In practical teaching, the arts were divided into two groups: the trivium, comprising grammar, rhetoric, and dialectic (or logic); and the quadrivium, arithmetic, geometry, astronomy (astrology), and music. Geoffrey of St. Victor, in his _Fons philosophiae_, gives[555] an allegorical description of the arts as a spring which divides into two main streams, the trivium and quadrivium, that in turn separate into three and four lesser streams respectively. The teaching of practically all the natural science of the Middle Ages was included in the quadrivium. Geometry was generally expanded to include geography and quite naturally so in view of prevalent opinions regarding its origin. Adelard of Bath, in his _De eodem et diverso_, repeats an old story to the effect that in the early days men began to set up stones as boundaries.[556] Disputes about claims inevitably arose, in Libya because of sand, and in Egypt because the Nile often obliterated or destroyed the stones. This necessitated the invention of the science of geometry, or surveying, by the application of which the bounds might be replaced so that it would be “possible for all the centuries to have an everlasting rule for the measurement of land.”[557] Out of the invention of geometry, Adelard adds, arose subsequently the custom of subdividing territory into areas of various sizes.[558] Thus it happened that geometry had become closely allied in the classical and medieval mind with matters of geographical or topographical interest. Capella includes his long geographical discourse among chapters devoted to geometry and makes his symbolical figure of the latter science carry in one hand a compass and in the other a sphere to represent the terrestrial globe.[559] Alan of Lille, in the _Anticlaudianus_, describes Geometry as carrying a scale with which she measured the earth: “The maid carries a rod by which she encircles the entire earth.”[560] In the sculptured figures of the cathedrals Geometry is often depicted compass in hand.[561] GEOGRAPHY INCLUDED UNDER ASTROLOGY Geography was not always placed in a subordinate position to geometry in the quadrivium. In the _De divisione philosophiae_ of Dominicus Gondisalvi, which follows the Aristotelian rather than the Platonic division of knowledge, we find our science grouped under astrology. Of the latter art, Dominicus says,[562] there are three parts: the first is concerned with the number and shape of the heavenly bodies; the second with their movements; and the third with the earth, those regions that are inhabited and those that are not, the climates, and the varying influences exerted by the location of places and the revolutions of the universe over happenings on the earth’s surface.[563] GEOGRAPHY AND THE ARISTOTELIAN DIVISION OF LEARNING Both geometry and astrology belonged in the quadrivium. Where did the higher study of the arts of the quadrivium fall in the general classification of knowledge?