ods inherited from Rome. Algebra, with its rules for solving linear and quadratic equations, had been made accessible to the Latins. The geometry of Euclid, the Sphœrica of Theodosius, the astronomy of Ptolemy, and other works were now accessible in the Latin tongue. Thus a great amount of new scientific material had come into the hands of the Christians. The talent necessary to digest this heterogeneous mass of knowledge was not wanting. The figure of Leonardo of Pisa adorns the vestibule of the thirteenth century.
It is important to notice that no work either on mathematics or astronomy was translated directly from the Greek previous to the fifteenth century.
The First Awakening and its Sequel.
Thus far, France and the British Isles have been the headquarters of mathematics in Christian Europe. But at the beginning of the thirteenth century the talent and activity of one man was sufficient to assign the mathematical science a new home in Italy. This man was not a monk, like Bede, Alcuin, or Gerbert, but a merchant, who in the midst of business pursuits found time for scientific study. Leonardo of Pisa is the man to whom we owe the first renaissance of mathematics on Christian soil. He is also called Fibonacci, i.e. son of Bonaccio. His father was secretary at one of the numerous factories erected on the south and east coast of the Mediterranean by the enterprising merchants of Pisa. He made Leonardo, when a boy, learn the use of the abacus. The boy acquired a strong taste for mathematics, and, in later years, during his extensive business travels in Egypt, Syria, Greece, and Sicily, collected from the various peoples all the knowledge he could get on this subject. Of all the methods of calculation, he found the Hindoo to be unquestionably the
