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instructed women were secured. How different was all this from the state of things in Europe: the Christian peasant, fever-stricken or overtaken by accident, hied to the nearest saint-shrine and expected a miracle; the Spanish Moor relied on the prescription or lancet of his physician, or the bandage and knife of his surgeon.

khalifs.

In mathematics the Arabians acknowledged their indebtedness to two sources, Greek and Indian, but they greatly improved upon both. The Asiatic khalifs the Asiatic had made exertions to procure translations of Euclid, Apollonius, Archimedes, and other Greek geometers. Almaimon, in a letter to the Emperor Theophilus, expressed his desire to visit Constantinople if his public duties would have permitted. He requests of him to allow Leo the mathematician to come to Bagdad to impart to him a portion of his learning, pledging his word that he would restore him quickly and safely again. "Do not," says the high-minded 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."

Their great improvements in arithmetic.

From the Hindus the Arabs learned arithmetic, especially that valuable invention termed by us the Arabic numerals, but honourably 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 Their astroastronomy and physics they had been long dis- nomical distinguished. Almaimon had determined with considerable accuracy the obliquity of the ecliptic. His result, with those of some other Saracen astronomers, is as follows:

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23° 35' 52"

23° 35' 00

23° 35' 00

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23° 34' 00

Almaimon had also ascertained the size of the earth from the measurement of a degree on the shore of the Red Seaan 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 preserved, 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.

Europe tries to hide its

them.

I have to deplore the systematic manner in which the literature of Europe has contrived to put out of sight our scientific obligations to the Mohamobligations to medans. Surely they cannot be much longer hidden. Injustice founded on religious rancour and national conceit cannot be perpetuated for ever. 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

arts of life.

of science, perhaps only because our ancestors were better prepared to take advantage of things connected Improvewith daily affairs. They set an example of ments in the skilful agriculture, the practice of which was regulated by a code of laws. Not only did they attend to the cultivation of plants, introducing very many new ones, they likewise paid great attention to the breeding of cattle, especially the sheep and horse. To them we owe the introduction of the great products, rice, sugar, cotton, and also, as we have previously observed, nearly all the fine garden and orchard fruits, together with many less important plants, as spinach and saffron. To them Spain owes the culture of silk; they gave to Xeres and Malaga their celebrity for wine. They introduced the Egyptian system of irrigation by flood-gates, wheels, and pumps. They also promoted many important branches of industry; improved the manufacture of textile fabrics, earthenware, iron, steel; the Toledo sword-blades were everywhere prized for their temper. The Arabs, on their expulsion from Spain, carried the manufacture of a kind of leather, in which they were acknowledged to excel, to Morocco, from which country the leather itself has now taken its name. They also introduced inventions of a more ominous kind-gunpowder and artillery. The cannon they used appeared to have been made of wrought iron. But perhaps they more than compensated for these evil contrivances by the introduction of the mariner's compass.

The mention of the mariner's compass might lead us correctly to infer that the Spanish Arabs Their comwere interested in commercial pursuits, a con- merce. clusion to which we should also come when we consider the revenues of some of their khalifs. That of Abderrahman III. is stated at five and a half million sterling-a vast sum if considered by its modern equivalent, and far more than could possibly be raised by taxes on the produce of the soil. It probably exceeded the entire revenue of all the sovereigns of Christendom taken together. From Barcelona and other ports an immense trade with the Levant was maintained, but it was mainly in the hands of the Jews, who, from the first invasion of Spain by Musa, had ever been the firm allies and

collaborators of the Arabs. Together they had participated in the dangers of the invasion; together they had shared its boundless success; together they had held in irreverent derision, nay, even in contempt, the woman-worshippers and polytheistic savages beyond the Pyrenees-as they mirthfully called those whose long-delayed vengeance they were in the end to feel; together they were expelled. Against such Jews as lingered behind the hideous persecutions of the Inquisition were directed. But in the days of their prosperity they maintained a merchant marine of more than a thousand ships. They had factories and consuls on the Tanaïs. With Constantinople alone they maintained a great trade; it ramified from the Black Sea and East Mediterranean into the interior of Asia; it reached the ports of India and China, and extended along the African coast as far as Madagascar. Even in these commercial affairs the singular genius of the Jew and Arab shines forth. In the midst of the tenth century, when Europe was about in the same condition that Caffraria is now, enlightened Moors, like Abul Cassem, were writing treatises on the principles of trade and commerce. As on so many other occasions, on these affairs they have left their traces. The smallest weight they used in trade was the grain of barley, four of which were equal to one sweet pea, called in Arabic carat. We still use the grain as our unit of weight, and still speak of gold as being so many carats fine.

Such were the Khalifs of the West; such their splenObligations to dour, their luxury, their knowledge; such some the Khalifs of of the obligations we are under to themthe West. obligations which Christian Europe, with singular insincerity, has ever been fain to hide. The cry against the misbeliever has long outlived the Crusades. Considering the enchanting country over which they ruled, it was not without reason that they caused to be engraven on the public seal, "The servant of the Merciful rests contented in the decrees of God." What more, indeed, could Paradise give them? But, considering also the evil end of all this happiness and pomp, this learning, liberality, and wealth, we may well appreciate the solemn truth which these monarchs, in their day of pride and

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