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trious men assembled in the museum of Alexandria*, the centre of arts and sciences, were greeks by birth. All this grandeur had the fate of every thing human, it gradually decayed.

Already the jealousy that reigned among the dif ferent states of Greece had excited in it's bosom several bloody wars, fatal to it's political constitution. As long as the nation at large preserved it's morals, as long as it continued invariably attached to the principles of justice and moderation, it triumphed over it's foreign enemies. People came from distant countries to study it's laws and institutions. Weakened by intestine discord, it fell at length under the yoke, which the romans imposed on all the Earth; but while it yielded to the power of arms, it retained in a great measure it's superiority in the domains of genius. If Virgil and Cicero have equalled Homer and Demosthenes; if Herodotus, Thucydides, and Xenophon, have been surpassed by Livy, Sallust, and Tacitus; in two extensive regions, those of the fine arts and the accurate sciences, the greeks remain absolute masters. The ambition of the romans, ever active, ever young, was to enlarge their dominion abroad at home, the eternal rivalry, which divided the senate and the tribunes of the people, from the expulsion of the kings to the fall of the republic, stimulated the minds of the romans, and produced a crowd of great orators, who were followed by a number of great poets. Painting, sculpture, and archi

* The museum of Alexandria was founded by Ptolemy Philadel phus, king of Egypt, about 320 years before the christian era. The mathematics flourished in that city near ten centuries.

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tecture were far from having equal success at Rome, Yet we must acknowledge, that the work of Vitruvius, on the subject of architecture, written in the time of Augustus, is a valuable record of curious information respecting that art. In the accurate sciences, which require cool attention, silence, and profound meditation, the romans never went beyond mediocrity. Useless as means of attaining the chief offices in the state, they were the occupation of a few obscure individuals, remote from the turmoil of public affairs. The roman mathematicians were little more than translators or commentators of Archimedes, Apollonius, &c. We can remark among them only a few learned astronomers under Augustus and his earliest successors: after this period every thing fell into decay.

On the death of Theodosius, the division of the empire between his two sons, Arcadius and Honorius, having weakened that huge body, the western portion, long ravaged, dismembered, and at length subjugated by the barbarians, sunk into the profoundest ignorance; while the schools of the East were wholly employed in wretched theological disputes. The accurate sciences had taken refuge in the museum of Alexandria, almost exclusively; and there, destitute of support and encouragement, they could not fail to degenerate. Nevertheless, they still preserved, at least by tradition or imitation, that ancient and strict character, which had been stamped on them by the greeks.

Of this asylum they were soon deprived. About the middle of the seventh century of the christian


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era, the arabs, conducted by the immediate successors of Mohammed, spread carnage and devastation throughout the East: the museum of Alexandria was destroyed artists and men of science perished. or were dispersed.

However, though the chain of mathematical discovery was broken by this fatal catastrophe, a few links remained, which this very nation of destroyers, softened by the charms of peace and idleness, `strove to collect and unite afresh. In less than a century we find the arabs cultivating astronomy, of which they had before some general notions. This taste for a particular science gradually extended to all the branches of human knowledge. For the space of seven hundred years the mathematics flourished in all the countries that were subject to the dominion of the arabs, and afterward of the persians, when these two people became united. By the moors they were carried into Spain; and some rays of them penetrated into Germany.

The conquests of the turks brought back ignorance and barbarism into the delightful countries, which the arabs inhabited. At the taking of Constantinople by Mohammed II, a persecution arose against artists and men of learning, by which many were destroyed: but some escaped by flight, and carried with them the remains of the mathematical sciences into Italy, France, Germany, and England; countries in which, in Italy particularly, a taste for literature and the arts had already begun to take root.


From this period every thing was changed: the human mind was regenerated in every part. Algebra, Geometry, Astronomy, proceeded with rapid steps: and at length, in the last thirty years of the seventeenth century, the grand discovery of the method of fluxions was made.

Here a new order of things, for which men could not have ventured to hope, took place in the accurate sciences. By the method of fluxions we have been put into possession of an infinite number of problems, inacceffible to all the mathematicians of antiquity. Let us not forget, however, that these great men were our first masters: let us not imagine, that the moderns of Europe have excelled the greeks in genius: but let us be satisfied with saying, that, in consequence of the natural progress of knowledge, they have surpassed them in science. In the arts of imagination, as poetry, eloquence, painting, &c., perfection is the work of genius, not of time: and in this point of view, the only glory to which the moderns can pretend, is that of having equalled the ancients. But in the sciences the discoveries of ages are added to each other; they are disseminated by writing or printing; and at length a general mass of information is accumulated among a studious people, as it would be by an individual who should live for many centuries. Were Archimedes to return to this World, he must pursue a long course of study, ere he could place himself on a level with Newton, though it is perhaps very difficult to decide, which of the two excelled the other in genius.


The chinese and hindoos partook not in this great movement made by the sciences, and in this respect they cannot enter into competition with the people of Europe.

It appears, that the americans have never had any distinct notions of the mathematics. Before their communication with europeans, they were acquainted only with those mechanical arts, which are most necessary to the wants of life: their minds never had any tendency to reflection.

My design in this work is to give an historical abstract of the mathematical sciences, from their origin to the present day, and at the same time to honour the memories of those great men, by whom their limits have been extended. I shall not enter into systematic discussions, frequently founded on very dubious grounds; and I shall avoid the formality of geometrical demonstrations, as I write chiefly for those readers, who add to a general taste for erudition a true and steady desire of being acquainted with the progress of the human mind in the noblest exercise of it's faculties. Sometimes however I shall explain different methods sufficiently at large, to enable the professed mathematican to discover the demonstration of those conclusions, to which I must necessarily confine myself. If I cannot satisfy him entirely, I shall at least point out to him the sources, whence he may derive more ample instruc


In the history of mathematics I remark four ages. The first exhibits in the commencement faint gleams of their origin, then their rapid progress among the greeks,


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