After these references to the polite literature of the Arabs, it will be expected that they should have paid attention to the natural sciences. They were not, indeed, discoverers and inventors, but they considerably improved upon what they acquired in their extensive intercourse with other nations; and, as forming the link which unites ancient and modern letters, they are entitled to our respect and gratitude. We derive our mathematics from them; and to them, also, we owe much of our astronomical knowledge. Almamoun, by a liberal reward, sought to engage in his service a famous mathematician of Constantinople; and Ibn Korrah enriched the stores of his country in this department with translations of Archimedes and the conics of Apollonius. Some have said that, on the revival of European literature in the fifteenth century, mathematical science was found nearly in the state in which it had been left by Euclid; and the justly celebrated Brucker contends, that the Arabs made no progress whatever in this {258} most important branch of knowledge; later writers, however, and particularly Montucia, the author of the Histoire des Mathematiques, have done ample justice to their researches. Numerical characters, without which our study of the exact sciences were almost in vain, beyond all doubt came to us from the Arabs: not that they invented them--it is probable they were originally words, perhaps Hindu words, expressing the quantities they respectively represent, but abbreviated and brought to their present convenient form by the followers of the Prophet. Trigonometry and algebra are both indebted to their genius. The sines of the one of these sciences instead of the more ancient chord, and the representatives of quantities in the other, descend through the Arabs to us, if they did not at first invent them. Original works on spherical trigonometry are among the productions of Ibn Musa and Geber, the former of whom is accounted the inventor of the solution of equations of the second degree. The University of Leyden still retains a manuscript treatise on the algebra of cubic equations, by Omar ibn Ibrahim; and Casiri, who, preserved and classed 1851 manuscripts, even after a fire had destroyed the magnificent collection or the Escurial, informs us, that the principles and praises of algebraic science were sung in an elaborate poem by Alcassem, a native of Grenada. {259} These departments of knowledge were studied by the Arabs as early as the eighth and ninth centuries.