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the most active of the translators was Plato of Tivoli, who studied Arabic in Spain about it 1116, and translated Albategnius’s Astronomy (§ 59), as well as other astronomical books. At about the same time Euclid’s Elements, among other books, was translated by Athelard of Bath. Gherardo of Cremona (1114-1187) was even more industrious, and is said to have made translations of about 70 scientific treatises, including the Almagest, and the Toletan Tables of Arzachel (§ 61). The beginning of the 13th century was marked by the foundation of several Universities, and at that of Naples (founded in 1224) the Emperor Frederick II., who had come into contact with the Mahometan learning in Sicily, gathered together a number of scholars whom he directed to make a fresh series of translations from the Arabic.

Aristotle’s writings on logic had been preserved in Latin translations from classical times, and were already much esteemed by the scholars of the 11th and 12th centuries. His other writings were first met with in Arabic versions, and were translated into Latin during the end of the 12th and during the 13th centuries; in one or two cases translations were also made from the original Greek. The influence of Aristotle over mediæval thought, already considerable, soon became almost supreme, and his works were by many scholars regarded with a reverence equal to or greater than that felt for the Christian Fathers.

Western knowledge of Arab astronomy was very much increased by the activity of Alfonso X. of Leon and Castile (1223-1284), who collected at Toledo, a recent conquest from the Arabs, a body of scholars, Jews and Christians, who calculated under his general superintendence a set of new astronomical tables to supersede the Toletan Tables. These Alfonsine Tables were published in 1252, on the day of Alfonso’s accession, and spread rapidly through Europe. They embodied no new ideas, but several numerical data, notably the length of the year, were given with greater accuracy than before. To Alfonso is due also the publication of the Libros del Saber, a voluminous encyclopædia of the astronomical knowledge of the time, which, though compiled largely from Arab sources, was not, as has sometimes been thought, a mere collection of translations. One of the curiosities in this book is a diagram representing Mercury’s orbit as an ellipse, the earth being in the centre (cf. chapter VII., § 140), this being probably the first trace of the idea of representing the celestial motions by means of curves other than circles.

67. To the 13th century belong also several of the great scholars, such as Albertus Magnus, Roger Bacon, and Cecco d’ Ascoli (from whom Dante learnt), who took all knowledge for their province. Roger Bacon, who was born in Somersetshire about 1214 and died about 1294, wrote three principal books, called respectively the Opus Majus, Opus Minus, and Opus Tertium, which contained not only treatises on most existing branches of knowledge, but also some extremely interesting discussions of their relative importance and of the right method for the advancement of learning. He inveighs warmly against excessive adherence to authority, especially to that of Aristotle, whose books he wishes burnt, and speaks strongly of the importance of experiment and of mathematical reasoning in scientific inquiries. He evidently had a good knowledge of optics and has been supposed to have been acquainted with the telescope, a supposition which we can hardly regard as confirmed by his story that the invention was known to Caesar, who when about to invade Britain surveyed the new country from the opposite shores of Gaul with a telescope!

Another famous book of this period was written by the Yorkshireman John Halifax or Holywood, better known by his Latinised name Sacrobosco, who was for some time a well-known teacher of mathematics at Paris, where he died about 1256. His Sphaera Mundi as an elementary treatise on the easier parts of current astronomy, dealing in fact with little but the more obvious results of the daily motion of the celestial sphere. It enjoyed immense popularity for three or four centuries, and was frequently re-edited, translated, and commented on: it was one of the very first astronomical books ever printed; 25 editions appeared between 1472 and the end of the century, and 40 more by the middle of the 17th century.

68. The European writers of the Middle Ages whom we have hitherto mentioned, with the exception of Alfonso and his assistants, had contented themselves with collecting and rearranging such portions of the astronomical knowledge of the Greeks and Arabs as they could master; there were no serious attempts at making progress, and no observations of importance were made. A new school, however, grew up in Germany during the 15th century which succeeded in making some additions to knowledge, not in themselves of first-rate importance, but significant of the greater independence that was beginning to inspire scientific work. George Purbach, born in 1423, became in 1450 professor of astronomy and mathematics at the University of Vienna, which had soon after its foundation (1365) become a centre for these subjects. He there began an Epitome of Astronomy based on the Almagest, and also a Latin version of Ptolemy’s planetary theory, intended partly as a supplement to Sacrobosco’s textbook, from which this part of the subject had been omitted, but in part also as a treatise of a higher order; but he was hindered in both undertakings by the badness of the only available versions of the Almagest—Latin translations which had been made not directly from the Greek, but through the medium at any rate of Arabic and very possibly of Syriac as well (cf. § 56), and which consequently swarmed with mistakes. He was assisted in this work by his more famous pupil John Müller of Königsberg (in Franconia), hence known as Regiomontanus, who was attracted to Vienna at the age of 16 (1452) by Purbach’s reputation. The two astronomers made some observations, and were strengthened in their conviction of the necessity of astronomical reforms by the serious inaccuracies which they discovered in the Alfonsine Tables, now two centuries old; an eclipse of the moon, for example, occurring an hour late and Mars being seen 2° from its calculated place. Purbach and Regiomontanus were invited to Rome by one of the Cardinals, largely with a view to studying a copy of the Almagest contained among the Greek manuscripts which since the fall of Constantinople (1453) had come into Italy in considerable numbers, and they were on the point of starting when the elder man suddenly died (1461).

Regiomontanus, who decided on going notwithstanding Purbach’s death, was altogether seven years in Italy; he there acquired a good knowledge of Greek, which he had already begun to study in Vienna, and was thus able to read the Almagest and other treatises in the original; he completed Purbach’s Epitome of Astronomy, made some observations, lectured, wrote a mathematical treatise42 of considerable merit, and finally returned to Vienna in 1468 with originals or copies of several important Greek manuscripts. He was for a short time professor there, but then accepted an invitation from the King of Hungary to arrange a valuable collection of Greek manuscripts. The king, however, soon turned his attention from Greek to fighting, and Regiomontanus moved once more, settling this time in Nürnberg, then one of the most flourishing cities in Germany, a special attraction of which was that one of the early printing presses was established there. The Nürnberg citizens received Regiomontanus with great honour, and one rich man in particular, Bernard Walther (1430-1504), not only supplied him with funds, but, though an older man, became his pupil and worked with him. The skilled artisans of Nürnberg were employed in constructing astronomical instruments of an accuracy hitherto unknown in Europe, though probably still inferior to those of Nassir Eddin and Ulugh Begh (§§ 62, 63). A number of observations were made, among the most interesting being those of the comet of 1472, the first comet which appears to have been regarded as a subject for scientific study rather than for superstitious terror. Regiomontanus recognised at once the importance for his work of the new invention of printing, and, finding probably that the existing presses were unable to meet the special requirements of astronomy, started a printing press of his own. Here he brought out in 1472 or 1473 an edition of Purbach’s book on planetary theory, which soon became popular and was frequently reprinted. This book indicates clearly the discrepancy already being felt between the views of Aristotle and those of Ptolemy. Aristotle’s original view was that sun, moon, the five planets, and the fixed stars were attached respectively to eight spheres, one inside the other; and that the outer one, which contained the fixed stars, by its revolution was the primary cause of the apparent daily motion of all the celestial bodies. The discovery of precession required on the part of those who carried on the Aristotelian tradition the addition of another sphere. According to this scheme, which was probably due to some of the translators or commentators at Bagdad (§ 56), the fixed stars were on a sphere, often called the firmament, and outside this was a ninth sphere, known as the primum mobile, which moved all the others; another sphere was added by Tabit ben Korra to account for trepidation (§ 58), and accepted by Alfonso and his school; an eleventh sphere was added towards the end of the Middle Ages to account for the supposed changes in the obliquity of the ecliptic. A few writers invented a larger number. Outside these spheres mediaeval thought usually placed the Empyrean or Heaven. The accompanying diagram illustrates the whole arrangement.

Fig. 36.—The celestial spheres. From Apian’s Cosmographia.

These spheres, which were almost entirely fanciful and in no serious way even professed to account for the details of the celestial motions, are of course quite different from the circles known as deferents and epicycles, which Hipparchus and Ptolemy used. These were mere geometrical abstractions, which enabled the planetary motions to be represented with tolerable accuracy. Each planet moved freely in space, its motion being represented or described (not controlled) by a particular geometrical arrangement of circles. Purbach suggested a compromise by hollowing out Aristotle’s crystal spheres till there was room for Ptolemy’s epicycles inside!

From the new Nürnberg press were issued also a succession of almanacks which, like those of to-day, gave the public useful information about moveable feasts, the phases of the moon, eclipses, etc.; and, in addition, a volume of less popular Ephemerides, with astronomical information of a fuller and more exact character for a period of about 30 years. This contained, among other things, astronomical data for finding latitude and longitude at sea, for which Regiomontanus had invented a new method.43

The superiority of these tables over any others available was such that they were used on several of the great voyages of discovery of this period, probably by Columbus himself on his first voyage to America.

In 1475 Regiomontanus was invited to Rome by the Pope to assist in a reform of the calendar, but died there the next year at the early age of forty.

Walther carried on his friend’s work and took a number of good observations; he was the first to make any successful attempt to allow for the atmospheric refraction of which Ptolemy had probably had some knowledge (chapter II., § 46); to him is due also the practice of obtaining the position of the sun by comparison with Venus instead of with the moon (chapter II., § 39), the much slower motion of the planet rendering greater accuracy possible.

After Walther’s death other observers of less merit carried on the work, and

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