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.
But while we are dazzled by the brilliancy of these clusters of men of letters and science who graced the court of Alexandria, we must not shut our eyes to those faults which are always found in works called forth rather by the fostering warmth of royal pensions than by a love of knowledge in the people. The well-fed and well-paid philosophers of the museum were not likely to overtake the mighty men of Athens in its best days, who had studied and taught without any pension from the government, without taking any fee from their pupils; who were urged forward towards excellence by the love of knowledge and of honour; who had no other aim than that of being useful to their hearers, and looked for no reward beyond their love and esteem.
In oratory Alexandria made no attempts whatever; it is a branch of literature not likely to flourish under a despotic monarchy. In Athens it fell with the loss of liberty, and Demetrius Phalereus was the last of the real Athenian orators. After his time the orations were declamations written carefully in the study, and coldly spoken in the school for the instruction of the pupils, and wholly wanting in fire and genius; and the Alexandrian men of letters forbore to copy Greece in its lifeless harangues. For the same reasons the Alexandrians were not successful in history. A species of writing, which a despot requires to be false and flattering, is little likely to flourish; and hence the only historians of the museum were chronologists, antiquaries, and writers of travels. The coins of Euergetes bear the name of “Ptolemy the king,” round the head on the one side, with no title by which they can be known from the other kings of the same name.
But his portrait is known from his Phoenician coins. In the same way the coins of his queen have only the name of “Berenicê the queen,” but they are known from those of the later queens by the beauty of the workmanship, which soon fell far below that of the first Ptolemies.
Euergetes had married his cousin Berenicê, who like the other queens of Egypt is sometimes called Cleopatra; by her he left two sons, Ptolemy and Magas, to the eldest of whom he left his kingdom, after a reign of twenty-five years of unclouded prosperity. Egypt was during this reign at the very height of its power and wealth. It had seen three kings, who, though not equally great men, not equally fit to found a monarchy or to raise the literature of a people, were equally successful in the parts which they had undertaken. Euergetes left to his son a kingdom perhaps as large as the world had ever seen under one sceptre; and though many of his boasted victories were like letters written in the sand, of which the traces were soon lost, yet he was by far the greatest, and possibly the wisest, monarch of his day.
We may be sure that in these prosperous reigns life and property were safe, and justice was administered fairly by judges who were independent of the crown; as even centuries afterwards we find that it was part of a judge’s oath on taking office, that, if he were ordered by the king to do what was wrong, he would not obey him. But here the bright pages in the history of the Ptolemies end.