178 A SHORT HISTORY OF SCIENCE 



itself with expounding, analysing and debating the new treasures 

 unfolded before its eyes. . . . 



And of the scientific side of this revival Italy was the centre. 

 This branch of the movement began, indeed, before the twelfth 

 century. It was in Italy that the Latin world first came into con- 

 tact with the half-forgotten treasures of Greek wisdom, with the 

 wisdom which the Arabs had borrowed from the Greeks and with 

 original products of the remoter East. Of the Medical School of Sa- 

 lerno we have already spoken. It was probably in Italy and through 

 the Arabic that the Englishman Adelard of Bath translated Euclid 

 into Latin during the first half of the eleventh century. At about 

 the same time modern musical notation originated with the discoveries 

 of the Camaldulensian monk, Guido of Arezzo. In the first years of 

 the following century the Algebra and the Arithmetic which the 

 Arabs had borrowed from the Hindus were introduced into Italy 

 by the Pisan merchant, Leonardo Fibonacci. ... It was to this 

 Arabo-Greek influence that Bologna owed its very important School 

 of Medicine and Mathematics two subjects more closely connected 

 then than now through their common relationship to Astrology. 



Rashdall. 



MATHEMATICAL SCIENCE IN THE THIRTEENTH CENTURY. 

 Increasing activity in mathematical science was due largely to 

 Leonardo Pisano of Italy, Jordanus Nemorarius of Saxony, and 

 Roger Bacon of England. 



Leonardo Pisano or Fibonacci (born 1175) was educated in 

 Barbary, where his father was in charge of the custom-house, and 

 thus became familiar with Alkarismi's algebra, and the Arabic 

 decimal system. He appreciated their advantages and on his 

 return to Italy published in his Liber Abaci an account which 

 gave them currency in Europe " in order that the Latin race 

 might no longer be deficient in that knowledge." As the mathe- 

 matical masterpiece of the Middle Ages, it remained a standard 

 for more than two centuries. His algebra is rhetorical, but gains 

 by the employment of geometrical methods. He discusses the 

 fundamental operations with whole numbers and fractions, using 

 the present line for division. Fractions are decomposed into parts 

 with unit numerators as in early Egypt. Through the Arabs 



