ng if there were
not some less difficult path to the mysteries. But the Greek Geometry
was in no wise confined to the elements. Before Euclid, Plato is said to
have written over the entrance to his garden,--"Let no one enter, who is
unacquainted with geometry,"--and had himself unveiled the geometrical
analysis, exhibiting the whole strength and weakness of the instrument,
and applying it successfully in the discussion of the properties of
the Conic Sections. Various were the discoveries, and various the
discoverers also, all now at rest, like Archimedes, the greatest of them
all, in his Sicilian tomb, overgrown with brambles and forgotten, found
only by careful research of that liberal-minded Cicero, and recognized
only by the sphere and circumscribed cylinder thereon engraved by the
dead mathematician's direction.

Meanwhile, let us turn elsewhere, to that singular people whose name
alone is suggestive of all the passion, all the deep repose of the
East. Very unlike the Greeks we shall find these Arabs, a nation
intellectually, as physically, characterized by adroitness rather than
endurance, by free, careless grace rather than perfect, well-ordered
symmetry. Called forth from centuries of proud repose, not unadorned by
noble studies and by poesy, they swept like wildfire, under Mohammed and
his successors, over Palestine, Syria, Persia, Egypt, and before the
expiration of the Seventh Century occupied Sicily and the North of
Africa. Spain soon fell into their hands;--only that seven-days' battle
of Tours, resplendent with many brilliant feats of arms, resonant with
shoutings, and weightier with fate than those dusty combatants knew,
saved France. Then until the last year of the Eleventh Century,
almost four hundred years, the Caliphs ruled the Spanish Peninsula.
Architecture, music, astrology, chemistry, medicine,--all these arts,
were theirs; the grace of the Alhambra endures; deep and permanent are
the traces left by these Saracens upon European civilization. During
all this time they were never idle. Continually they seized upon the
thoughts of others, gathering them in from every quarter, translating
the Greek mathematical works, borrowing the Indian arithmetic and system
of notation, which we in turn call Arabic, filling the world with wild
astrological fantasies. Nay, the "good Haroun Al Raschid," familiar to
us all as the genial-hearted sovereign of the World of Faery, is said to
have sent from Bagdad, in the y