To illustrate the reasoning as to geometrical forms which preceded the finding of Euclid we quote from Maurus, who says that the science of geometry "found realization also at the building of the tabernacle and the temple; and that the same measuring rod, circles, spheres, hemispheres, quadrangles, and other figures were employed. The knowledge of all this brings to him, who is occupied with it, no small gain for his spiritual culture." (R. 74 e). After Gerbert's time some geometry proper and the elements of land surveying were introduced. The real study of geometry in Europe, however, dates from the twelfth century, when Euclid was translated into Latin from the Arabic. 6. ASTRONOMY. In astronomy the chief purpose of the instruction was to explain the seasons and the motions of the planets, to set forth the wonders of the visible creation, and to enable the priests "to fix the time of Easter and all other festivals and holy days, and to announce to the congregation the proper celebration of them." (R. 74 g). [Illustration: FIG. 46. AN ANGLO-SAXON MAP OF THE WORLD (From a tenth-century map in the British Museum) This is one of the better maps of the period. Note the mixture of Biblical and classical geography (Bethlehem, Jerusalem, Pillars of Hercules), and the animal life (lion) introduced in the upper corner. The Mediterranean Sea in the center, the Greek islands, the British isles, the Italian peninsula, the Nile, and the northern African coast are easily recognized. Western Europe, the best-known part of the world at that time, is very poorly done.] Even after Ptolemy's _Mechanism of the Heavens_ (p. 49) and Aristotle's _On the Heavens_ had filtered across the Pyrenees from the Saracens, in the eleventh century, the Ptolemaic theory of a flat earth located at the center of the heavenly bodies and around which they all revolved, while a very pleasing theological conception, was absolutely fatal to any instruction in astronomy worth while and to any astronomical advance. All mediaeval astronomy, too, was saturated with astrology, as the selection on the motion of the heavenly bodies reproduced from Bartholomew Anglicus shows (R. 77 b), and the supernatural was invoked to explain such phenomena as meteors, comets, and eclipses. The Copernican theory of the motion of the heavenly bodies was not published until 1543, and all our modern ideas date from that time. Physics was often taught as a part of the instruction in astronomy, and consisted of lessons on the properties of matter (R. 77 a) and some of the simple principles of dynamics. Little else of what we to-day know as physics was then known.