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 year 807 or thereabout, a royal present to Charlemagne, a very singular clock, which marked the hours by the sonorous fall of heavy balls into an iron vase.  At noon, appeared simultaneously, at twelve open doors, twelve knights in armor, retiring one after another, as the hour struck.  The time-piece then had superseded the sun-dial and hour-glass:  the mechanical arts had attained no slight degree of perfection.  But passing over all ingenious mechanism, making no mention here of astronomical discoveries, some of them surprising enough, it is especially for the Algebraic analysis that we must thank the Moors.  A strange fascination, doubtless, these crafty men found in the cabalistic characters and hidden processes of reasoning peculiar to this science.  So they established it on a firm basis, solving equations of no inconsiderable difficulty, (of the fourth degree, it is said,) and enriched our arithmetic with various rules derived from this source, Single and Double Position among others.  Trigonometry became a distinct branch of study with them; and then, as suddenly as they had appeared, they passed away.  The Moorish cavalier had no longer a place in the history of the coming days; the sage had done his duty and departed, leaving among his mysterious manuscripts, bristling with uncouth and, as the many believed, unholy signs, the elements of truth mingled with much error,—­error which in the advancing centuries fell off as easily as the husk from ripe corn.  Whether the present civilization of Spain is an advance upon that of the Moors might in many respects become a matter of much doubt.