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almost totally neglected. Scarcely any particulars connected with early researches of this kind have been noticed by historians; and of the few facts which have been casually transmitted to us, the accounts are so involved in obscurity and contradiction, that very little dependence can be placed on them m. In what follows therefore, we shall merely notice the countries where the Mathematics are reported to have been first cultivated, and the principal nations and individuals, by which they have been successively improved, and at length transmitted down to us. It is is generally believed that the mathematical sciences were first cultivated by the Assyrians and Chaldeans, the two most ancient nations on record, at an early period after the flood ". Of the nature and extent of these sciences, as they then stood, we are not informed; but it is generally believed that these ancient people were accustomed to make celestial observations in order to understand the seasons, and for the purposes of astrology, a fallacious art for which they appear to have been early distinguished. We likewise gather from circumstances, that Numbering, Measuring, practical Mechanics, and Building, were arts with which they were not unacquainted. From Chaldea the science was transmitted to other neighbouring countries, among which Egypt is celebrated as being for a long time the seat, and chief source of learning. The Egyptian priests, “directed by the laws of their institution to study and collect the secrets of nature, were become the depositaries of all human knowledge;” they were consulted on every difficult subject, not only by their own unlearned countrymen, but the most renowned philosophers of all the neighbouring parts flocked to them for instruction ". The Phenicians were a trading and flourishing people as early as A. C. 1500, they excelled in learning and manufactures, and to them have been attributed the invention of letters", arithmetic, commerce, and navigation ".

m Dr. Robertson.

* With the state of knowledge among the antediluvians we are almost entirely unacquainted. “Tubal Cain was an instructor of every artificer in brass and iron,” and Jubal “was the father of all such as handle the harp and organ :” this is, I believe, all that Moses says on the subject. Josephus affirms, that the sons of Seth were astronomers. Indeed we have reason to conclude from the great length of human life, and the consequent excessive population of the world before the flood, that arts and sciences might have been cultivated by them to a considerable extent. Probably Noah's sons possessed all the learning of that period: if so, it will help to account for the skill in Architecture, Astronomy, &c. which we find displayed within about a century after the flood.

• According to the president Goguet, Egypt has the honour of being the first nation which established a public Library; this was contained in one of the buildings forming a part of the magnificent tomb of their king Osymandyas, who lived about the time of the Trojan war, A. C. 1200; over the door of this library was written, "12+gov puzzis, The shop for the Physic of the Sout. See the Origines Sacrae, by Stillingfleet, vol. 1. p. 55. The learned and industrious Sir Walter Ralegh has, from the writings of Diodorus, Diogenes Laertius, Iamblicus. Philo Judaeus, Eusebius, &c. collected a summary of the Egyptian learning, as it was in the days of Moses; but he does not pretend to answer for its correctness: “It was divided,” says he, “into four parts, viz. Mathematicall, Naturall, Divine, and Morall. In the mathematicall part, which is distinguisht into Geometrie, Astronomie, Arithmetick, and Musick, the ancient Egyptians exceed all others.” Historie of the JJ’orld, Part I. B. 2. Ch. 6. P Lucan thus expresses the current opinion on this subject : Phoenices primi (Famae si creditur) ausi Mansuram rudibus vocem signare figuris. The Phenician alphabet, consisting of sixteen letters, was carried to Greece by Cadmus, A. C. 1493; to these eight were afterwards added, viz. four by Palamedes, A. C. 1190, and the remaining four by Simonides, A.C. 540. The invention of writing is likewise ascribed (by a writer whom Pliny has mentioned) te Memnon, an AEthiopian king, who flourished during the Trojan war. q According to the following verse of Tibullus, Prima ratem ventis credere docta Tyros. The Phenicians passed the Strait of Gibraltar as early as A. C. 1250; and (as Bochart supposes) discovered the Cassiterides, or Scilly islands, A. C. 004. According to Herodotus (lib. 4.) they were the first who sailed round Africa; for this purpose they were furnished with ships by Nechus, King of Egypt. Sailing from the Red Sea westward, they doubled the Cape of Good Hope, and after three years spent on the voyage, continued their route to Egypt. Three other attempts of the same kind were made, as we are informed, by the ancients, but only one of these succeeded. If the tradition respecting these voyages was known in Europe, it does not seem to have obtained much credit; for we find, that as late as the fifteenth century, the passage round the south of Africa was deemed impossible, and therefore never attempted. The success of Vasco da Gama, who in 1497 doubled the Cape of Good Hope, was heard of, throughout Europe, with the utmost astonishment. The Phenicians were almost the only people among whom we find any very early traces of a system of Philosophy. Palestine contained public schools for

Thales and other Grecian philosophers travelled through the castern 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, CEnopides, 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 furmished 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 Pergaeus has left us a masterpiece on the Comic 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 X w.rafts, 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 ProLEMAIC 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 Pergaeus, 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 Moharren, 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.

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