"After having established that the highest degree of science consists in giving rise to phenomena oneself and at will, the celebrated scientist Humboldt adds: "The Arabs reached to this height, which was almost unknown to the ancients." "The study of mathematics enjoyed overspread favour among the Arabs, and the progress accomplished in algebra metamorphosed that science to such an extent that its invention has been attributed to them. To them also are due the first application of algebra to geometry, and the introduction of tangents into trigonometry. "Astronomy was passionately studied in their schools of Bagdad, Damascus, Samarcand, Cairo, Fez, Toledo, Cordova, etc., and their discoveries may be summed up in the following enumeration: introduction of tangents into astronomical calculation; construction of tables of planetary movement; strict determination of the obliquity of the ecliptic and of its gradual diminution; exact estimation of the procession of the equinoxes; and the first precise determination of the year's duration. To them also we owe the ascertainment of the irregularities of the greatest latitude of the moon, and the discovery of the third lunar inequality, now called variation. "In geography, the contribution of these bold travellers is most remarkable from a scientific viewpoint. They made those exact astronomical determinations which form the first foundation of cartography, and rectified the enormous errors of position committed by the Greeks. "From the standpoint of exploration, they published accounts of travel which caused different parts of the world, scarcely suspected before them, to be known, and where no European had ever set foot. The sources of the Nile, running through the great equatorial lakes, are exactly set out on a map by Al-Idrisi, dating from the year 1160, and which were only discovered by Europeans during the second half of the nineteenth century. "In physical sciences, the sum total of their discoveries is still more considerable. The following enumeration proves their importance: high attainment of knowledge in theoretical physics, especially in optics and in the creation of the most ingenious mechanical apparatus; discovery of the most fundamental bodies of chemistry, such as alcohol, nitric acid, sulphuric acid; and the most essential operation, such as distillation; application of chemistry to pharmacy and commerce, especially as regards the extraction of metals, the manufacturing of paper from rags, which they caused to take the place of parchment, papyrus, or Chinese silk-paper. "They were probably the first to use the compass in navigation; at any rate, they certainly introduced this fundamental invention to Europe.