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ARITHMETIC AND ASTRONOMY. 355.
would restore him quickly and safely again. “Do not,” says the highminded khalif, “let diversity of religion or of country cause you to refuse my request. Do what friendship would concede to a friend. In return, I offer you a hundred weight of gold, a perpetual alliance and peace.” True to the instincts of his race and the traditions of his city, the Byzantine sourly and insolently refused the request, saying that “the learning which had illustrated the Roman name should never be imparted to a barbarian.” From the Hindus the Arabs learned arithmetic, especially that valuable invention termed by us the Arabic numerals, but honorably ascribed by them to its proper source, under the designation of “Indian numerals.” They also entitled their treatises on the subject “Systems of Indian Arithmetic.” This admirable notation by nine digits and cipher occasioned a complete revolution in arithmetical computations. As in the case of so many other things, the Arab impress is upon it; our word cipher, and its derivatives, ciphering, etc., recall the Arabic word tsaphara or ciphra, the name for the 0, and meaning that which is blank or void. Mohammed Ben Musa, said to be the earliest of the Saracen authors on algebra, and who made the great improvement of substituting sines for chords in trigonometry, wrote also on this Indian system. He lived at the end of the ninth century; before the end of the tenth it was in common use among the African and Spanish mathematicians. Ebn Junis, A.D. 1008, used it in his astronomical works. From Spain it passed into Italy, its singular advantage in commercial computation causing it to be eagerly adopted in the great trading cities. We still use the word algorithm in reference to calculations. The study of algebra was intently cultivated among the Arabs, who gave it the name it bears. Ben Musa, just referred to, was the inventor of the common method of solving quadratic equations. In the application of mathematics to astronomy and physics they had been long distinguished. Almaimon had determined with considerable accuracy the obliquity of the ecliptic. His result, with those of some other Saracen astronomers, is as follows: A.D. 830. Almaimon. 230 3′ 52″ ” 879. Albategnius, at Aracte. 23.
35′ 00 ” 987. Aboul Wefa, at Bagdad. 23 35′ 00 ” 995. Aboul Rihau, with a quadrant of 25 feet radius. 23.
35′ 00 ” 1080. Arzachael. 23 34′ 00 Almaimon had also ascertained the size of the earth from the measurement of a degree on the shore of the Red Sea-an operation implying true ideas of its form, and in singular contrast with the doctrine of Constantinople and Rome. While the latter was asserting, in all its absurdity, the flatness of the earth, the Spanish Moors were teaching geography in their common schools from globes. In Africa, there was still pre.
356 ASTRONOMICAL DISCOVERIES.
served, with almost religious reverence, in the library at Cairo, one of brass, reputed to have belonged to the great astronomer Ptolemy. Al Idrisi made one of silver for Roger II., of Sicily; and Gerbert used one which he had brought from Cordova in the school he established at Rheims. It cost a struggle of several centuries, illustrated by some martyrdoms, before the dictum of Lactantius and Augustine could be overthrown. Among problems of interest that were solved may be mentioned the determination of the length of the year by Albategnius and Thebit Ben Corrah; and increased accuracy was given to the correction of astronomical observations by Alhazen’s great discovery of atmospheric refraction. Among the astronomers, some composed tables; some wrote on the measure of time; some on the improvement of clocks, for which purpose they were the first to apply the pendulum; some on instruments, as the astrolabe. The introduction of astronomy into Christian Europe has been attributed to the translation of the works of Mohammed Fargani. In Europe, also, the Arabs were the first to build observatories; the Giralda, or tower of Seville, was erected under the superintendence of Geber, the mathematician, A.D. 1196, for that purpose. Its fate was not a little characteristic. After the expulsion of the Moors it was turned into a belfry, the Spaniards not knowing what else to do with it. I have to deplore the systematic manner in which the literature of to Europe has contrived to put out of sight our scientific obligations to the Mohammedans. Surely they can not be much longer hidden. Injustice founded on religious rancor and national conceit can not be perpetuated forever. What should the modern astronomer say when, remembering the contemporary barbarism of Europe, he finds the Arab Abul Hassan speaking of tubes, to the extremities of which ocular and object diopters, perhaps sights, were attached, as used at Meragha? what when he reads of the attempts of Abderrahman Sufi at improving the photometry of the stars? Are the astronomical tables of Ebn Junis (A.D. 1008), called the Hakemite tables, or the Ilkanic tables of Nasser Eddin Tasi, constructed at the great observatory just mentioned, Meragha, near Tauris, A.D. 1259, or the measurement of time by pendulum oscillations, and the methods of correcting astronomical tables by systematic observations-are such things worthless indications of the mental state? The Arab has left his intellectual impress on Europe, as, before long, Christendom will have to confess; he has indelibly written it on the heavens, as any one may see who reads the names of the stars on a common celestial globe. Our obligations to the Spanish Moors in the arts of life are even more marked than in the higher branches of science, perhaps only because our ancestors were better prepared to take advantage of things connected with daily affairs. They set an example of skill-

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