Page:The Outline of History Vol 2.djvu/57

 At Cordoba in particular there were great numbers of Christian students, and the influence of Arab philosophy coming by way of Spain upon the universities of Paris, Oxford, and North Italy and upon Western European thought generally, was very considerable indeed. The name of Averroes (Ibn-rushd) of Cordoba (1126-1198), stands out as that of the culminating influence of Arab philosophy upon European thought. He developed the teachings of Aristotle upon lines that made a sharp division between religious and scientific truth, and so prepared the way for the liberation of scientific research from the theological dogmatism that restrained it both under Christianity and under Islam. Another great name is that of Avicenna (Ibnsinā), the Prince of Physicians (980-1037), who was born at the other end of the Arabic world at Bokhara, and who travelled in Khorasan.... The book-copying industry flourished at Alexandria, Damascus, Cairo, and Bagdad, and about the year 970 there were twenty-seven free schools open in Cordoba for the education of the poor.

"In mathematics," say Thatcher and Schwill, "the Arabs built on the foundations of the Greek mathematicians. The origin of the so-called Arabic numerals is obscure. Under Theodoric the Great, Boethius made use of certain signs which were in part very like the nine digits which we now use. One of the pupils of Gerbert also used signs which were still more like ours, but the zero was unknown till the twelfth century, when it was invented by an Arab mathematician named Muhammad-Ibn-Musa, who also was the first to use the decimal notation, and who gave the digits the value of position. In geometry the Arabs did not add much to Euclid, but algebra is practically their creation; also they developed spherical trigonometry, inventing the sine, tangent, and cotangent. In physics they invented the pendulum, and produced work on optics. They made progress in the science of astronomy. They built several observatories, and constructed many astronomical instruments which are still in use. They calculated the angle of the ecliptic and the precession of the equinoxes. Their knowledge of astronomy was undoubtedly considerable.

"In medicine they made great advances over the work of the