persons in Italy, Germany, France, and England, knowledge began to make a perceptible progress. Pope Sylvester II. 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. Hoveden, 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 other mathematicians flourished in the fourteenth 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 Visco, 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, Tartalea, 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 calendar. 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,

y 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.

Newton, Caleb Smith, Dollond, Ramsden, &c. Drebell, a Dutchman, is said to have invented the microscope about 1621; but Fontana assumes the honour of the discovery, which he says took place in 1618. Torricellius invented the Barometer; and the Thermometer has been ascribed to different persons, as Galileo, Father Paul, Sanctorio, and Cornelius Drebell of Alkmaer. Antonio de Dominis first explained the phenomenon of the rainbow; as did Wellebrord Snellius the laws of refraction: Columbus first observed the variation of the magnetic needle; Edward Wright discovered the true method of dividing the meridian line, and of constructing the charts usually ascribed to Mercator. Napier was the first who published a system of Logarithms, viz. in 1614, which numbers were greatly improved by Briggs. Stevinus of Bruges was the inventor of Decimal Arithmetic, 1610. Harriot was the father of modern Algebra, 1631. Geometry and Analysis are indebted to Roberval, Cavalerius, Comiers, l'Hôpital, Leibnitz, Mercator, Pascal, Wren, Sauveur, Parent, Barrow, and Wallis, for several new, useful, and interesting theories. Gassendi, Kepler, Picard, Hevelius, Flamstead, Horrox, Recciolus, Hooke, Longomontanus, Kircher, Bayer, and Galileo, were eminent in Astronomy. Des Cartes excelled in Geometry and Algebra, and was the inventor of the Cartesian Philosophy, depending on the absurd theory of the vortices, the foundation of which existed only in the imagination of the author. Sir Isaac Newton excelled in almost every branch of knowledge, and appears to have been the highly honoured instrument, designed by Providence to dispel the mists of error which had hitherto inveloped the human mind; his discoveries and improvements in Analysis are numerous and valuable; his Doctrine of Fluxions, in addition to its extensive application, is a masterpiece of ingenuity; he first established the true theory of Light and Colours in his excellent work on Optics: he confirmed the system of Copernicus; and by his discovery of the universality of the principle of gravitation, and his newly invented Analysis, he explained and demonstrated the laws by which that system is regulated. Bacon and Boyle were among the first who taught philosophers to reason from experiment and observation, and to emancipate the human mind from that slavery to Hypothesis, in which it had been triumphantly detained for several ages by the

schoolmen. During this century several Institutions for the joint purposes of cultivating, extending, and registering every part of science were formed in different parts of Europe, viz. at Soissons, Beaujolois, Nismes, Angers, Bologna, Florence, Naples, Verona, Brescia, and Padua. The Royal Society at London was founded in 1660; and the Academie des Sciences at Paris in 1666; the Observatory at Paris was built in 1672; that of Flamstead House, at Greenwich, in 1676.

The recent discoveries and improvements by Vieta, Des Cartes, Harriot, Newton, Leibnitz, and others, opened a new and extensive field for the exercise of talent, in every department of science. The Newtonian Analysis has been applied with equal zeal and success to some of the most difficult and interesting problems in Mechanics, Astronomy, &c. the solution

z The learned men who flourished between the time of the Conquest and the revival of learning are usually denominated schoolmen, though some writers place them within narrower limits. The schoolmen had the vanity to pretend to account for every thing; they explained the Phenomena of Nature by Hypotheses, instead of facts deduced from experiment and observation; their hypotheses were always conjectural, and very frequently improbable and false, consequently their reasonings and conclusions must have been injurious to the progress of sound knowledge. They substituted hard and unintelligible words and phrases, for causes which they did not at all com. prehend, in order to conceal their ignorance; and wished mankind to believe, that by referring to these they had explained the nature of things. Logical arguments were their grand resource, and the defence and support of favourite bypotheses, their chief employ. Their disputations were carried on with a view to obtain victory rather than for the discovery of truth. They infected every subject with their jargon; Law, Physic, Divinity, and Science abound with their sophisticated phraseology, consisting of little else than grave and pedantic displays of ostentatious trifling; especially the books on those subjects written about three centuries ago, which on this account the modern reader will be at considerable loss to understand. The logic of Aristotle, as the grand engine of the schoolmen, has met with indiscriminate censure from a great number of later writers; but I think without justice, as it is not the science, but its misapplication that deserves blame. Bacon, Boyle, Barrow, Locke, and other reformers of science have made great use of the Aristotlean logie in their discoveries, and the only difference is, that the reasonings of these were always founded on truth or (where that could not be obtained) strong probability, and had the discovery of truth for their object; while those of the schoolmen were too often founded on vague or improbable hypotheses, and terminated in procuring their authors undeserved renown, but made mankind neither wiser nor better.