ARAB CIVILISATION IN SPAIN 3s by a higher mind. While Europe fell to the level of her conquerors, Arabian civilisation rose, and, spreading through Africa to Spain, it maintained for the Western world the moral ideals and the intellectual enlightenment which, without the refuge afforded them in Spain, had perhaps been wholly lost.

Medieval Arabian achievements in the higher paths of learning are well known. There is no branch of scientific development among the Western nations upon which the Arabs have not set their mark, either by original research, or by the service which they rendered in transmitting to their European posterity the learning accumulated by other generations in other lands. They initiated the Renaissance in Europe by preserving and translating at a much earlier period the great works of the Greeks. They gave a vivifying impulse to all the intellectual life of the West by introducing to it the hoarded knowledge of the East. In mathematics they imported much from India, amongst other things the numerals known to us as "Arabic" numerals, and with them the advantages of the decimal system. The word cypher, with all its derivations, is an Arabic word. They translated from the Greek Euclid and the earlier geometers ; but it was to the original studies of an Arab geometer — Ben Musa — of the ninth century, that Europe owed its use of the improved science to which the Arabs gave its modern name of algebra. Ben Musa was the inventor of the common method of solving quadratic equations, as well as of the substitution of sines for chords in trigonometry. His system was the system commonly adopted by the Arab schools. The Arabs were ardent students of mathematics, and a long list of astronomers and physicists, from Al Maimon, who determined the obliquity of the ecliptic in 830 ; through Ebn Junis, who constructed the Hakemite tables of the stars in 1008 ; Avicenna, the well-known physician and philosopher, who wrote, amongst other things, in the early part of the eleventh century, an encyclopaedia of human knowledge in twenty volumes ;