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afflictive event, even this was not without its beneficial conse-
of these and many others, the sciences, which had been in a manner lost, were recovered, improved, and preserved; and from their country at length transmitted into the western mations of Europe'. The means by which the latter was effected arose principally from the inroads and final settlement of the Moors or Saracens in Spain, A. D. 713, into which country they carried the sciences; and the necessary intercourse between them and the natives, and the occasional visits of inquisitive foreigners terminated in the gradual diffusion of mathematical learning through the neighbouring countries. From the Arabs the Europeans received translations of several Greek treatises on the sciences, before it was known here that the originals were in existence. Euclid's Elements were first translated from the Arabic into Latin, at a time when no Greek copy was to be found".
The Europeans manifested, at first, considerable aversion to the sciences *; but by the labours and address of a few learned
* The diffusion of science is to be ascribed partly to the Jewish people, whose extensive commerce with almost every part of the world was favourable to this purpose. Historians mention the names of several learned men of the Hebrew nation, among whom are Rabba Judah, Isaac Ebn Baruch, who read lectures on the Mathematics; Beren Al Pherec, Rabbi Abi, Judah de Toledo, Ebn Ragel; Alquibuts de Toledo, Ebn Music, Mahommed de Savellia, Joseph Ebn Hali, and Jacob Abvena, were skilful astronomers: Ebn Ezra was one of the most learned men of the age, (A. D. 1170;) he excelled as an astronomer, philosopher, physician, poet, and critic, and wrote on Geometry, Algebra, Arithmetic, Logic, Astronomy, Astrology, &c. In every country where learning was beginning to be cultivated, the Jews seem to have been among the first of those who were employed as teachers, especially in Britain; probably they were the only persons at all qualified to undertake the arduous and (at that time) unthankful employment. See Dr. Henry's History of Britain, vol. iv. p. 168.
* It is stated in some of our public prints, that Dorville (on Chariton, p. 49, 50) says he was in possession of the works of Euclid in manuscript, dated A. D. 995, which manuscript is now lost: the oldest manuscript at present extant is part of the works of Plato, dated A. D. 996. .*
* It is said that learning, such as it was, flourished in Britain from the end of the first century after Christ to the middle of the fourth, when it began to decline. During the sixth century, this island was a continued scene of war, confusion, and misery; very few paid any attention to learning, and they were despised and insulted on account of it. Books were so extremely scarce, that none but kings, bishops, and abbots, could afford to purchase them : King Alfred, in 690, gave eight hides of land to Benedict Biscop, Abbot of Weremouth, for ene single volume of cosmography. There were no schools at this period, except in kings' palaces, bishops' seats, or monasteries; hence the little
persons in Italy, Germany, France, and England, knowledge began to make a perceptible progress. Pope Sylvester 11. acquired Arithmetic from the Arabs, A. D. 960; Alphonsus II. King of Castile, founded a College for the advancement of Astronomy, and placed it under the direction of some learned Arabs; Leonard de Pisa was skilled in Algebra, according to M. Cossali, as early as 1202; Jordanus Nemorarius wrote on Arithmetic, Geometry, and the Planisphere, A.D. 1230; and about the same time Johannes de Sacro-bosco, an Englishman, was professor of Mathematics at Paris, and wrote on Arithmetic, the Sphere, the Calendar, and the Astrolabe. Twenty years after Campanus de Novara wrote on the Sphere, Theories of the Planets, &c. and translated Euclid's Elements ; and Gerard of Cremona translated the works of Aristotle, the Almagest of Ptolemy, with Geber's Commentary, Alhazen's Treatise on Twi
learning then in vogue was necessarily confined to princes, priests, and a few of the chief nobility. The eighth century was more dark, barbarous, and ignorant than any preceding; many of the priests could not even read. The ninth century was little better; but it produced a few learned men, as Alfred, Aldhelm, Bede, Egbert, and Alcuinus. The tenth century has been called the unhappy age, which “for its barbarism and wickedness” says Baronius) “may be called the age of iron; for its dulness and stupidity, the age of lead; and for its blindness and ignorance, the age of darkness.” The little learning of the eleventh and twelfth centuries (although patronized by princes and great men) was chiefly confined to the monks; it consisted of Metaphysics, Natural Philosophy, Law, Medicine, School Divinity, Geometry, Astronomy, (as these sciences then stood) and Astrology. Ingulphus, Lanfranc, Anselm, Pullus, Eadmerus, William of Malmsbury, Simon of Durham, Matthew Paris, Roger Howeden, Benedict Abbas, Peter of Blois, and John of Salisbury, were among the most distinguished scholars of this age. The thirteenth and fourteenth centuries are chiefly remarkable for the theological disputes of the schoolmen, and for the vain and ridiculous pursuits of astrologers, magicians, and alchymists, which abounded every where. The fifteenth century (as we have observed above) witnessed the dawnings of science. These dark and barbarous times include that space which is usually denominated in history, the middle ages. Those who aspired to the rank of philosophers, in these ages of ignorance, endeavoured to persuade themselves and others, that by consulting the various configurations and positions of the planets, they could determine the future destinies of kingdoms, states, and individuals; they laboured with incessant assiduity to find the philosopher's stone, or a composition whereby it was pretended that base metals might be changed into gold; or in equally vain and foolish attempts to discover the Panacea or universal remedy, which they supposed would cure every disease and prolong life, if not wholly prevent the approach of death.
light, &c. into Latin; he likewise wrote a work on the planets. In 1260 Thomas Peckam, Archbishop of Canterbury, and Vitellio, a Pole, wrote treatises on Optics, as did Albertus Magnus on Arithmetic, Geometry, Astronomy, and Mechanics: at this period flourished the famous Roger Bacon, who possessed an extensive and accurate knowledge of the sciences rarely to be met with in those barbarous times. The invention of Spectacles, by Alexander de Spina of Pisa, a Jacobin friar, took place about the same date; and that of the Mariner's Compass in 1802. Peter d'Apono wrote on the Astrolabe; and Ascoli, professor of Mathematics at Bologna, composed a commentary on the Sphere of Sacro-bosco; both these were considered as heretics and sorcerers; in consequence of which the former was burnt in effigy, and the latter in person, at Bologna, A.D. 1328. A few othermathematicians flourished in thefourteenth century; as John de Muris, Nicholas d'Oresme, Suisset, John de Lignieres, Bradwarden, &c. But these dark ages are principally famed for the schoolmen, a class which comprised all the learned men of those times; in their hands the Logic of Aristotle became an engine for solving all manner of doubts and difficulties; knotty questions, frequently on the most trivial subjects, in some cases indecent, and in others profane, furnished matter for their almost endless disputes, which were urged with vehemence and acrimony, not so much to discover truth as to obtain victory; indeed the sole tendency of their labours was to obscure truth, and involve the human mind in the grossest ignorance; however, notwithstanding this clouded and inactive state of knowledge, two inventions in mechanics, during this period, deserve our notice, viz. a machine for grinding rags for the purpose of making paper, by Ulman Strame, of Nuremberg; and wheel-work clocks, both fixed and portable. The fifteenth century, which may be considered as “the dawn of science, produced many able mathematicians, among whom may be mentioned John Gmunden, Dailli, George of Trebizonde, Cardinals Bessarian and Cusa; Purbach and Regiomontanus, the two great restorers of Astronomy; Waltherus, Lefevre, Novera, Bianchini, Angelo, Ferdinand of Cordova, Henry Duke of Wisco, and Lucas de Burgo, the introducer of Algebra into Europe. This century is famous for the invention of Printing, by Faust of Strasburg, in 1440, and also for the first and grand applications of the theory of the Loadstone, and of mathematical knowledge to the useful purposes of navigation and commerce, namely, in the voyages of Diaz, Vasco da Gama, and Columbus: the first reached the Cape of Good Hope in 1486, the second doubled it in 1492, and the same year Columbus crossed the Atlantic, and discovered the West Indies. The sixteenth century is the era of the complete revival of mathematical learning, and of important discoveries and improvements in several of its branches. Algebra is indebted in this respect to the labours of Carden, Ferrei, Tai talea, Ferrari, Bombelli, Maurolycus, Scheubelius, Sturmius, Recorde, Stifelius, Clavius, and Vieta whose improvements were great and valuable. Tartalea, Commandine, Durer, Nonius, Ubaldi, Saville, Ramus, and Vieta excelled in Geometry; Copernicus revived the Pythagorean system of the universe; Tycho Brahe was called The great Observer; Kepler was the creator of true physical Astronomy; Schonerus, Fracastorius and William prince of Hesse Cassel were diligent observers of the heavenly bodies; and Aloysius Lilius, an astronomer of Verona, was the person whose plan was adopted by Pope Gregory XIII. for reforming the calendary. John Baptista Porta invented the Camera Obscura ; and Maurolycus was a considerable writer on Optics. The numerous inventions and discoveries which took place in the seventeenth century, advanced the theory and practice of mathematical learning to a pitch until then unknown, and far exceeded the most sanguine expectations or hopes of any preceding age. One of the most noble and useful of these was the invention of the Telescope, which is ascribed by some to John Lippersheim, in 1605; by others to Zachary Jansen; and again by others to James Metius; but it was claimed by Fontana. Kepler first explained this useful instrument; and it received various improvements from Galileo, Reive, Borelli, Hartsoeker, Cox, Campani, Hevelius, Scheiner, Reita, Gregory, Huygens,
* The method now in use of computing from the birth of Christ was instituted by Rabbi Samuel, Rector of the Jewish School at Sora in Mesopotamia, probably about the year 250. It was first used in the West, A.D. 527, by Dionysius Exiguus, by birth a Scythian, and at that time a Roman abbot. Venerable Bede employed it in his writings: the recommendation it thereby obtained, occasioned it to be brought into common use, and the great convenience of this epoch has caused it to be retained ever since.