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] with their s and s, and with their aid it is possible to reconstruct the maps. These maps existed, as a matter of course, before such an index could be compiled, but it is doubtful whether the maps in our available manuscript, which are attributed to Agathodaemon, are copies of Ptolemy’s originals or have been compiled, after their loss, from this index. Book VIII. gives further details with reference to the principal s of each map, as to geographical position, length of day, climata, &c.

’s great merit consists in having accepted the views of with respect to a projection suited for a map of the world. Of the two projections proposed by him one is a modified conical projection with curved parallels and straight s; in the second projection (see fig. 3) both parallels and s are curved. The correct relations in the length of degrees of and  are maintained in the first case along the  of  and the equator, in the second along the parallel of Agisymba, the equator and the parallels of, Syene and Thule. Following he divided the equator into 360° drawing his prime  through the Fortunate Islands (Canaries). The 26 special maps are drawn on a rectangular projection. As a map compiler does not take a high rank. In the main he copied whose work he revised and supplemented in some points, but he failed to realize the peninsular shape of, erroneously exaggerated the size of  , and suggested that the  had no connexion with the western ocean, but formed Mare Clausum. knew but of a few s which had been determined by actual observation, while of three s resulting from simultaneous observation of eclipses he unfortunately accepted the least satisfactory, namely, that which placed 45° to the east of, while the actual  distance only amounts to 34°. An even graver source of error was ’s acceptance of a degree of 500 instead of 700. The extent to which the more correct proportion would have affected the delineation of the is illustrated by fig. 4. But in spite of his errors the scientific method pursued by was correct, and though he was neglected by the Romans and during the, once he had become known, in the 15th century, he became the teacher of the modern world.

Map-Making among the Romans.—We learn from, , , , and others, that the Romans had both general and topographical maps. Thus, (De rustici) mentions a map of  engraved on, in the temple of , Pliny, a map of the seat of war in Armenia, of the time of the emperor Nero, and the more famous map of the Roman Empire which was ordered to be prepared for Julius Caesar (44 ), but only completed in the reign of , who placed a copy of it, engraved in marble, in the Porticus of his sister Octavia (7 ). , the son-in-law of Augustus (d. 12 ), who superintended the completion of this famous map, also wrote a commentary illustrating it, quotations from which of Ammianus Marcellinus of (d. 330),  and others, afford the only means of judging of its character. The map is supposed to be based upon actual surveys or rather reconnaissances, and if it be borne in mind that the Roman Empire at that time was traversed in all directions by roads furnished with mile-stones, that the Agrimensores employed upon such a duty were skilled surveyors, and that the official reports of the commanders of military expeditions and of provincial governors were available, this map, as well as the provincial maps upon which it was based, must have been a work of superior excellence, the loss of which is much to be regretted. A copy of it may possibly have been utilized by and  in their compilations. The Romans have been reproached for having neglected the scientific methods of map-making advocated by. Their maps, however, seem to have met the practical requirements of political administration and of military undertakings.

Only two specimens of Roman cartography have come down to us, viz. parts of a plan of, of the time of the emperor ( 193–211), now in the Museo Capitolino, and an itinerarium scriptum, or road map of the world, compressed within a strip 745 mm. in length and 34 mm. broad. Of its character the reduced copy of one of its 12 sections (fig. 5) conveys an idea. The map, apparently of the 3rd century, was copied by a at, in 1265, who fortunately contented himself with adding a few scriptural names, and having been acquired by the learned Conrad Peutinger of Augsburg it became known as Tabula peutingeriana. The original is now in the  of.

Map-Making in the Middle Ages.—In scientific matters the early middle ages were marked by stagnation and retrogression. The fathers of the church did not encourage scientific pursuits, which Lactantius (4th century) declared to be unprofitable. The doctrine of the sphericity of the earth was still held by the more learned, but the heads of the church held it to be unscriptural. Pope Zachary, when in 741 he condemned the views of Virgilius, the learned bishop of, an who had been denounced as a  by , declares it to be perversa et iniqua doctrina. Even after Gerbert of Aurillac, better known as Pope Sylvester II. (999–1063), Adam of Bremen (1075), Albertus Magnus (d. 1286), Roger Bacon (d. 1294), and indeed all men of leading had accepted as a fact and not a mere hypothesis the geocentric system of the universe and sphericity of the globe, the authors of maps of the world, nearly all of whom were monks, still looked in the main to the Holy Scriptures for guidance in outlining the inhabited world. We have to deal thus with three types of these early maps, viz. an oblong rectangular, a circular and an oval type, the latter being either a compromise between the two former, or an artistic development of the circular type. In every instance the inhabited world is surrounded by the ocean. The authors of rectangular maps look upon the Tabernacle as an image of the world at large, and believe that such expressions as the “four corners of the earth” (Isa. x. 12), could be reconciled only with a rectangular world. On the other hand there was the expression “circuit of the earth” (Isa. xl. 22), and the statement (Ezek. v. 5) that “God had set Jerusalem in the midst of the nations and countries.” In