[Sidenote: Their great improvements in arithmetic.] From the Hindus the Arabs learned arithmetic, especially that valuable invention termed by us the Arabic numerals, but honourably ascribed by them to its proper source, under the designation of "Indian numerals." They also entitled their treatises on the subject "Systems of Indian Arithmetic." This admirable notation by nine digits and cipher occasioned a complete revolution in arithmetical computations. As in the case of so many other things, the Arab impress is upon it; our word cipher, and its derivatives, ciphering, etc., recall the Arabic word tsaphara or ciphra, the name for the 0, and meaning that which is blank or void. Mohammed Ben Musa, said to be the earliest of the Saracen authors on algebra, and who made the great improvement of substituting sines for chords in trigonometry, wrote also on this Indian system. He lived at the end of the ninth century; before the end of the tenth it was in common use among the African and Spanish mathematicians. Ebn Junis, A.D. 1008, used it in his astronomical works. From Spain it passed into Italy, its singular advantage in commercial computation causing it to be eagerly adopted in the great trading cities. We still use the word algorithm in reference to calculations. The study of algebra was intently cultivated among the Arabs, who gave it the name it bears. Ben Musa, just referred to, was the inventor of the common method of solving quadratic equations. [Sidenote: Their astronomical discoveries.] In the application of mathematics to astronomy and physics they had been long distinguished. Almaimon had determined with considerable accuracy the obliquity of the ecliptic. His result, with those of some other Saracen astronomers, is as follows: A.D. 830. Almaimon 23° 35' 52" " 879. Albategnius, at Aracte 23° 35' 00 " 987. Aboul Wefa, at Bagdad 23° 35' 00 " 995. Aboul Rihau, with a quadrant of 25 feet radius 23° 35' 00 " 1080. Arzachael 23° 34' 00