BEGINNINGS IN GREECE 41 



A simple numerical computation of late date in the Greek 

 alphabetic numerals and its modern equivalent are 



265 



a | e 265 



s a 40 000, 12 000, 1000 



MM t /3 ,a 



a 



M , ,7 X T 12 000, 3 600, 300 



,a T jge 1 OOP, 300, 25 



70 225 

 M a- K e 



Gow. 



Division was an exceedingly laborious process of repeated sub- 

 traction. 



Probably nothing in the modern world would have more aston- 

 ished a Greek mathematician than to learn that, under the influence 

 of compulsory education, the whole population of Western Europe, 

 from the highest to the lowest, could perform the operation of division 

 for the largest numbers. Whitehead. 



Approximate square roots were found by the later Greeks. 

 Theon in the fourth century A.D. for example gives the following 

 rule : 



When we seek a square-root, we take first the root of the nearest 

 square-number. We then double this and divide with it the re- 

 mainder reduced to minutes and subtract the square of the quotient, 

 then we reduce the remainder to seconds and divide by twice the 

 degrees and minutes (of the whole quotient). We thus obtain nearly 

 the root of the quadratic. 



The reckoning board, or abacus, known in so many different 

 forms throughout the world, - - came into very early use, but 

 actual evidence in regard to its form is meagre. A sharp dis- 

 tinction was made between the art of calculation (logistica), and 

 the science of numbers (arithmetical . The former was deemed 

 unworthy the attention of philosophers, and to their attitude may 

 be fairly attributed the fact that Greek mathematics was always 



