the prophetess foretells the coming greatness of Rome; that the children of AEneas will raise the crown upon their spears, and seize the sceptres of sea and land.  Lycophron was the friend of Menedemus and Aratus; and it is not easy to believe that these lines were written before the overthrow of Hannibal in Italy, and of the Greek phalanx at Cynocephale, or that one who was a man in the reign of Philadelphus should have foreseen the triumph of the Roman arms.  These words must have been a later addition to the poem, to improve the prophecy.

Conon, one of the greatest of the Alexandrian astronomers, has left no writings for us to judge of his merits, though they were thought highly of, and made great use of, by his successors.  He worked both as an observer and an inquirer, mapping out the heavens by his observations, and collecting the accounts of the eclipses which had been before observed in Egypt.  He was the friend of Archimedes of Syracuse, to whom he sent his problems, and from whom he received that great geometrician’s writings in return.

Apollonius of Perga came to Alexandria in this reign, to study mathematics under the pupils of Euclid.  He is well known for his work on conic sections, and he may be called the founder of this study.  The Greek mathematicians sought after knowledge for its own sake, and followed up those branches of their studies which led to no end that could in the narrow sense be called useful, with the same zeal that they did other branches out of which sprung the great practical truths of mechanics, astronomy, and geography.  They found reward enough in the enlargement of their minds and in the beauty of the truth learnt.  Alexandrian science gained in loftiness of tone what its poetry and philosophy wanted.  Thus the properties of the ellipse, the hyperbola, and the parabola, continued to be studied by after mathematicians; but no use was made of this knowledge till nearly two thousand years later, when Kepler crowned the labours of Apollonius with the great discovery that the paths of the planets round the sun were conic sections.  The Egyptians, however, made great use of mathematical knowledge, particularly in the irrigation of their fields; and Archimedes of Syracuse, who came to Alexandria about this time to study under Conon, did the country a real service by his invention of the cochlea, or screw-pump.  The more distant fields of the valley of the Nile, rising above the level of the inundation, have to be watered artificially by pumping out of the canals into ditches at a higher level.  For this work Archimedes proposed a spiral tube, twisting round an axis, which was to be put in motion either by the hand or by the force of the stream out of which it was to pump; and this was found so convenient that it soon became the machine most in use throughout Egypt for irrigation.