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With the fall of Alexandria and the victory of Mohammed throughout the West, and a consequent decline in learning, supremacy in science passed to the East and centered round the caliphs of Bagdad in the seventh and eighth centuries. They were interested in astronomy only as a practical, and to them useful, science, in adjusting the complicated lunar calendar of the Mohammedans, in ascertaining the true direction of Mecca which every Mohammedan must know, and in the revival of astrology, to which the Greeks had not attached any particular significance.

Harun al-Rashid ordered the Almagest and many other Greek works translated, of which the modern world would otherwise no doubt never have heard, as the Greek originals are not extant.

Splendid observatories were built at Damascus and Bagdad, and fine instruments patterned after Greek models were continuously used in observing. The Arab astronomers, although they had no clocks, were nevertheless so fully impressed with the importance of time that they added extreme value to their observations of eclipses, for example, by setting down the altitudes of sun or stars at the same time. On very important occasions the records were certified on oath by a body of barristers and astronomers conjointly—a precedent which fortunately has never been followed.

About the middle of the ninth century, the Caliph Al-Mamun directed his astronomers to revise the Greek measures of the earth's dimensions, and they had less reverence for the Almagest than existed in later centuries: indeed, Tabit ben Korra invented and applied to the tables of the Almagest a theoretical fluctuation in the position of the ecliptic which he called "trepidation," which brought sad confusion into astronomical tables for many succeeding centuries.

Albategnius was another Arab prince whose record in astronomy in the ninth and tenth centuries was perhaps the best: the Ptolemaic values of the precession of the equinoxes and of the obliquity of the ecliptic were improved by new observations, and his excellence as mathematician enabled him to make permanent improvements in the astronomical application of trigonometry.

Abul Wefa was the last of the Bagdad astronomers in the latter half of the tenth century, and his great treatise on astronomy known as the Almagest is sometimes confused with Ptolemy's work. Following him was Ibn Yunos of Cairo, whose labors culminated in the famous Hakemite Tables, which became the standard in mathematical and astronomical computations for several centuries.

Mohammedan astronomy thrived, too, in Spain and northern Africa. Arzachel of Toledo published the Toledan Tables, and his pupils made improvements in instruments and the methods of calculation. The Giralda was built by the Moors in Seville in 1196, the first astronomical observatory on the continent of Europe; but within the next half century both Seville and Cordova became Christian again, and Arab astronomy was at an end.

Through many centuries, however, the science had been kept alive, even if no great original advances had been achieved; and Arab activities have modified our language very materially, adding many such words as almanac, zenith, and radii, and a wealth of star names, as Aldebaran, Rigel, Betelgeuse, Vega, and so on.

Meanwhile, other schools of astronomy had developed in the East, one at Meraga near the modern Persia, where Nassir Eddin, the astronomer of Hulagu Khan, grandson of the Mongol emperor Genghis Khan, built and used large and carefully constructed instruments, translated all the Greek treatises on astronomy, and published a laborious work known as the Ilkhanic Tables, based on the Hakemite Tables of Ibn Yunos.

More important still was the Tartar school of astronomy under Ulugh Beg, a grandson of Tamerlane, who built an observatory at Samarcand in 1420, published new tables of the planets, and made with his excellent instruments the observations for a new catalogue of stars, the first since Hipparchus, the star places being recorded with great precision.

The European astronomy of the Middle Ages amounted to very little besides translation from the Arabic authors into Latin, with commentaries. Astronomers under the patronage of Alfonso X of Leon and Castile published in 1252 the Alfonsine Tables, which superseded the Toledan tables and were accepted everywhere throughout Europe. Alfonso published also the "Libros del Saber," perhaps the first of all astronomical cyclopedias, in which is said to occur the earliest diagram representing a planetary orbit as an ellipse: Mercury's supposed path round the earth as a center.

Purbach of Vienna about the middle of the 15th century began his "Epitome of Astronomy" based on the "Almagest" of Ptolemy, which was finished by his collaborator Regiomontanus, who was an expert in mathematics and published a treatise on trigonometry with the first table of sines calculated for every minute from 0° to 90°, a most helpful contribution to theoretical astronomy.

Regiomontanus had a very picturesque career, finally taking up his residence in Nuremberg, where a wealthy citizen named Walther became his patron, pupil, and collaborator. The artisans of the city were set at work on astronomical instruments of the greatest accuracy, and the comet of 1472 was the first to be observed and studied in true scientific fashion. Regiomontanus was very progressive and the invention of the new art of printing gave him an opportunity to publish Purbach's treatise, which went through several editions and doubtless had much to do in promoting dissatisfaction with the ancient Ptolemaic system, and was thus most significant in preparing a background for the coming of the new Copernican order.

The Nuremberg presses popularized astronomy in other important ways, issuing almanacs, the first precursors of our astronomical Ephemerides. Regiomontanus was practical as well, and invented a new method of getting a ship's position at sea, with tables so accurate that they superseded all others in the great voyages of discovery, and it is probable that they were employed by Columbus in his discovery of the American continent. Regiomontanus had died several years earlier, in 1475 at Rome, where he had gone by invitation of the Pope to effect a reformation in the calendar. He was only forty, and his patron Walther kept on with excellent observations, the first probably to be corrected for the effect of atmospheric refraction, although its influence had been known since Ptolemy. The Nuremberg School lasted for nearly two centuries.

Nearly contemporary with Regiomontanus were Fracastoro and Peter Apian, whose original observations on comets are worthy of mention because they first noticed that the tails of these bodies always point away from the sun. Leonardo da Vinci was the first to give the true explanation of earth-shine on the moon, and similarly the moon-illumination of the earth; and this no doubt had great weight in disposing of the popular notion of an essential difference of nature between the earth and celestial bodies—all of which helped to prepare the way for Copernicus and the great revolution in astronomical thought.