable. 



HINDU MATHEMATICS. The far-reaching conquests of Alex- 

 ander the Great (330 B.C.) immensely stimulated communica- 

 tion of ideas between the Mediterranean world and Asia, and the 

 East was able to make certain great contributions to mathematical 

 science just where the Greeks were relatively weakest, namely 

 in arithmetic and the rudiments of algebra and trigonometry. 

 Several centuries before our era the Pythagorean theorem and an 

 excellent approximation for ^2 were known in India in connection 

 with the rules for the construction of altars. The mathematicians 

 however from whom we trace the later development of mathematics 

 date from the sixth and following centuries. 



About 530 A.D. Arya-bhata wrote a book in four parts dealing 

 with astronomy and the elements of spherical trigonometry, and 

 enunciating numerous rules of arithmetic, algebra and plane trigo- 

 nometry. He gives the sums of the series 



1 + 2 + ... +n 



1 2 + 2 2 + ... + n 2 



1 3 + 2 3 + ... + n*, 



solves quadratic equations, gives a table of sines of successive mul- 

 tiples of 3f i.e. twenty-fourths of a right angle, and even 

 uses the value TT = 3.1416, correct to five places. His geometry 

 is in general inferior. 



Some years later, Brahmagupta composed a system of as- 

 tronomy in verse, with two chapters on mathematics. In this 

 he discusses arithmetical progression, quadratic equations, areas 

 of triangles, quadrilaterals and circles, volume and surface of 

 pyramids and cones. His value of T is *10 = 3.16 -K Typical 

 problems and discussions are the following : 



Two apes lived at the top of a cliff of height 100, whose base was 

 distant 200 from a neighboring village. One descended the cliff, and 

 walked to the village, the other flew up a height x and then flew in a 



