not sufficient mathematical genius to greatly improve; for thousands of observations made to increase the accuracy of the tables of the motions of the sun and planets; for catalogues of the position and brilliancy of the fixed stars; and last and not least, for keeping the lamp of learning burning in their great schools, or universities, in Spain and elsewhere during the centuries from the eighth to the fifteenth. Since the time of the Greek schools of Alexandria the home of the exact sciences has been successively in Bagdad, Cordova, Seville, Tangiers, Bokhara and Samarkand. It was only in the sixteenth century that they were firmly domiciled in christian Europe.
Even in the shortest sketch it is necessary to point out that a great part of the astronomical learning of the Moorish schools was due to Jews; and that it is to orientals and not to Europeans that we owe the earliest recognition of the fundamental truth that all sound progress in astronomy must be based on actual and continued observation of the places of the heavenly bodies; that theory must be based upon practise. It is usual to credit this insight to Tycho Brahe, and it is certain that his greatest claim to our gratitude is based upon a thorough recognition of the fact that until observations have shown us exactly how the planets move we can form no adequate theories to account for their motions. But the astronomers of India and Persia in the ninth and tenth centuries thoroughly understood this fundamental notion, as did Ulugh Beg (1393-1449) at Samarkand, and they invented means to obtain observations of adequate accuracy and in sufficient number.
The need for more observations and for greater precision was also fully realized by Purbach as early as 1450. Regiomontanus returned from Italy in 1471 to set up in Nuremberg an observatory for the especial purpose of correcting the Alphonsine tables, which Purbach and himself had found to be so defective a score of years earlier. Landgrave Wilhelm IV of Cassel and his astronomers were working in the same direction in Tycho 's time. It is Tycho 's merit that he was the first in Europe to create instruments of sufficient power, and to use them with exceeding diligence over a long series of years. There was little knowledge in Denmark of what was doing in the orient. Tycho 's plans were made quite independently of the further east. At the same time Europe touched the orient closely, through Venice, and sent many of her sons to study at Moorish schools; and it is not conceivable that Tycho was entirely ignorant of the details of the work done, a century and a half before his time, in Samarkand.
The debt of Europe to the remoter east has never yet been fully reckoned out. For thirty centuries the culture of the orient has, in one way or another, created, informed or modified our own. The religion, the learning, the art, the architecture of the east have most
