Gerbert's form for expressing numbers may be shown from the following simple sum in addition:
_Arabic Form_ _Roman Form_ _Gerbert's Form_ _M C X I_
1204 MCCIV I II IV 538 DXXXVIII V III VIII 2455 MMCCCCLV II IV V V 619 DCXIX VI I IX ----- --------- ------------------- 4816 MMMMDCCCXVI IV VIII I VI
No study of arithmetic of importance was possible, however, until the introduction of Arabic notation and the use of the zero.
5. GEOMETRY. This study consisted almost entirely of geography and reasoning as to geometrical forms until the tenth century, when Boethius' work on _Geometry_, containing some extracts from Euclid, was discovered by Gerbert. The geography of Europe, Asia, and Africa also was studied, as treated in the textbooks of the time, and a little about plants and animals as well was introduced. The nature of the geographic instruction may be inferred from Figure 46, which reproduces one of the best world maps of the day. The main geographical features of the known world can be made out from this, but many of the mediaeval maps are utterly unintelligible.
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)