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