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battle of Actium, caused herself, as is related in the legends, to be bitten by an asp. She took poison that she might not fall captive to Octavianus, and be led in his triumph through the streets of Rome.

If we possessed a complete and unbiassed history of these Greek kings, it would doubtless uphold their title to be regarded as the most illustrious of all ancient sovereigns. Even after their political power had passed into the hands of the Romans-a nation who had no regard to truth and to right-and philosophy, in its old age, had become extinguished or eclipsed by the faith of the later Cæsars, enforced by an unscrupulous use of their power, so strong was the vitality of the intellectual germ they had fostered, that, though compelled to lie dormant for centuries, it shot up vigorously on the first occasion that favouring circumstances allowed.

This Egyptian dynasty extended its protection and patronage to literature as well as to science. Thus Philadelphus did not consider it beneath him to count umong his personal friends the poet Callimachus, . who had written a treatise on birds, and honour- tronic litera

They paably maintained himself by keeping a school in ture is well Alexandria. The court of that sovereign was, moreover, adorned by a constellation of seven poets, to which the gay Alexandrians gave the nickname of the Pleiades. They are said to have been Lycophron, Theocritus, Callimachus, Aratus, Apollonius Rhodius, Nicander, and Homer the son of Macro. Among them may be distinguished Lycophron, whose work, entitled Cassandra, still remains; and Theocritus, whose exquisite bucolics prove how sweet a poet he was.

To return to the scientific movement. The school of Euclid was worthily represented in the time of Euergetes by Apollonius Pergæus, forty years later than The writings Archimedes. He excelled both in the mathe- of Apollonius. matical and physical department. His chief work was a treatise on Conic Sections. It is said that he was the first to introduce the words ellipse and hyperbola. So late as the eleventh century his complete works were extant in Arabic. Modern geometers describe him as handling his subjects with less power than his great predecessor

chus.

Archimedes, but nevertheless displaying extreme precision and beauty in his methods. His fifth book, on Maxima and Minima, is to be regarded as one of the highest efforts uf Greek geometry. As an example of his physical inquiries may be mentioned his invention of a clock.

Fifty years after Apollonius, B.C. 160-125, we meet with the great astronomer Hipparchus. He does not appear to have made observations himself in Alexandria, but he uses those of Aristyllus and Timochares of that place. Indeed, his great discovery of the precession of the equinoxes was essentially founded on the discussion of the Alexandrian observations on Spica Virginis made by Timochares. In pure mathematics he gave methods for solving all triangles The writings

plane and spherical: he also constructed a table of Hippar- of chords. In astronomy, besides his capital

discovery of the precession of the equinoxes just mentioned, he also determined the first inequality of the moon, the equation of the centre, and all but anticipated Ptolemy in the discovery of the evection. To him also must be attributed the establishment of the theory of epicycles and eccentrics, a geometrical conception for the purpose of resolving the apparent motions of the heavenly bodies, on the principle of circular movement. In the case The theory of

of the sun and moon, Hipparchus succeeded in epicycles and the application of that theory, and indicated

that it might be adapted to the planets. Though never intended as a representation of the actual motions of the heavenly bodies, it maintained its ground until the era of Kepler and Newton, when the heliocentric doctrine, and that of elliptic motions, were incontestably established. Even Newton himself, in the 37th proposition of the third book of the Principia," availed himself of its aid. Hipparchus also undertook to make a register of the stars by the method of alineations—that is, by indicating those which were in the same apparent straight line. The number of stars catalogued by him was 1,080. If he thus depicted the aspect of the sky for his times, he also endeavoured to do the same for the surface of the earth by marking the position of towns and other places by lines of latitude and longitude.

Subsequently to Hipparchus, we find the astronomers Geminus and Cleomedes; their fame, however, is totally

eccentrics.

eclipsed by that of Ptolemy, A.D. 138, the author of the great work“ Syntaxis," or the mathematical con- The writings struction of the heavens- a work fully deserving of Ptolemy. the epithet which has been bestowed upon it, “ a noble exposition of the mathematical theory of epicycles and eccentrics.” It was translated by the Arabians after the Mohammedan conquest of Egypt; and, under the title of Almagest, was received by them as the highest authority in the mechanism and phenomena of the universe. It maintained its ground in Europe in the same eminent position for nearly fifteen hundred years, justifying the encomium of Synesius on the institution which gave it birth, “the divine school of Alexandria.” The Almagest commences with the doctrine that the earth is his great globular and fixed in space; it describes the work: th

mechanic :) construction of a table of chords and instruments construction for observing the solstices, and deduces the of the heavens. obliquity of the ecliptic. It finds terrestrial latitudes by the gnomon ; describes climates; shows how ordinary may be converted into sidereal time; gives reasons for preferring the tropical to the sidereal year: furnishes the solar theory on the principle of the sun's orbit being a simple eccentric; explains the equation of time; advances to the discussion of the motions of the moon; treats of the first inequality, of her eclipses, and the motion of the node. It then gives Ptolemy's own great discovery—that which has made his name immortal—the discovery of the moon's evection or second inequality, reducing it to the epicyclic theory. It attempts the determination of the distances of the sun and moon from the earth, with, however, only partial success, since it makes the sun's distance but onetwentieth of the real amount. It considers the precession of the equinoxes, the discovery of Hipparchus, the full period for which is twenty-five thousand years. It gives a catalogue of 1,022 stars; treats of the nature of the Milky Way; and discusses, in the most masterly manner, the motions of the planets. This point constitutes Ptolemy's second claim to scientific fame. His determination of the planetary orbits was accomplished by comparing his own observations with those of former astronomers, 38pecially with those of Timochares on Venus.

His geograpby.

To Ptolemy we are also indebted for a work on Geography ased in European schools as late as the fifteenth century. The known world to him was from the Canary Islands

eastward to China, and from the equator north

ward to Caledonia. His maps, however, are very erroneous ; for, in the attempt to make them correspond to the spherical figure of the earth, the longitudes are too much to the east; the Mediterranean Sea is twenty degrees too long. I tolemy's determinations are, therefore, inferior in accuracy to those of his illustrious predecessor Eratosthenes, who made the distance from the sacred promontory in Spain to the eastern mouth of the Ganges to be seventy thousand stadia. Ptolemy also wrote on Optics, the Planisphere, and Astrology. It is not often given to an author to endure for so many ages; perhaps, indeed, few deserve it. The mechanism of the heavens, from his point of view, has however, been greatly misunderstood. Neither he nor Hipparchus ever intended that theory as anything more than a geometrical fiction. It is not to be regarded as a representation of the actual celestial motions. And, as might be expected, for such is the destiny of all unreal abstractions, the theory kept advancing in complexity as facts accumulated, and was on the point of becoming altogether unmanageable, when it was supplanted by the theory of universal gravitation, which has ever exhibited the inalienable attribute of a true theory-affording an explanation of every new fact as soon as it was discovered, without requiring to be burdened with new provisions, and prophetically foretelling phenemona which had not as yet been observed.

From the time of the Ptolemies the scientific spirit of the Alexandrian school declined; for though such mathematicians as Theodosius, whose work on Spherical Geometry was greatly valued by the Arab geometers; and

Pappus, whose mathematical collections, in eight Alexandrian books, still for the most part remain ; and Theon,

doubly celebrated for his geometrical attainments, and as being the father of the unfortunate Hypatia, A.D. 415, lived in the next three centuries, they were not men like their great predecessors. That mental strength which gives birth to original discovery had passed away

The later

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The commantator had succeeded to the philosopher. No new development illustrated the physical sciences; they were destined long to remain stationary. Mechanics could boast of no trophy like the proposition of Archimedes on the equilibrium of the lever; no new and exact ideas like those of the same great man on statical and hydrostatical pressure; no novel and clear views like those developed in his treatise on floating bodies; no mechanical invention like the first of all steam-engines—that of Hero. Natural Philosophy had come to a stop. Its great, and hitherto successfully cultivated department, Astronomy, exhibited no farther advance. Men were content with Decline of the what had been done, and continued to amuse Greek age of themselves with reconciling the celestial pheno- Reison. mena to a combination of equable circular motions. To what are we to attribute this pause? Something had occurred to enervate the spirit of science. A gloom had settled on the Museum.

There is no difficulty in giving an explanation of this unfortunate condition. Greek intellectual life had passed the period of its maturity, and was entering on old age. Moreover, the talent which might have been devoted to the service of science was in part allured to another pursuit, and in part repressed. Alexandria had sapped Athens, and in her turn Alexandria was sapped by Rome. Causes of that From metropolitan pre-eminence sto nad sunk to decline. be a mere provincial town. The great prizes of life were not so likely to be met with in such a declining city as in Italy or, subsequently, in Constantinople. Whatever affected these chief centres of Roman activity, necessarily influenced her; but, such is the fate of the conquered, she must await their decisions. In the very institutions by which she had once been glorified, success could only be attained by a conformity to the manner of thinking fashionable in the imperial metropolis, and the best that could be done was to seek distinction in the path so marked out. Yet even with all this restraint Alexandria asserted her intellectual power, leaving an indelible impress on the new theology of her conquerors. During three centuries the intellectual atmosphere of the Roman empire had been changing. Men were unable to resist the steadily increasing

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