386 THE HISTORY OF MEDIEVAL EUROPE logians and gave a further impetus to their science, although, inasmuch as Aristotle believed neither in the creation of the world nor the immortality of the soul, they experienced some difficulty in reconciling all his utterances with their Bibles. But most of such difficulties had been smoothed away by Albertus and Thomas. Albertus and Aquinas also wrote many theological works, and the latter is generally regarded by Roman Catholics as their greatest medieval theologian. Both men were indefatigable writers and the col- lected works of either to-day fill about forty portly volumes. In natural science, too, further progress was made in the thirteenth century with the translation of Aristotle's books Natural of natural philosophy and of numerous other science in Greek and Arabian scientists. In some branches the thir- . t , teenth of science, moreover, an advance was made be- •century yond the knowledge of previous ages. In phys- ical science this was true in optics and dynamics. A branch of mathematics with an Arabian name, algebra, now be- gan to develop in addition to the older subjects of arith- metic and geometry. Early in the century Leonardo of Pisa introduced into western Europe the so-called Arabic numerals, which were really derived from the Hindus by the Arabs. As we have said before, this was probably the greatest improvement in writing made since the invention of the phonetic alphabet, for the new figures could be written in much less time than could the clumsy Roman numerals and were far handier in written reckoning than any previous system. In astronomy new tables of the movements of the heavenly bodies were drawn up under the direction of Alfonso the Wise of Castile, and the need of further re- forming the calendar was generally recognized. Many new facts were collected from personal experience and observa- tion concerning animals, plants, and countries which were either unmentioned at all or incorrectly described in those works which had come down from antiquity. Such inno- vations were partly the work of the Arabs and of the Ori- ental learning from which they drew, but were also in part the work of the Latins themselves. A
