98

HISTORICAL VIEW OP THE

astronomer Nasseer-ad-deen flourished, known by histables and other works (about a. d. 1220). Amongthe successors of Timour , though at a considerably laterperiod (a. d. 1440), Ulugh Beg, sovereign of Samar-cand, established one of the largest observatories re-corded in history, and fitted it up with various instru-ments, especially quadrants of very great radius. Withthe help of many scientific assistants he publishedelaborate collections of tables, and a catalogue of thestais. Their accuracy has been admitted to be con-siderably superior to that of the Greek tables.

The same patronage was extended to science by thesuccessors of Gengis-khan on the throne of China .The thirteenth century may be considered, owing to thiscause, and the importation of the astronomy of thewestern nations, as the most brilliant epoch of Chinese science.

The subject of the quadrature of the circle engagedthe attention of the Arabian mathematicians, who car-ried somewhat further the approximation by whichArchimedes and Apollonius had expressed the ratio ofthe diameter to the circumference. They gave theratio as that of 1250 to 3927, which is a very nearapproach. Another value in still simpler terms, andnearly as accurate, was afterwards given by Metius ,which is easily remembered, from its containing onlythe first three odd numbers, each repeated twice inorder ; viz. 113 to 355 .

This subject is, in fact, one which has continued toexercise the speculations of men in a most singular de-gree in all ages. It seems to stand forth as an excep-tion to the general truth of the indifference manifestedtowards the abstract researches of geometry. Here wehave a problem which, as far as it is connected withany practical application, has ages ago received such asolution as to suffice amply for all purposes of com-putation in which it can be introduced; and whichlater mathematicians have found means of expressing,by a decimal continued to any number of places of