by Will Durant
Delighted with this demonstration, the King asked Archimedes to design some engines of war. It was characteristic of the two men that Archimedes, having designed them, forgot them, and that Hieron, loving peace, never used them. Archimedes, says Plutarch,
possessed so high a spirit, so profound a soul, and such treasures of scientific knowledge, that though these inventions had now obtained for him the renown of more than human sagacity, he yet would not deign to leave behind him any writing on such subjects; but, repudiating as sordid and ignoble . . . every sort of art that lends itself to mere use and profit, he placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life—studies whose superiority to all others is unquestioned, and in which the only doubt can be whether the beauty and grandeur of the subjects examined, or the precision and cogency of the methods and means of proof, most deserve our admiration.11
But when Hieron was dead Syracuse became embroiled with Rome, and the doughty Marcellus assailed it by land and sea. Though Archimedes was now (212) a man of seventy-five, he superintended the defense on both fronts. Behind the walls that protected the harbor he set up catapults able to hurl heavy stones to a considerable distance; their rain of projectiles was so devastating that Marcellus retreated until he could advance by night. But when the ships were seen near the shore the sailors were harassed by bowmen who shot at them through the holes that Archimedes’ aides had pierced in the wall. Moreover, the inventor had arranged within the walls great cranes which, when the Roman vessels came within reach, were turned by cranks and pulleys so as to drop upon the ships heavy weights of stone or lead that sank many of them. Other cranes, armed with gigantic hooks, grasped vessels, lifted them into the air, dashed them against the rocks, or plunged them end-foremost into the sea.*12 Marcellus withdrew his fleet, and put his hopes in an attack by land. But Archimedes bombarded the troops with large stones thrown by catapults to such effect that the Romans fled, saying that they were being opposed by gods; and they refused to advance again.14 “Such a great and marvelous thing,” comments Polybius, “does the genius of one man show itself to be when properly applied. The Romans, strong both by sea and by land, had every hope of capturing the town at once if one old man of Syracuse were removed; as long as he was present they did not venture to attack.”15
Abandoning the idea of taking Syracuse by storm, Marcellus resigned himself to a slow blockade. After a siege of eight months the starving city surrendered. In the slaughter and pillage that followed Marcellus gave orders that Archimedes should not be injured. During the sack a Roman soldier came upon an aged Syracusan absorbed in studying figures that he had traced in the sand. The Roman commanded him to present himself at once to Marcellus. Archimedes refused to go until he had worked out his problem; he “earnestly besought the soldier,” says Plutarch, “to wait a little while, that he might not leave what he was at work upon inconclusive and imperfect, but the soldier, nothing moved by this entreaty, instantly killed him.”16 When Marcellus heard of it he mourned, and did everything in his power to console the relatives of the dead man.17 The Roman general erected to his memory a handsome tomb, on which was engraved, in accordance with the mathematician’s expressed wish, a sphere within a cylinder; to have found formulas for the area and volume of these figures was, in Archimedes’ view, the supreme achievement of his life. He was not far wrong; for to add one significant proposition to geometry is of greater value to humanity than to besiege or defend a city. We must rank Archimedes with Newton, and credit him with “a sum of mathematical achievement unsurpassed by any one man in the world’s history.”18
But for the abundance and cheapness of slaves Archimedes might have been the head of a veritable Industrial Revolution. A treatise on Mechanical Problems wrongly attributed to Aristotle, and a Treatise on Weights wrongly ascribed to Euclid, had laid down certain elementary principles of statics and dynamics a century before Archimedes. Strato of Lampsacus, who succeeded Theophrastus as head of the Lyceum, turned his deterministic materialism to physics, and (about 280) formulated the doctrine that “nature abhors a vacuum.”19 When he added that “a vacuum can be created by artificial means,” he opened the way to a thousand inventions. Ctesibius of Alexandria (ca. 200) studied the physics of siphons (which had been used in Egypt as far back as 1500 B.C.), and developed the force pump, the hydraulic organ, and the hydraulic clock. Archimedes probably improved—and unwittingly gave his name to—the ancient Egyptian water screw, which literally made water flow uphill.20 Philon of Byzantium, about 150, invented pneumatic machines, and various engines of war.21 The steam engine of Heron of Alexandria, which came after the Roman conquest of Greece, brought this period of mechanical development to a climax and close. The philosophical tradition was too strong; Greek thought went back to theory, and Greek industry contented itself with slaves. The Greeks were acquainted with the magnet, and the electrical properties of amber, but they saw no industrial possibilities in these curious phenomena. Antiquity unconsciously decided that it was not worth while to be modern.
III. ARISTARCHUS, HIPPARCHUS, ERATOSTHENES
Greek mathematics owed its Hellenistic stimulus and blossoming to Egypt, Greek astronomy to Babylon. Alexander’s opening of the East led to a resumption and extension of that trade in ideas which, three centuries earlier, had assisted at the birth of Greek science in Ionia. To this fresh contact with Egypt and the Near East we may ascribe the anomaly of Greek science reaching its height in the Hellenistic age, when Greek literature and art were in decline.
Aristarchus of Samos was a bright interregnum in the rule of the geocentric theory over Greek astronomy. He burned with such zeal that he studied almost all its branches, and achieved distinction in many of them.23 In his only extant treatise, On the Sizes and Distances of the Sun and the Moon,* there is no hint of heliocentricism; on the contrary it assumes that the sun and the moon move in circles about the earth. But Archimedes’ Sand-Reckoner explicitly credits Aristarchus with the “hypothesis that the fixed stars and the sun remain unmoved; the earth revolves about the sun in the circumference of a circle, the sun lying in the middle of the orbit”;24 and Plutarch reports that Cleanthes the Stoic held that Aristarchus should be indicted for “putting the Hearth of the Universe” (i.e., the earth) “in motion.”25 Seleucus of Seleucia defended the heliocentric view, but the opinion of the Greek scientific world decided against it. Aristarchus himself seems to have abandoned his hypothesis when he failed to reconcile it with the supposedly circular movements of the heavenly bodies; for all Greek astronomers took it for granted that these orbits were circular. Perhaps a distaste for hemlock moved Aristarchus to be the Galileo as well as the Copernicus of the ancient world.
It was the misfortune of Hellenistic science that the greatest of Greek astronomers attacked the heliocentric theory with arguments that seemed irrefutable before Copernicus. Hipparchus of Nicaea (in Bithynia), despite what seems to us an epoch-making blunder, was a scientist of the highest type—endlessly curious to know, devotedly patient in research, and so carefully accurate in observation and report that antiquity called him “the lover of truth.”26 He touched and adorned nearly every field of astronomy, and fixed its conclusions for seventeen centuries. Only one of his many works remains—a commentary on the Phainomena of Eudoxus and Aratus of Soli; but we know him from Claudius Ptolemy’s Almagest (ca. A.D. 140), which is based upon his researches and calculations; “Ptolemaic astronomy” should be called Hipparchian. He improved, probably on Babylonian models, the astrolabes and quadrants that were the chief astronomical instruments of his time. He invented the method of determining terrestrial positions by lines of latitude and longitude, and tried to organize the astronomers of the Mediterranean world to make observations and measurements that would fix in these terms the location of all important cities; political disturbances frustrated the plan until Ptolemy’s more orderly age. His mathematical studies of astronomic relations led Hipparchus to formulate a
table of sines, and thereby to create the science of trigonometry. Helped, no doubt, by the cuneiform records which had been brought from Babylonia, he determined with approximate accuracy the length of the solar, lunar, and sidereal years. He reckoned the solar year as 365¼ days minus 4 minutes and 48 seconds—an error of 6 minutes according to current calculations. His time for a mean lunar month was 29 days, 12 hours, 44 minutes, and 2½ seconds—less than a second away from the accepted figure.27 He computed, with impressive approximation to modern measurements, the synodic periods of the planets, the obliquity of the ecliptic and of the moon’s orbit, the apogee of the sun, and the horizontal parallax of the moon.28 He estimated the distance of the moon from the earth as 250,000 miles—an error of only five per cent.
Armed with all this knowledge, Hipparchus concluded that the geocentric view better explained the data than did the hypothesis of Aristarchus; the heliocentric theory could not stand mathematical analysis except by supposing an elliptical orbit for the earth, and this supposition was so uncongenial to Greek thought that even Aristarchus does not appear to have considered it. Hipparchus verged upon it by his theory of “eccentrics,” which accounted for the apparent irregularities in the orbital velocities of the sun and the moon by suggesting that the centers of the solar and lunar orbits were slightly to one side of the earth. So near did Hipparchus come to being the greatest theorist, as well as the greatest observer, among ancient astronomers.
Watching the sky night after night, Hipparchus was surprised one evening by the appearance of a star where he was sure there had been none before. To certify later changes he made, about 129 B.C., a catalogue, a map, and a globe of the heavens, giving the positions of 1080 fixed stars in terms of celestial latitude and longitude—an immense boon to subsequent students of the sky. Comparing his chart with that which Timochares had made 166 years before, Hipparchus calculated that the stars had shifted their apparent position some two degrees in the interval. On this basis he made the subtlest of his discoveries*—the precession of the equinoxes—the slight advance, day by day, of the moment when the equinoctial points come to the meridian,† He calculated the precession as thirty-six seconds per year; the current estimate is fifty.
We have displaced from his chronological position between Aristarchus and Hipparchus a scholar whose ecumenical erudition won him the nicknames of Pentathlos and Beta—because he attained distinction in many fields, and ranked second only to the best in each. Tradition gave Eratosthenes of Cyrene exceptional teachers: Zeno the Stoic, Arcesilaus the skeptic, Callimachus the poet, Lysanias the grammarian. By the age of forty his reputation for varied knowledge was so great that Ptolemy III made him head of the Alexandrian Library. He wrote a volume of verse, and a history of comedy. His Chronographia sought to determine the dates of the major events in Mediterranean history. He wrote mathematical monographs, and devised a mechanical method for finding mean proportions in continued proportion between two straight lines. He measured the obliquity of the ecliptic at 23° 51′, an error of one half of one per cent. His greatest achievement was his calculation of the earth’s circumference as 24,662 miles;30 we compute it at 24,847. Observing that at noon on the summer solstice the sun at Syene shone directly upon the deep surface of a narrow well, and learning that at the same moment the shadow of an obelisk at Alexandria, some five hundred miles north, showed the sun to be approximately 7½° away from the zenith as measured on the meridian of longitude that connected the two cities, he concluded that an arc of 7½° on the earth’s circumference equaled five hundred miles, and that the entire circumference would equal 360÷7.5×500, or 24,000 miles.
Having measured the earth, Eratosthenes proceeded to describe it. His Geographica brought together the reports of Alexander’s surveyors, of travelers like Megasthenes, voyagers like Nearchus, and explorers like Pytheas of Massalia, who, about 320, had sailed around Scotland to Norway, and perhaps to the Arctic Circle.31 Eratosthenes did not merely depict the physical features of each region, he sought to explain them through the action of water, fire, earthquake, or volcanic eruption.32 He bade the Greeks abandon their provincial division of mankind into Hellenes and barbarians; men should be divided not nationally but individually; many Greeks, he thought, were scoundrels, many Persians and Hindus were refined, and the Romans had shown a greater aptitude than the Greeks for social order and competent government.33 He knew little of northern Europe or northern Asia, less of India south of the Ganges, nothing of south Africa; but he was, so far as we know, the first geographer to mention the Chinese. “If,” said another significant passage, “the extent of the Atlantic Ocean were not an obstacle, we might easily pass by sea from Iberia (Spain) to India, keeping in the same parallel.”34
IV. THEOPHRASTUS, HEROPHILUS, ERASISTRATUS
Zoology never rose again in antiquity to the level that it had reached in Aristotle’s History of Animals. Probably by an agreed division of labor his successor Theophrastus wrote a classic treatise, The History of Plants, and a more theoretical discussion called The Causes of Plants. Theophrastus loved gardening, and knew every aspect of his subject. In many ways he was more scientific than his master, more careful of his facts, and more orderly in his exposition; a book without classification, he said, was as untrustworthy as an unbridled horse.35 He divided all plants into trees, bushes, shrubs, and herbs, and distinguished the chief parts of a plant as root, stem, branch, twig, leaf, flower, and fruit—a classification not improved on till A.D. 1561.36 “A plant,” he wrote, “has the power of germination in all its parts, for it has life in them all. . . . The methods of generation of plants are these: spontaneous, from a seed, a root, a piece torn off, a branch, a twig, pieces of wood cut up small, or from the trunk itself.”37 He had no clear idea of sexual reproduction in plants, except in a few species like the fig tree or the date palm; here he followed the Babylonians in describing fertilization and caprification. He discussed the geographical distribution of plants, their industrial uses, and the climatic conditions most conducive to their health. He studied the minutiae of half a thousand species with an accuracy of detail astonishing in an age that had no microscope. Twenty centuries before Goethe he recognized that the flower is a metamorphosed leaf.38 He was a naturalist in more ways than one, stoutly rejecting the supernatural explanations current in his day for certain curiosities of botany.39 He had all the inquisitiveness of a scientist, and did not think it beneath his dignity as a philosopher to write monographs on stones, minerals, weather, winds, weariness, geometry, astronomy, and the physical theories of the pre-Socratic Greeks.40 “If there had been no Aristotle,” says Sarton, “this period would have been called the time of Theophrastus.”41
Theophrastus’ ninth “book” summarized all that the Greeks knew about the medicinal properties of plants. One passage hinted at anesthesia in describing “dittany, a plant especially useful for labor in women; people say that either it makes labor easy, or it stops the pains.”42 Medicine progressed rapidly in this age, perhaps because it had to keep pace with the novel and multiplying diseases of a complex urban civilization. The Greek study of Egyptian medical lore stimulated a fresh advance. The Ptolemies were ruthlessly helpful; they not only permitted the dissection of animals and cadavers, but turned over some condemned criminals for vivisection.43 Under these encouragements human anatomy became a science, and the absurdities into which Aristotle had fallen were substantially reduced.
Herophilus of Chalcedon, working at Alexandria about 285, dissected the eye and gave a good account of the retina and the optic nerves. He dissected the brain, described the cerebrum, the cerebellum, and the meninges, left his name in the torcular Herophili* and restored the brain to honor as the seat of thought. He understood the role of the nerves, originated their division into sensory and motor, and separated the cranial from the spinal nerves. He distinguished arteries from veins, discerned the function of the arteries as carrying blood from the heart to various parts of the body, and in effect discovered the circulation of the blood
nineteen centuries before Harvey.44 Following a suggestion of the Coan physician Praxagoras, he included the taking of the pulse in diagnosis, and used a water clock to measure its frequency. He dissected and described the ovaries, the uterus, the seminal vesicles, and the prostate gland; he studied the liver and the pancreas, and gave to the duodenum the name that it still bears.45“Science and art,” wrote Herophilus, “have nothing to show, strength is incapable of effort, wealth is useless, and eloquence is powerless, where there is no health.”46
Herophilus was, so far as we can now judge, the greatest anatomist of antiquity, and Erasistratus was the greatest physiologist. Born in Ceos, Erasistratus studied in Athens, and practiced medicine in Alexandria about 258 B.C. He distinguished more carefully than Herophilus between cerebrum and cerebellum, and made experiments on living subjects to study the operation of the brain. He described and explained the working of the epiglottis, the lacteal vessels of the mesentery, and the aortic and pulmonary valves of the heart. He had some notion of basal metabolism, for he devised a crude respiration calorimeter47 Every organ, said Erasistratus, is connected with the rest of the organism in three ways—by artery, vein, and nerve. He sought to account for all physiological phenomena by natural causes, rejecting any reference to mystical entities. He discarded the humoral theory of Hippocrates, which Herophilus had retained. He conceived the art of medicine as prevention through hygiene rather than as cure through therapy; he opposed the frequent use of drugs and bloodletting, and relied upon diet, bathing, and exercise.48