A work on Arithmetic or Algebra. Euclid, with a thirteenth century commentary. The “Theorica Planetarum,” which was either a free translation of Ptolemy’s _Almagest_ or an exposition of its principles. The Alfonsine Tables. The Canons of De Lignières (of Amiens, 1330 A.D.), _i.e._ rules for the use of astronomical tables to determine the motions of the heavenly bodies. Portions of the Canon of Avicenna (the Arab philosopher). A treatise on the Astrolabe by a Jewish astrologer of the ninth century. A treatise on the Quadrant. The astrological works of Ptolemy, with a commentary. A book by Alchabicius (fl. _c._ 850 A.D.), probably his work on astrology. A book on astrological medicine. [Sidenote: Alfonso X. 1223-1284.] From the above we gather that a past master in Astrology would understand the elements of mathematics, and all the astronomy that Ptolemy’s translator or commentator could teach; that he had learned—at least in theory—the use of astronomical instruments and tables, and a good deal of astrology, including its use in medical practice. The tables were intended mainly for astrological predictions. The standard Alfonsine Tables had been drawn up in 1252 by Christians, Jews, and Moors, under the direction of Alfonso X. king of Castile. They contained lists of positions of the planets, dates of Easter moons, “golden numbers” and “dominical letters” of the ecclesiastical calendar, times and other details of eclipses, together with methods for finding the places of planets, and for casting horoscopes. This is the Alfonso who was so much shocked at the complexity of Ptolemy’s multitudinous circles that “the ointment of his name is marred,” says Fuller, “with the dead fly of his atheisticall speech”: “If only the Creator had consulted me, when He made the world, I would have given some good advice!” [Sidenote: Sylvester II. (Gerbert) Pope, 999-1003.] Not one of all these books pretended to add any new discovery to astronomy: all intellectual energy was absorbed in eagerly assimilating the knowledge stored by Greeks and Arabs. Nor were any great observatories founded in Europe yet, in imitation of Alexandria, Rhodes, or Baghdad. The instruments in use were celestial globes and small portable astrolabes and quadrants for determining positions and angular distances between the heavenly bodies. The learned pope, Sylvester II., who had studied astronomy among the Moors in Spain, was so skilful in making astrolabes that some accused him of gaining the art by selling his soul to the devil! [Sidenote: Albertus Magnus 1193-1280.] [Sidenote: Aquinas 1225-1274.]