CHAP. II. Geometry of the Arabs. AMONG the arabs are reckoned many skilful geometricians. Their first care was to translate the elementary works of the greeks, such as the Elements of Euclid, the Treatise on the Sphere and Cylinder by Archimedes, the Spherics of Theodosius, the Treatise on Spherical Triangles by Menelaus, &c. Soon after they rose to the higher geometry, or that of the ancient curves; Apollonius's doctrine of conic sections became familiar to them; and the fifth, sixth, and seventh books of his work on this subject have reached us only in an arabic version. By degrees their knowledge extended to statics and hydrostatics, and through their means we have received the work of Archimedes on Bodies floating on a Fluid. Practical geometry and astronomy owe the arabs eternal gratitude, for having given to trigonometrical calculation the simple and commodious form, which it has at present. They reduced the theory of the resolution of triangles, both rectilinear and spherical, to a small number of easy propositions; and by the substitution of sines, which they introduced instead of the chords of double arcs employed before, they made abridgments in calculations, of inestimable value to those who had a great number of triangles to resolve. These discoveries are ascribed chiefly to a geome a geometrician and astronomer of the name of Mohammed Ben Musa, the author of a work still extant, entitled Of Plane and Spherical Figures; and to another geometrician and astronomer much better known, Geber Ben Aphla, who lived in the eleventh century, and of whom we have a commentary on Ptolemy. On geodesia, or the art of surveying, we have an elegant work by Mohammed of Bagdat, which some authors have ascribed to Euclid, without assigning any reason for it. CHAP CHAP. III. Astronomy of the Arabs. Of all the mathematical sciences astronomy is that, which the arabs have most cultivated, and in which they have made the most remarkable discoveries. A great number of their khalifs themselves were excellent astronomers. Nothing could equal the magnifi cence of the observatories and instruments, which they caused to be constructed, to promote the progress of this science, which has more need than any other of the patronage of monarchs. I shall here mention only the principal arabian astronomers; and among them I shall particularly notice the khalifs, who have merited this distinction; because those exemplary princes, who add to the glory of governing well that of enlightening the men they govern, have a peculiar claim to the respect, admiration, and gratitude of posterity. The arabs regulated time by the motion of the Moon. Their months were of twenty nine and thirty days alternately, which gave 354 days for the duration of the lunar year. But as the synodical month, or the duration of each lunar revolution with respect to the Sun, consists of 29 days, 12 hours, 44 minutes, 3 seconds; the term of the arabian lunar year was 8 hours, 48 minutes, 36 seconds, less than the true length of twelve lunar revolutions with respect to the Sun. Sun. Accordingly, to remedy this difference, which left the Moon behind the Sun, in their course from West to East, and to make the positions of these two heavenly bodies coincide, a day was occasionally added to this period of 354. Among the different branches of astronomy, the theory of the Sun first drew the attention of the arabs, and occupied them for a long time. They quickly remarked, that Ptolemy had found or supposed the obliquity of the ecliptic a little too great. Flamsteed, in his Historia celestis, records the progress of their labours on this subject. We see them continually approaching the truth; and at length, at the end of about seven hundred years, they determined the obliquity of the ecliptic with nearly the same precision, as it is now given by the best modern observations; a result so much the more singular, as they had not, like us, the assistance of telescopes. The khalif Abou Giafar, surnamed Almansor, or the victorious, who ascended the throne in 754, and died in 775, ranks among the first of the arabian astronomers. This studious and philosophical prince had a taste for all the sciences, but particularly for astronomy, on which he bestowed every moment, that his indispensable duties left at his disposal. His reign is the epoch, at which the whole circle of the sciences received an impulse, that continued to increase among the arabs for several centuries. Almost all the successors of Almansor thirsted like him after knowledge. His grandson Haroun, sur*named Al Rashid, who reigned from 786 to 809, cul tivated tivated astronomy and mechanics. On occasion of a solemn embassy, which the great fame of Charlemagne, king of France, drew from him in 799, he sent this monarch as a present a clepsydra, or waterclock, of a very ingenious construction. In the dial were twelve small doors, forming the divisions of the hours; and each of these doors opened in succession at the hour it marked, and let out little balls, which, falling on a brazen bell, struck the hour. The doors continued open till twelve o'clock, when twelve little knights, mounted on horseback, came out together, paraded round the dial, and shut all the doors. This machine astonished all Europe, when men's minds were employed chiefly on futile questions of theology or grammar. Haroun had two sons, who reigned in succession after him. The second, named Al Maimon, who held the sceptre from 813 to 833, was taught the sciences by Musva, a christian physician; and neglected neither gifts, exhortations, nor example, to induce his subjects to pursue them with ardour. He caused all the writings of the greeks he could procure to be translated, and in particular Ptolemy's Almagest. Some authors even assert, that in a treaty of peace with Michael 111, when he made his own terms with the emperor, he demanded several greek manuscripts, which were in the imperial library at Constantinople. He also made observations himself, and directed the making of others, for which affairs of state did not allow him time; as for instance those at Bagdat and Damascus, undertaken by his command, to ascertain the obliquity of the ecliptic, which was |