Thales and other Grecian philosophers travelled through the eastern countries in quest of knowledge, to civilize and enrich their own: Eypt appears to have been their principal resource; from that country they carried the knowledge of the sciences into Greece about A. C. 600. But, however highly the learning of the Egyptian priests may be esteemed, it does not appear that the Mathematics merited the honourable name of a science, until some time after it had passed from them to the Greeks; in the hands of this diligent and ingenious people, a few detached principles, theories, and observations, were digested into form and consistence, and soon began to assume the appearance of symmetry and beauty: we may therefore consider the Greeks as the inventors of science; for, if it be affirmed that they received the principles and materials from other countries, it must likewise be granted that these were altogether rude and indigested, with scarcely any trait that could entitle them to the appellation of science.

Among the earliest of the Greeks who applied to this subject were Thales, Pythagoras, Cleostratus, Anaximander, Enopides, Anaxagoras, Euetemon,Meton, Zenodorus, Hippocrates, Plato,&c. and the branches chiefly cultivated by these were Geometry, Astronomy, and Arithmetic. The school of Plato produced many excellent mathematicians, of whom Leodamus improved the analysis of his master, Theaetetus wrote Elements, and Archytas first applied Mathematics to practical uses. Eudoxus, according to some, was the first founder of a regular system of Astronomy. Aristotle's works abound with Mathematics; and Theophrastus composed a mathematical history.

The building of Alexandria in Egypt by Alexander the Great, A. C. 332. forms an important epoch in mathematical history. This magnificent city, shortly after the death of its founder, became celebrated for its commerce, and still more so as the seat of learning. Ptolemy Lagus, the immediate successor of Alexander over Egypt, established here the famous Museum, consisting of a society of learned men, maintained at the public expense, and employed in the advancement of philosophy, science, and the liberal arts: he founded, besides, a magnificent teaching the sciences Kirjath Sepher, mentioned by Joshua, Chap. xv. v. 15, A. C. 1444, denotes the City of Books or Letters; which name seems to signify, that the city contained a great number of learned men.

library, which his successors endowed with valuable collections of books, amounting in the whole to 700,000 volumes, and likewise with mathematical and astronomical instruments of every description then known. Here were schools of Astronomy, Physic, Theology, &c. Here were constantly assembled learned men and students from every quarter, who met with great encouragement; and in distant countries, it was considered as a high recommendation to have studied at Alexandria. It is scarcely necessary to observe, that favoured by such an institution the Mathematics was cultivated with ardour, and flourished in an uncommon degree. Among the numerous philosophers furnished by these schools Euclid must not be omitted, A. C. 280; he wrote the Elements of Geometry now in use, to which Aristeus, Isidorus, and Hypsicles added the books on Solids, Philolaus asserted the annual motion of the earth about the sun; and Hicetas of Syracuse taught that the earth has likewise a diurnal motion about her own axis. Archimedes was an excellent Geometer, and the inventer of various machines for raising water, lifting heavy bodies, hurling stones, darts, &c. Apollonius Pergæus has left us a masterpiece on the Conic Sections; Sosigenes instituted the Julian year; Hipparchus wrote on the Chords of Arcs; Theodosius on Spherics; and Vitruvius on Architecture '.

In the first century after Christ lived Menelaus; he wrote on chords and spherical triangles. Ptolemy, who died A. D. 147, has left us an entire summary of ancient Geography and Astronomy; the latter in a work entitled Meydan Zúrrağı, the great system; in which he asserts that the earth is the centre of the universe, an hypothesis since distinguished by the name of THE PTOLEMAIC SYSTEM. Nicomachus is celebrated for his arithmetical, geometrical, and musical works; Theon for his commentaries on ancient geometricians; and Proclus for his commentaries on Euclid. Serenus wrote on the section of the

The learned and eccentric Cardan ranks Vitruvius among the twelve persons whom he supposes to have excelled all others in force of genius and invention; and he thinks Vitruvius would have been deserving of the first place, if it could be certain that he delivered nothing but his own discoveries. These twelve persons were Euclid, Archimedes, Apollonius Pergæus, Aristotle, Ar hytas, Vitruvius, Alkindus, Mahomed Ebn Musa, Duns Scotus, Suisset, Galen, and Heber of Spain.

Cylinder; Ctesibius and Hero invented pumps, syphons, and fountains; Pappus has left us six books of mathematical collections; we have commentaries on Archimedes and Apollonius by Eutocius, the friend and disciple of Isidore, a learned architect, who built the church of St. Sophia at Constantinople; and Diophantus was the only Greek author who has left us any work on Algebra: but when he lived is uncertain.

After the division of the Roman Empire, A.D. 364, the eastern portion became the retreat of the sciences. But here, in consequence of the perpetual confusion arising from the rapid progress of vice and profligacy, they were but feebly supported, and at length almost wholly confined to the museum and schools of Alexandria. Here the sciences, although in a manner unprotected, still continued to flourish, until that city fell a prey to the victorious arms of the Arabs. In the year 642 Alexandria was taken, and nearly all the documents of science which the world had ever possessed, perished with its fall. The schools were deserted, the philosophers dispersed, and the numerous volumes, which the munificence and learning of the Ptolemies had accumulated, were consigned to the flames '; a few only were spared, not from any regard to their inherent worth, but for the beauty and elegance of their execution, which tempted the avarice of their fierce and barbarous possessors.

Historians are at a loss for language to express their horror at this sad catastrophe; but dreadful as it was, like every other

The city was taken by the Arabs on Friday, in the beginning of the month Al Moharrem, and the twentieth year of the Hejira; after they had besieged it fourteen months, and lost before it 23000 men.

Some time after the surrender, John the grammarian, a learned man of Alexandria, having found means to ingratiate himself with the Arabian General Amru Ebn Al As, begged, that as the books of the library were of no use to the Arabs, he might be permitted to have them. To this request the general replied, that as he had not the power to give them, he would immediately write to the Kalif Omar, his prince, to know his pleasure. He wrote, and received for answer, " If the books you speak of are in all respects agreeable to the Koran, that is perfect without them, and there is no occasion for them: but if they are contrary to the Koran, they ought to be destroyed; therefore let them be burned." Omar's cruel mandate was unfortunately obeyed with too scrupulous a punctuality; and the numerous volumes supplied fuel during the space of six months for 4000 baths, which contributed to the health and convenience of that famous city.

afflictive event, even this was not without its beneficial consequences; for the dispersion of the learned obliged many of them to seek an asylum in the territories of their conquerors ; who by degrees, and notwithstanding the prohibitory clauses in the Koran, acquired, by means of unavoidable intercourse, a taste for those sciences which but a few years before they had used all their endeavours to proscribe. The reader who knows how to set a just value on knowledge, need not be reminded, that a tribute of unfeigned gratitude is due to ALMIGHTY PROVIDENCE for an event equally unexpected, as it has been happy in its consequences to us; an event whereby useful learning was wonderfully (not to say miraculously) preserved, and at length transmitted, not without improvements, to the barbarous nations of Europe.

Under the reign of the Kalif Abu Gaifer Almansor, which began A.D. 754, the sciences had taken root, and began to flourish; they were zealously patronized by his grandson Harun Al Raschid, who himself was well skilled in Astronomy and Mechanics. No fewer than eleven Kalifs of the family of Al Abbas are mentioned as cultivators or patrons of science; but not one of all the Arabian princes cultivated the sciences with so much ardour and success as Al Mamon, who ascended the Moslem throne A. D. 813. The virtues and attainments of this excellent prince, and his zeal in the pursuit, encouragement, and diffusion of knowledge, would have done honour to a more enlightened age and nation. On the revival of learning among the Arabs, their first care was to procure the works of the best Greek writers on Arithmetic, Geometry, Trigonometry, Mechanics, Natural Philosophy, and particularly Astronomy; they translated into the Arabian language, Euclid's Elements, Archimedes on the Sphere and Cylinder, with other parts of his works, the Trigonometry of Menelaus, the Conics of Apollonius, Ptolemy's Almagest, Aristotle's Analytics, &c. and enriched their translations with various observations, commentaries, and improvements. The principal Arabian astronomers and mathematicians of this era were Alkindus, Habesh al Merwazi of Baghdad, Ebn Musa al Kowarazmi, Ebn Sahel, Ebn Batrick, Alfragan surnamed the Calculator, Ebn Thebit, Musa Ebn Shaker, Abu Gaifar Ebn Musa, Achmed Ebn Musa, Al Hazen, Albategnius, surnamed the Arabian Ptolemy, Honain Ebn Al Ebadi, Ishak Ebn Honain, &c.: by the labours

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 nations 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 Musio, 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 one single volume of cosmography. There were no schools at this period, except in kings' palaces, bishops' seats, or monasteries; hence the little