ear 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superseded the sun-dial and hour-glass: the mechanical arts had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.

Long lethargy and intellectual inanition brooded over Christian Europe.
The darkness of the Middle Ages reached its midnight, and slowly the
dawn arose,--musical with the chirping of innumerable trouveres and
minnesingers. As early as the Tenth Century, Gerbert, afterwards Pope
Sylvester II., had passed into Spain and brought thence arithmetic,
astronomy, and geometry; and five hundred years after, led by the old
tradition of Moorish skill, Camille Leonard of Pisa sailed away over the
sea into the distant East, and brought back the forgotten algebra and
trigonometry,--a rich lading, better than gold-dust or many negroes.
Then, in that Fifteenth Century, and in the Sixteenth, followed much
that is of interest, not to be mentioned here. Copernicus, Galileo,
Kepler,--we must pass on, only indicating these names of men whose lives
have somet