wrote, besides, on morals, history, grammar, and various other subjects.

The most celebrated of ancient mathematicians was Archime'des, born at Syracuse, about 287 B.C., and a student in the school of Euclid. Our imperfect knowledge of the previous state of mathematical science prevents us from correctly estimating the merits of Archimedes, but discoveries of the utmost importance are known to be his. His great treatises on the "Sphere and Cylinder," on "Spheroids and Conoids," and on the "Measurement of the Circle," are among his most valuable contributions to this science.

He may almost be said to have originated the theory of mechanics, and the science of hydrostatics, and he first established the truth that a body plunged in a fluid loses a part of its weight just equal to the weight of the displaced fluid. It was by this law that he discovered how much alloy the goldsmith, whom King Hiero had commissioned to make a crown of pure gold, had mixed with the precious metal.

He discovered the principle of the lever, and was so elated over his discovery as to boast that if he had a proper fulcrum for his lever he could move the world. Another of his important productions is the water screw, by which water is made, as it were, to lift itself by its own weight.

During the siege of Syracuse by the Romans Archimedes exerted all his mechanical genius in defense of the city, inventing machines which astonished and baffled the assailants. When finally the Romans took the city by surprise, Archimedes, according to tradition, was found sitting in the public square, with a number of geometrical figures drawn before him in the sand. As a Roman soldier rushed upon him, he called out to the rude warrior not to spoil the circle. But the soldier cut him down.

By his own directions there was engraved on his tombstone a cylinder enclosing a sphere, in commemoration of

his discovery of the relation between these solids- on which discovery he set particular value.

Another noted mathematician of the Alexandrian school was Apollo'nius of Perga, who lived in the latter part of the second century B.C., and made some important additions to the discoveries of Euclid. He perfected the theory of conic sections, his work on this subject being still preserved, partly in the original Greek, and partly in an Arabic translation.

The next of these Alexandrian scientists to whom we will allude is Hippar'chus, the celebrated astronomer, and the first to reduce astronomy to a systematic science. He was born about the beginning of the second century B.C., but nothing is known of his personal history. Of his many works on the science only the least important, the "Commentary on Aratus," has come down to us. His other works treated on astronomy and geography.

All we know concerning his discoveries comes from the Syntaxis of Ptolemy, from which we learn that Hipparchus discovered the precession of the equinoxes, corrected the previous estimate of the length of the year, established the solar and lunar theories, and originated or greatly extended the theory of epicycles. He also invented the astrolabe, and drew up a catalogue of 1080 fixed stars, with the celestial latitude and longitude of each.

Ptolemy, to whom our knowledge of the discoveries of Hipparchus is due, was a native of Egypt, and was living in Alexandria in 139 A.D., which is all we know of his personal history. A number of his works on astronomy and geography exist, the most important of them being the Syntaxis, or the Almagest, as the Arabians have named it; and the Geography. These works became the standard textbooks to succeeding ages; the first continuing in vogue till the time of Copernicus; the second till our knowledge of geography was extended by the maritime discoveries of the fifteenth century.

His astronomical work was largely a compilation from the labors of his predecessors, principally Hipparchus, but as he remains the only existing authority on ancient astronomy the system set forth in the Almagest has received his name.

This system is that known as the theory of epicycles. In his theory the earth was the center of the universe, all the heavenly bodies rotating around it. Earth, the most stable of the elements, held the lowest place; then came water, then air, then fire, and next ether, extending indefinitely upward. Beyond ether were certain zones or heavens, each containing an immense crystal shell, in which the heavenly bodies were fixed, and carried round by the rotation of the shell. There were eight of these spheres, one for each of the known planets and one for the fixed stars. But as new discoveries were made in the heavens it became necessary to invent new epicycles, until the system grew so cumbrous that it fell to pieces of its own weight, and was swept aside by the Copernican theory, after holding supreme sway for twenty centuries.

In geography Ptolemy also appears as an editor and improver, basing his work on that of the little known Mari’nus of Tyre, and making many valuable corrections to the previous systems of geographical knowledge.

With Ptolemy ends the list of noted Greek scientists.

LATER GREEK HISTORIANS.

AFTER the conquest of Greece by Rome a number of historians of some eminence and much industry arose, of Greek extraction, but employing their pens principally upon the glories and the conquests of Rome.

Of these the first and most talented was Polybius. He was preceded by a number of others, however, who viewed the history of Rome as of less importance, but to whom he frequently refers. We will therefore glance at some of the more noted of these.

The work of Polybius was expressly intended to continue the history of Timæ'us, an industrious writer, who was born about 352 B.C., and whose principal works bear the following titles: Concerning Syria; History of Italy and Sicily; History of Greece and Sicily; The Olympic Victors, etc. Of these works only fragments remain. Timæus, though faulty, and incurring much censure from Polybius, was probably industrious and careful in his research. But the chief interest in his lost histories comes from their relation to Polybius, who commenced where he left off, and who constantly refers to him.

Another writer of some note was Ara'tus of Sicyon, who carried down the history of Greece to 220 B.C. His work is praised by Polybius, who makes occasional use of it.

Polybius was indebted also to several other writers of less importance, and seems, indeed, to have studied all the preceding history available to him.

POLYB'IUS.

BORN 204 B.C.

This most celebrated of the later Greek historians was a native of Megalop'olis, an Arcadian town. From his father, who was a general of the Achæ'an League, Polybius received valuable instruction in politics and military science. He afterward himself became a military commander, and one of the most influential men of his native country. In 168 B.C., when Rome summoned one thousand noble Achæans to that city to answer the charge of failing to assist her armies against King Per'seus, Polybius was included in the number.

They remained in Italy seventeen years, not being tried, but distributed among the Etrurian towns. Polybius, having gained the friendship of Scipio, was allowed to reside in Rome, having access, through the favor of his friend, to the public documents, and attending Scip'io in all his military expeditions. After the release of the Achæans, and their return home, he rejoined Scipio, attended him in his African expeditions, and was present at the taking of Carthage.

But war breaking out between the Achæans and Rome he returned to his native country, and exerted all his influence to procure favorable terms for the vanquished. His countrymen were so grateful for his services in this respect that they erected statues to him in several of their towns.

The remainder of his life seems to have been occupied in writing his historical work, and in traveling for information. We know from himself that he visited Africa, Spain and Gaul, and that he traveled in Egypt in the latter part of his life. He died in his eighty-second year, in consequence of a fall from his horse.