success. "But though the alchemists failed in the execution of their grand project, many useful discoveries were made by them, while vainly spending their time and labour in attempts to make silver and gold. Some important combinations were produced, by which pharmacy has been enriched, and the science of medicine promoted. The method of preparing alcohol, aqua-fortis, volatile alkali, vitriolic acid, gunpowder, and many other chemical compounds, might have remained unknown, but for the persevering labours and patient experiments of the alchemists of the middle ages."

SECTION IV.

ON THE EUROPEAN MATHEMATICIANS AND ASTRONOMERS OF THE MIDDLE AGES.

214. THE partial revival of literature and science in Arabia, has been first noticed, because it preceded, in the order of time, that which took place in Europe during the twelfth and two following centuries; and, because the impulse was first received from Arabian scholars, which subsequently extended itself over the European continent. Having taken a very cursory view of the state of mathematical and physical science in the East, after its expulsion from Greece and Egypt, we now return to that portion of the world, which has, for many ages, excelled every other in civilization and general knowledge. Passing over a period of not less than six or seven

centuries, we recommence our review of European literature with the beginning of the thirteenth century; and as, at that period, mathematical and astronomical science kept pace with each other, and were usually cultivated by the same individuals, they will be jointly considered in this place.

215. Spain and Italy were the two provinces of Europe that first caught the reflected rays of science from Arabia. In the former of these countries, the revival of knowledge is chiefly to be attributed to the residence of eminent Arabian scholars in some of its principal cities - the establishment of schools and colleges-and the collection of large and valuable libraries, consisting of MSS. on every department of science. Into the latter country (Italy) it seems to have been rather accidentally than designedly introduced. LEONARDO, an opulent merchant of Pisa, visited the Asiatic provinces for purposes of commerce. During his temporary residence at Bagdad, he associated frequently with the Arabian literati of that city, and made himself acquainted with their most important discoveries, especially those which related to arithmetic and algebra, in both which sciences he became a distinguished proficient. The knowledge thus acquired, he lost no time in imparting to his countrymen; and, by doing this, obtained the honour of introducing into Europe, a science before wholly unknown, but which has ever since occupied a chief place among the objects of human intelligence. Though he was well known to have left many valuable MSS. (chiefly on the new algebraic science,) none were supposed to have

escaped the wreck of ages, till about the close of the last century; when a learned Italian referred to a MS. written by Leonardo of Pisa, which he had discovered in a monastic library, bearing the date of A. D. 1202, and which has since been published. From this ancient document it is evident, that its author was a skilful algebraist; that he was not unacquainted with the problems of Diophantus; and that he had, at least, proceeded as far as to the resolution of cubic equations.

216. In a more advanced period of the same century, several mathematicians and astronomers flourished in different parts of Europe, whom it will be sufficient cursorily to notice. (1.) Jordanus Nemorarius, author of a treatise on the Astrolabe, and a work on Arithmetic, in ten books. (2.) John of Halifax, (better known by the name of Sacrobosco), an Englishman by birth, but resident at Paris, as professor of mathematics. His principal work, on "the Sphere," acquired great celebrity; besides which, he wrote treatises on the Astrolabe, the Calendar, and the Arabian Arithmetic. He flourished about A. D. 1250. (3.) Campanus of Novara, is best known as one of the first European Commentators on Euclid's Elements; and also as the author of several works on astronomy, which were designed to make known the discoveries of the ancient astronomers, together with the improvements which had been more recently suggested by the Arabians. (4.) To the preceding may be added, Gerard of Cremona, and his illustrious patron, the Emperor FREDERIC II; the latter of whom liberally

patronized the arts, by founding the university of Naples; and the former, having been appointed its first professor of astronomy, rendered an important service to science, by translating, from the Arabic into Latin, the Almagest of Ptolemy, with Geber's Commentary; those parts of Aristotle's writings which relate to Physics; and Alhazen's treatise on Twilight, besides composing several original works. (5.) A name far more celebrated in the history of science than any of the above-mentioned mathematicians, must not be passed over in this place, though we shall reserve for a future section, the more distinct record of his scientific discoveries. This was ROGER BACON, an English friar, who was born A. D. 1214, and died in 1294. When the ignorance of the age in which he lived, and of the monks with whom he associated, compared with his almost universal knowledge, is considered, it must be acknowledged that he was a prodigy of genius and erudition; and that very few, either in ancient or modern times, have surpassed him, either in originality of invention, or in profundity of research.

217. The thirteenth century is chiefly memorable in the annals of astronomical science, as the era in which the celebrated Alphonsine Tables were prepared by the united labours of the most distinguished astronomers of the age, both Asiatic and European, whether Christians, Saracens, or Jews. They derive their name from ALPHONSUS II. who reigned in Castile, A.D. 1240. Their object was to correct the errors which had been discovered in the calculations of Ptolemy, and

produce a new series, more complete and accurate than any which had preceded them. The expense incurred by this scientific undertaking is said, by some historians of that age, to have exceeded 40,000, and by others 400,000 ducats. As soon as the Alphonsine Tables were made public, they attracted the attention of the principal mathematicians and astronomers both of Europe and Asia; several of whom wrote treatises explanatory of their details, or intended to correct their supposed errors.

218. The following century (the fourteenth) was one in which true science manifestly declined throughout Europe, in consequence of the ecclesiastical domination maintained by the clergy, and the frivolous logomachics of the scholastics, to which we shall allude more particularly hereafter. Scarcely do the literary annals of that age furnish us with the name of an individual, who excelled either in mathematics or astronomy, though many were laboriously employed in writing commentaries on the works of the ancients. One exception to the above remark must be made in favour of Richard of Swineshead, who taught the mathematics and astronomy in the university of Oxford, about A. D. 1350. His works chiefly "consist of profound and subtle applications of algebraic calculations to physics and metaphysics." He wrote treatises" on astronomical calculations," which indicate, to say the least, the patient industry and ingenuity of their writer, and his great skill in algebraic processes. Passing over this inauspicious æra, we shall immediately advance to the fifteenth century, during which these sciences