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MODERN MATHEMATICS ALGEBRA 23 

Europe. The Arab mathematical text-books and the Greek 
books from Arab translation were introduced into Western 
Europe by the Moors in the period 1150-1450, and by the 
end of the thirteenth century the Arabic arithmetic had been 
fairly introduced into Europe, and was practised by the side 
of the older arithmetic which was founded on the work of 
Bjethius (about 475-526). Then came the Renascence. 
Mathematicians had barely assimilated the knowledge obtained 
from the Arabs, including their translations of Greek writers, 
when the refugees who escaped from Constantinople after the 
fall of the Eastern Empire (1453) brought the original works 
and the traditions of Greek science into Italy. Thus by the 
middle of the fifteenth century the chief results of Greek and 
Arabian mathematics were accessible to European students. 

The invention of printing about that time rendered the 
dissemination of discoveries comparatively easy. 



CHAPTER II 

THE RISE AND PROGRESS OP MODERN MATHEMATICS 
ALGEBRA 

MODERN mathematics may be considered to have begun 
approximately with the seventeenth century. It is well 
known that the first 1500 years of the Christian era produced, 
in Western Europe at least, very little knowledge of value in 
science. The spirit of the Western Europeans showed itself to 
be different from that of the ancient Greeks, and only slightly 
less so from that of the more Easterly nations ; and, when 
Western mathematics began to grow, we can trace clearly the 
historical beginnings of the use, in a not quite accurate form, 
of those conceptions variable and function which are 
characteristic of modern mathematics. We may say, in 
anticipation, that these conceptions, thoroughly analysed by 
reasoning as they are now, make up the difference of our 
modern views of Mathematics from, and have caused the 
likeness of them to, those of the ancient Greeks. The Greeks, 
seem, in short, to have taken up a very similar position 
towards the mathematics of their day to that which logic forces 
us to take up towards the far more general mathematics of to-day.