46 SCIENCE OF THE MIDDLE AGES. FT. II. 



making it 365 days, 5 hours, 46 minutes, 24 seconds, which 

 was only two minutes shorter than it really is, and he cor- 

 rected many more of Ptolemy's observations. After him 

 the next famous Arabian astronomer was Ebn Junis, 

 A.D. 1008, who drew up several valuable astronomical 

 tables. 



Ben Musa, 900. Of mathematicians, one of the most 

 celebrated was Mohammed Ben Musa, who lived about 

 A.D. 900. He is the earliest Arabian writer on algebra, 

 or the working of sums by means of letters. This name 

 ' Algebra ' is an Arabian word, and the Arabs were very 

 clever at this way of making calculations. Ben Musa is 

 the first writer we know of who used the Indian numerals 

 i, 2, 3, 4, 5, 6, 7, 8, 9, o, instead of the clumsy Roman nu- 

 merals I, II, III, IV, &c. If you try to do a sum with the 

 Roman numerals you will see what a troublesome business 

 it is and what a great gain the Indian numerals are. The 

 Arabs learned these numbers from the Hindoos, and always 

 used them after the time of Ben Musa, so that they are now 

 generally called the Arabic numerals. About the year 1000. 

 a Frenchman named Gerbert, Archbishop of Rheims, and 

 afterwards Pope Sylvester the Second, who had been edu- 

 cated at the famous Arabian University of Cordova in 

 Spain, introduced them into Europe. The word cipher, 

 which we use for o, comes from an Arabic word, ciphra, 

 meaning empty or void. 



Alhazen's discoveries in Optics, 1000. Another Arabian 

 whom we must specially mention was an astronomer and 

 mathematician named Alhazen, who was born at Bassora, in 

 Asiatic Turkey, about the year A.D. 1000, but who spent 

 most of his life in Spain. He made discoveries chiefly in 

 optics i or the science of sight. He was the first to teach that 



