An important result of the observations of fixed stars made at Meraga was that the precession (chapter II., § 42) was fixed at 51″, or within about 1″ of its true value. Nassir Eddin also discussed the supposed trepidation (§ 58), but seems to have been a little doubtful of its reality. He died in 1273, soon after his patron, and with him the Meraga School came to an end as rapidly as it was formed. 63. Nearly two centuries later _Ulugh Begh_ (born in 1394), a grandson of the savage Tartar Tamerlane, developed a great personal interest in astronomy, and built about 1420 an observatory at Samarcand (in the present Russian Turkestan), where he worked with assistants. He published fresh tables of the planets, etc., but his most important work was a star catalogue, embracing nearly the same stars as that of Ptolemy, but observed afresh. This was probably the first substantially independent catalogue made since Hipparchus. The places of the stars were given with unusual precision, the minutes as well as the degrees of celestial longitude and latitude being recorded; and although a comparison with modern observation shews that there were usually errors of several minutes, it is probable that the instruments used were extremely good. Ulugh Begh was murdered by his son in 1449, and with him Tartar astronomy ceased. 64. No great original idea can be attributed to any of the Arab and other astronomers whose work we have sketched. They had, however, a remarkable aptitude for absorbing foreign ideas, and carrying them slightly further. They were patient and accurate observers, and skilful calculators. We owe to them a long series of observations, and the invention or introduction of several important improvements in mathematical methods.[40] Among the most important of their services to mathematics, and hence to astronomy, must be counted the introduction, from India, of our present system of writing numbers, by which the value of a numeral is altered by its position, and fresh symbols are not wanted, as in the clumsy Greek and Roman systems, for higher numbers. An immense simplification was thereby introduced into arithmetical work.[41] More important than the actual original contributions of the Arabs to astronomy was the service that they performed in keeping alive interest in the science and preserving the discoveries of their Greek predecessors. Some curious relics of the time when the Arabs were the great masters in astronomy have been preserved in astronomical language. Thus we have derived from them, usually in very corrupt forms, the current names of many individual stars, _e.g._ Aldebaran, Altair, Betelgeux, Rigel, Vega (the constellations being mostly known by Latin translations of the Greek names), and some common astronomical terms such as zenith and =nadir= (the invisible point on the celestial sphere opposite the zenith); while at least one such word, almanack, has passed into common language.