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ly； almost at the confines of the Greek territory in the west； the other in Asia Minor； notably on the island of Samosthe island which； it will be recalled； was at an earlier day the birthplace of Pythagoras。 But whereas in the previous century colonists from the confines of the civilized world came to Athens； now all eyes turned towards Alexandria； and so improved were the facilities for communication that no doubt the discoveries of one coterie of workers were known to all the others much more quickly than had ever been possible before。 We learn； for example； that the studies of Aristarchus of Samos were definitely known to Archimedes of Syracuse； out in Sicily。 Indeed； as we shall see； it is through a chance reference preserved in one of the writings of Archimedes that one of the most important speculations of Aristarchus is made known to us。 This illustrates sufficiently the intercommunication through which the thought of the Alexandrian epoch was brought into a single channel。 We no longer； as in the day of the earlier schools of Greek philosophy； have isolated groups of thinkers。 The scientific drama is now played out upon a single stage； and if we pass； as we shall in the present chapter； from Alexandria to Syracuse and from Syracuse to Samos； the shift of scenes does no violence to the dramatic unities。 Notwithstanding the number of great workers who were not properly Alexandrians； none the less the epoch is with propriety termed Alexandrian。 Not merely in the third century B。C。； but throughout the lapse of at least four succeeding centuries； the city of Alexander and the Ptolemies continued to hold its place as the undisputed culture…centre of the world。 During that period Rome rose to its pinnacle of glory and began to decline； without ever challenging the intellectual supremacy of the Egyptian city。 We shall see； in a later chapter； that the Alexandrian influences were passed on to the Mohammedan conquerors； and every one is aware that when Alexandria was finally overthrown its place was taken by another Greek city； Byzantium or Constantinople。 But that transfer did not occur until Alexandria had enjoyed a longer period of supremacy as an intellectual centre than had perhaps ever before been granted to any city； with the possible exception of Babylon。
EUCLID （ABOUT 300 B。C。） Our present concern is with that first wonderful development of scientific activity which began under the first Ptolemy； and which presents； in the course of the first century of Alexandrian influence； the most remarkable coterie of scientific workers and thinkers that antiquity produced。 The earliest group of these new leaders in science had at its head a man whose name has been a household word ever since。 This was Euclid； the father of systematic geometry。 Tradition has preserved to us but little of the personality of this remarkable teacher； but； on the other hand； his most important work has come down to us in its entirety。 The Elements of Geometry； with which the name of Euclid is associated in the mind of every school…boy； presented the chief propositions of its subject in so simple and logical a form that the work remained a textbook everywhere for more than two thousand years。 Indeed it is only now beginning to be superseded。 It is not twenty years since English mathematicians could deplore the fact that； despite certain rather obvious defects of the work of Euclid； no better textbook than this was available。 Euclid's work； of course； gives expression to much knowledge that did not originate with him。 We have already seen that several important propositions of geometry had been developed by Thales； and one by Pythagoras； and that the rudiments of the subject were at least as old as Egyptian civilization。 Precisely how much Euclid added through his own investigations cannot be ascertained。 It seems probable that he was a diffuser of knowledge rather than an originator； but as a great teacher his fame is secure。 He is credited with an epigram which in itself might insure him perpetuity of fame： 〃There is no royal road to geometry；〃 was his answer to Ptolemy when that ruler had questioned whether the Elements might not be simplified。 Doubtless this； like most similar good sayings； is apocryphal； but whoever invented it has made the world his debtor。
HEROPHILUS AND ERASISTRATUS The catholicity of Ptolemy's tastes led him； naturally enough； to cultivate the biological no less than the physical sciences。 In particular his influence permitted an epochal advance in the field of medicine。 Two anatomists became famous through the investigations they were permitted to make under the patronage of the enlightened ruler。 These earliest of really scientific investigators of the mechanism of the human body were named Herophilus and Erasistratus。 These two anatomists gained their knowledge by the dissection of human bodies （theirs are the first records that we have of such practices）； and King Ptolemy himself is said to have been present at some of these dissections。 They were the first to discover that the nerve… trunks have their origin in the brain and spinal cord； and they are credited also with the discovery that these nerve…trunks are of two different kindsone to convey motor； and the other sensory impulses。 They discovered； described； and named the coverings of the brain。 The name of Herophilus is still applied by anatomists； in honor of the discoverer； to one of the sinuses or large canals that convey the venous blood from the head。 Herophilus also noticed and described four cavities or ventricles in the brain； and reached the conclusion that one of these ventricles was the seat of the soula belief shared until comparatively recent times by many physiologists。 He made also a careful and fairly accurate study of the anatomy of the eye； a greatly improved the old operation for cataract。 With the increased knowledge of anatomy came also corresponding advances in surgery； and many experimental operations are said to have been performed upon condemned criminals who were handed over to the surgeons by the Ptolemies。 While many modern writers have attempted to discredit these assertions； it is not improbable that such operations were performed。 In an age when human life was held so cheap； and among a people accustomed to torturing condemned prisoners for comparatively slight offences； it is not unlikely that the surgeons were allowed to inflict perhaps less painful tortures in the cause of science。 Furthermore； we know that condemned criminals were sometimes handed over to the medical profession to be 〃operated upon and killed in whatever way they thought best〃 even as late as the sixteenth century。 Tertullian＇1＇ probably exaggerates； however； when he puts the number of such victims in Alexandria at six hundred。 Had Herophilus and Erasistratus been as happy in their deductions as to the functions of the organs as they were in their knowledge of anatomy； the science of medicine would have been placed upon a very high plane even in their time。 Unfortunately； however； they not only drew erroneous inferences as to the functions of the organs； but also disagreed radically as to what functions certain organs performed； and how diseases should be treated； even when agreeing perfectly on the subject of anatomy itself。 Their contribution to the knowledge of the scientific treatment of diseases holds no such place； therefore； as their anatomical investigations。 Half a century after the time of Herophilus there appeared a Greek physician； Heraclides； whose reputation in the use of drugs far surpasses that of the anatomists of the Alexandrian school。 His reputation has been handed down through the centuries as that of a physician； rather than a surgeon； although in his own time he was considered one of the great surgeons of the period。 Heraclides belonged to the 〃Empiric〃 school； which rejected anatomy as useless； depending entirely on the use of drugs。 He is thought to have been the first physician to point out the value of opium in certain painful diseases。 His prescription of this drug for certain cases of 〃sleeplessness； spasm； cholera； and colic；〃 shows that his use of it was not unlike that of the modern physician in certain cases； and his treatment of fevers； by keeping the patient's head cool and facilitating the secretions of the body； is still recognized as 〃good practice。〃 He advocated a free use of liquids in quenching the fever patient's thirsta recognized therapeutic measure to…day； but one that was widely condemned a century ago。
ARCHIMEDES OF SYRACUSE AND THE FOUNDATION OF MECHANICS We do not know just when Euclid died； but as he was at the height of his fame in the time of Ptolemy I。； whose reign ended in the year 285 B。C。； it is hardly probable that he was still living when a young man named Archimedes came to Alexandria to study。 Archimedes was born in the Greek colony of Syracuse； on the island of Sicily； in the year 287 B。C。 When he visited Alexandria he probably found Apollonius of Perga； the pupil of Euclid； at the head of the mathematical school there。 Just how long Archimedes remained at Alexandria is not known。 When he had satisfied his curiosity or completed his studies； he returned to Syracuse and spent his life there； chiefly under the pa