editions of the existing writings of Archimedes; but the most complete of any is the magnificent edition, in folio, lately printed at the Clarendon press, Oxford, 1792. This edition was prepared ready for the press by the learned Joseph Torelli, of Verona, and in that state presented to the university of Oxford. The Latin translation is a new one. Torelli also wrote a preface, a commentary on some of the pieces, and notes on the whole. An account of the life and writings of Torelli is prefixed by Clement Sibiliati. And at the end a large appendix is added, in two parts; the first being a commentary on Archimedes's paper upon bodies that float on fluids, by the Rev. Adam Robertson, of Christ Church college; and the latter is a large collection of various readings in the manuscript works of Archimedes, found in the library of the late King of France, and of another at Florence, as collated with the Basil edition above-mentioned.

APOLLONIUS, of Perga, a city in Pamphylia, was a celebrated geometrician, who flourished in the reign of Ptolemy Euergetes, about B.C. 240, being about sixty years after Euclid, and thirty years later than Archimedes. He studied a long time in Alexandria, under the disciples of Euclid; and afterwards he composed several curious and ingenious geometrical works, of which only his books of conic sections are now extant, and even those not perfect. For it appears from the author's dedicatory epistle to Eudemus, a geometrician in Pergamus, that this work consisted of eight books, only seven of which however have come down to us.

From the collections of Pappus, and the commentaries of Eutocius, it appears that Apollonius was the author of various pieces in geometry, on account of which he acquired the title of the great geometrician. His work on conics was the principal of them. Some have thought that Apollonius appropriated the writings and discoveries of Archimedes; Heraclius, who wrote the life of Archimedes, affirms it, though Eutocius endeavours to refute him. Although it should be allowed a groundless supposition, that Archimedes was the first who wrote upon conics, notwithstanding his treatise on conics was greatly esteemed; yet it is highly probable that Apollonius would avail himself of the writings of that author as well as others who had gone before him; and, upon the whole, he is allowed the honour of explaining a difficult subject better than had been done before, having made several improvements both in Archimedes's problems, and in Euclid. His work upon conics was doubtless the most perfect of the kind among the ancients, and in some respects among the moderns also. Before Apollonius, it had been customary, as we are informed by Eutocius, for the writers on conics to require three different sorts of cones to cut the three different sections from; viz. the paraVOL. I.

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bola from a right angled cone, the ellipse from an acute, and the hyperbola from an obtuse cone, because they always supposed the sections made by a plane cutting the cones to be perpendicular to the side of them; but Apollonius cut his sections all from any one cone, by only varying the inclination or position of the cutting plane; an improvement that has been followed by all other authors since his time. But that Archimedes was acquainted with the same manner of cutting any cone, is sufficiently proved against Eutocius, Pappus, and others, by Guido Ubaldrus, in the beginning of his commentary on the second book of Archimedes's Equiponderantus, published at Pisa in 1588.

The first four books of Apollonius's conics only have come down to us in their original Greek language; but the next three, the fifth, sixth, and seventh, in an Arabic version; and the eighth not at all. These have been commented upon, translated, and published by various authors. Pappus, in his mathematical collections, has left some account of his various works, with notes and comments upon them, and particularly on the conics. And Eutocius wrote a regular elaborate commentary on the propositions of several of the books of the

conics.

A neat edition of the first four books in Latin was published by Dr. Barrow, in 4to. at London, in 1675. A magnificent edition of all the books was published in folio, by Dr. Halley, at Oxford, in 1710; together with the Lemmas of Pappus, and the commentaries of Eutocius. The first four in Greek and Latin, but the latter four in Latin only, the eighth book being restored by himself.

ATHENÆUS, an ancient mathematician, who lived about B. C. 200. A tract of his on warlike machines was printed at Paris in 1693.

PAINTING.

CLESIDES, a Greek painter, who lived about B. C. 276, under Antiochus I. He revenged the injury he had received from queen Stratonice, by representing her in the arms of a fisherman. However indecent the painter might represent the queen, she was drawn with such personal beauty, that she preserved the piece, and liberally rewarded the artist.

METRODORUS, a famous painter and philosopher, flourished B. C. 171. He was sent by the Athenians to Paulus Æmilius, who, after the defeat of Perseus, had demanded a painter and philosopher; the former to paint his temples, and the latter to instruct his children. Metrodorus gave him satisfaction in both capacities,

SOSTRATUS, the most eminent architect of his time, was a native of Guidos, in Lesser Asia, and flourished in the third century before the Christian era. The patronage which he met with, caused him to be denominated the friend of kings; and he was in particular favour with Ptolemy Philadelphus, sovereign of Egypt. He is celebrated in history likewise for the terraces, supported on arcades, which adorned his native city, and the famous Pharos, the light-house of Alexandria, which was reckoned one of the wonders of the world. He transmitted his name to posterity by an inscription on this lighthouse, in the Greek language, of which the translation is, "Sostratus, the son of Dexiphanes, dedicates this to the gods, the protectors of navigators."

MEDICINE.

SERAPION, of Alexandria, lived about the year B. C. 280, and is affirmed by Celsus to have been the founder of the empyric sect of physicians, and accused by Galen of vaunting himself, and of mal-treating the character of Hippocrates.

ARÉAGATHUS, a Greek physician, who flourished B. C. 269. He practised with repute at Rome, till, for making use of caustics and the knife, he was banished.

PERIOD XIV.

FROM PTOLEMY PHILOMETOR TO SPARTACUS.

B.C.

[B. C. 200.]

REMARKABLE FACTS, EVENTS, AND DISCOVERIES.

194 Sparta and Hither Spain subdued by the Romans.

192 A census at Rome. The number of citizens, 243,704.

191 Antiochus defeated by the Romans at Thermopylæ.

190 The first Roman army enters Asia, and from the spoils of Antiochus brings the Asiatic luxury first to Rome.

188 The Spartans obliged to renounce the institutions of Lycurgus. 179 A census at Rome: 273,244 citizens.

173 The Jewish high-priesthood sold by Antiochus Epiphanes.

170 The Temple of Jerusalem plundered by Antiochus.

169 A census at Rome: 212,805 citizens.

168 Macedon reduced to the form of a Roman province. The first library erected at Rome.

169 The Temple of Jerusalem purified by Judas Maccabæus. 164 A census at Rome: 327,032 citizens.

162 Hipparchus began his astronomical observations at Rhodes.

161 Philosophers and rhetoricians banished from Rome.

149 The third Punic war commenced.

146 Corinth destroyed. Carthage razed to the ground by the Romans.

143 Hipparchus began his new cycle of the moon, consisting of 111,035

days.

141 The Numantine war commenced.

135 The History of the Apocrypha ends.

133 Numantia destroyed by Scipio.

124 A census at Rome: 390,736 citizens.

105 The Cimbri and Teutones defeated the Romans.

102 The Teutones and Ambrones defeated by Marius.

THIS period presents us with a view of the ruins of the Greek empire in the declining states of Syria and Egypt.

The general state of the world B. C. 146 was as follows:In Asia were the empires of India, Parthia, and Syria, with the lesser states of Armenia, Pontus, &c., in which we must add that of Arabia, which during the sixth period had become of some consequence, and had maintained its independence from the days of Ishmael, the son of Abraham. In Africa were the kingdoms of Egypt and Ethiopia; The Carthaginian territories, now subject to the Ro

mans, and the kingdoms of Numidia, Mauritania, and Getulia, ready to be swallowed up by the same ambitious and insatiable power, now that Carthage was destroyed, which had served as a barrier against it. To the south lay some unknown and barbarous nations, secure by their situation and insignificance, rather than their strength, or distance from Rome. In Europe we find none to oppose the progress of the Roman arms, except the Gauls, Germans, and some nations in Spain. These were brave indeed; but, through want of military skin, incapable of contending with such masters in the art of war as the Romans then were.

The Spaniards had, indeed, been subdued by Scipio Africanus, during the second Punic war, but in B. C. 155 they revolted; and, under the conduct of one Viriathus, formerly a robber, held out for a long time against all the armies the Romans could send into Spain. Him the consul Cæpio caused to be murdered, about B. C. 138, because he found it impossible to reduce him by force. Numantia defied the whole Roman power for six years longer; till at last, by dint of numbers, perseverance, and treachery, the inhabitants, reduced to extremity by famine, set fire to their houses, and perished in the flames, or killed one another; so that not one remained to grace the triumph of the conqueror; and this for a time quieted the rest of the Spaniards.

About this time, Attalus, king of Pergamus, left by will the Roman people heirs to all his goods, upon which they immediately seized on his kingdom, as part of those goods, and reduced it to a Roman province, under the name of Asia Proper. Thus they continued to enlarge their dominions on every side, without the least regard to justice, to the means they employed, or the miseries they brought upon the conquered people. In B. C. 122 the Balearic islands, now called Majorca, Minorca, and Ivica, were subdued, and the inhabitants exterminated; and soon after, several of the nations beyond the Alps were obliged to submit.

In Africa the crimes of Jugurtha soon gave these ambitious republicans an opportunity of conquering the kingdoms of Numidia and Mauritania; and indeed this is almost the only war in which we find the Romans engaged, where their pretensions had the least colour of justice, though in no case whatever could a nation show more degeneracy than the Romans did on this occasion. The event of it was the total reduction of Numidia, about the year B. C. 105; but Mauritania and Getulia preserved their liberty for some time longer. In the east, the empire of Syria continued daily to decline, by which means the Jews had not only an opportunity of recovering their liberty, but even of becoming almost as powerful, or at least of extending their dominions as far as in the days of David and Solomon. The Syrian empire was still further reduced by the civil dissentions between the two brothers, Antiochus Gryphus and Antiochus Cyzicenus, during which the cities of Tyre, Sidon, Ptolemais, and Gaza, declared themselves independent; and in other cities tyrants started up, who refused allegiance to any foreign power. This happened about B. C. 100; and seventeen years after, the whole was reduced by Tigranes, king of Armenia. On his defeat by the Romans, the latter