. We derive our mathematics from them; and to them, also, we
owe much of our astronomical knowledge. Almamoun, by a liberal reward,
sought to engage in his service a famous mathematician of
Constantinople; and Ibn Korrah enriched the stores of his country in
this department with translations of Archimedes and the conics of
Apollonius. Some have said that, on the revival of European literature
in the fifteenth century, mathematical science was found nearly in the
state in which it had been left by Euclid; and the justly celebrated
Brucker contends, that the Arabs made no progress whatever in this
{258} most important branch of knowledge; later writers, however, and
particularly Montucia, the author of the Histoire des Mathematiques,
have done ample justice to their researches. Numerical characters,
without which our study of the exact sciences were almost in vain,
beyond all doubt came to us from the Arabs: not that they invented
them--it is probable they were originally words, perhaps Hindu words,
expressing the quantities they respectively represent, but abbreviated
and brought to their present convenient form by the followers of the
Prophet. Trigonometry and algebra are both indebted to their genius.
The sines of the one of these sciences instead of the more ancient
chord, and the representatives of quantities in the other, descend
through the Arabs to us, if they did not at first invent them.
Original works on spherical trigonometry are among the productions of
Ibn Musa and Geber, the former of whom is accounted the inventor of the
solution of equations of the second degree. The University of Leyden
still retains a manuscript treatise on the algebra of cubic equations,
by Omar ibn Ibrahim; and Casiri, who, preserved and classed 1851
manuscripts, even after a fire had destroyed the magnificent collection
or the Escurial, informs us, that the principles and praises of
algebraic science were sung in an elaborate poem by Alcassem, a native
of Grenada. {259} These departments of knowledge were studied by the
Arabs as early as the eighth and ninth centuries.

Astronomy, the science of a pastoral people, and eminently so in
regions with an almost cloudless sky, like the East, was studied with
great eagerness by Arabian philosophers. Almamoun, who has been before
mentioned, was ardently devoted to it: at his cost the necessary
instruments of observation were provided, and a complete digest of the
science was made. T