death, because the sum of the figures in the successive multiples of 8 decreased successively by one; 9 was the symbol of immortality, since the sum of the figures in the multiples of 9 remains constant, etc.
Plato, the great philosopher of the later Athenian school, also regarded mathematics as the basis of his philosophy, placing over his door the famous inscription, "Let none ignorant of geometry enter here." It is also noteworthy that when he was questioned as to the occupation of the Deity, Plato replied, "He geometrizes continually." This lofty idealism was characteristic of Greece and entirely foreign to the prosaic civilizations of Egypt and Assyria. Only the combination of sea, mountain and climate found in Hellas could produce the unique type of the Grecian genius. This dependence of type on surroundings is evidenced by the fixity of type apparent in ancient races. Thus the Fellaheen still bear the imprint of the Pharaohs on their countenances, and draw water with the Shadoof as at the dawn of history, while the Chinaman is still found reckoning with the beaded "swan pan," invented twenty-six centuries before Christ.
Passing from Greece to Italy, as the next stage in the evolution of culture, another great change is manifest. Italy presents no such natural unity as offered by the valley of the Nile and the Tigro-Euphrates basin, nor does it present the diversity of Greece. A narrow peninsula bounded by the sea on three sides and lofty mountains on the fourth, the physical peculiarities of Italy naturally cemented the diverse tribes with which it was originally peopled into a single state. The origin of the Imperial city dated from a predatory band of Latin shepherds who received into their community the outcasts of the neighboring tribes, so that even at the outset the dominant idea was that of physical force, a principle which pervades the whole fabric of Roman civilization. The rape of the Sabine women confirms the tradition that the band, being without women, was a predatory union of outcasts, or what Livy calls a "colluvies." The growth of the Roman state was throughout a process of accretion, rather than the unfolding of a vital principle. The civilization of the Romans was likewise due to this policy of absorption, borrowing their religion and culture from surrounding nations. But while the gods of the Greeks and the Egyptians found a home on the banks of the Tiber, they were there worshipped in a spirit entirely foreign to that of their nativity, for whereas the Greeks worshipped their divinities from an innate love of abstract beauty, the Romans worshipped the same gods from a spirit of necessity, bargaining with them for physical protection and material success. Again, although the Romans borrowed the Grecian games, they had no idea of the esthethic pleasure derived by the Greeks from perfect physical development, but degraded them into mere gladiatorial combats or exhibitions of brute force in which they were spectators and
