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31 [48] ERATOSTHENES ERATOSTHENES [48] given him. He also went out of his way to treat Archimedes’ relatives kindly. Archimedes’ tomb was lost track of with time. In 75 b . c .,
Cicero, the Roman orator, then governing Sicily, reported having found it Since then, it has been lost to sight once more, though in 1965, Italian archaeologists report a find that possibly is the tomb. [48] ERATOSTHENES (er-uh-tos'-theh- neez)
Greek astronomer Bom: Cyrene (now Shahat, on the Libyan coast), about 276 b .
. Died: Alexandria, about 196 b . c . Eratosthenes, who was educated in Athens, was a friend of Archimedes [47] and a man with interests as universal as those of Aristotle [29]. He was not only an astronomer and geographer, he was also a historian. He attempted to set up a scientific chronology in which all events were dated from the Trojan war; he was the first man in history to con cern himself with the matter of accurate dating. He was even a literary critic and wrote a treatise on Greek comedy. In fact, he was known by the nickname of Beta, the second letter of the Greek al phabet, for in several of the directions in which he chose to exert his talents, he proved the second best in all the world. He was the ideal scholar to put in charge of the Library at Alexandria, and after he had graduated from the Athe nian schools and had turned out some well-regarded writings, he was sum moned to Alexandria by Ptolemy III, about 225 b . c .,
for precisely that post. He served also as tutor for Ptolemy’s son. In mathematics Eratosthenes worked out a system for determining prime num bers that is still called the “sieve of Eratosthenes.” He suggested the intro duction of an extra day every fourth year to keep the Egyptian solar calendar in line with the seasons. Egyptian conser vatism would not accept that sensible no tion and it was not acted upon till the time of Sosigenes [54] a century and a half later. In geography he made a map of the known world, from the British Isles to Ceylon and from the Caspian Sea to Ethiopia, that was better than any drawn before him, though it was to be suc ceeded by the still better work of Hip parchus [50] and Strabo [56] in the course of the next two centuries. In as tronomy he worked out the angle of the earth’s axis to the plane of the sun’s ap parent motion in the sky and got an al most exact value. This is the determi nation of the obliquity of the ecliptic. He also prepared a star map that in cluded 675 stars. However, the astonishing achievement for which Eratosthenes is best known, and for which he remained insufficiently appreciated until modern times, was that of determining the size of the earth about 240 b . c . To do this, he made note of the fact that on the day of the sum mer solstice, the sun was directly over head in Syene (the modem Aswan) in southern Egypt at the same time that it was seven degrees from the zenith in Alexandria. This difference could only be due to the curvature of the earth’s sur face between Syene and Alexandria. Knowing the actual north-south distance between Syene and Alexandria, it was possible to calculate the diameter of the earth, if one assumed it were a sphere with equal curvature on all parts of its surface.
Eratosthenes carried through the cal culation and obtained his results in Greek units of distance (“stadia”). We are not certain how long a stadion is in our units. Taking the most probable length, however, it would seem that Eratosthenes calculated the circum ference of the earth at a little over twenty-five thousand miles, which is al most correct. From this large figure and the comparatively small area of known land, he suspected the various seas to form a single interconnected ocean, a suspicion that proved true but was not verified till the voyage of Magellan [130] eighteen centuries later. Unfortunately this figure seemed too large to the ancients. It meant that the known world occupied only a small por tion of the earth’s total surface, not more 32 [49] APOLLONIUS HIPPARCHUS
than a quarter, and much of that quar ter was sea. The other three quarters ei ther contained other lands, unknown and unheard of, or were entirely water. Both alternatives seemed hard to accept, and the smaller value for the earth’s circum ference, worked out by Poseidonius [52], was accepted by the ancients in prefer ence.
At the age of eighty, Eratosthenes, blind and weary, died of voluntary star vation. [49] APOLLONIUS (ap-uh-loh'nee-us) Greek mathematician Born: Perga (on what is now the southern coast of Turkey), about 262 b
c .
190 b
c . Apollonius was educated at the Mu seum, possibly studying under Archi medes [47], and, in the tradition of Eu clid [40], wrote an eight-book treatise (of which the first seven books survive) on the “conic sections.” These books, which gained him the title of the Great Geometer, include three curves, ellipse, parabola, and hyperbola, with which Eu clid did not deal. All of these can be produced by cutting through a cone at particular angles (hence, “conic sec tion”).
For many centuries Apollonius’ conic sections seemed merely the play of math ematical ingenuity without practical ap plication. In the time of Kepler [169] and Newton [231], however, eighteen centuries later, it was found that the or bits of heavenly bodies were not neces sarily circles at all but could follow a path described by any of the conic sec tions. The most familiar heavenly bodies, the various planets and satellites, includ ing the moon and the earth itself, travel in ellipses. Apollonius may have tried to compro mise the views of Aristarchus [41] and Eudoxus [27] by supposing the planets to revolve about the sun, and the sun with its attendant planets to revolve about the earth. This was similar to the compro mise of Tycho Brahe [156] eighteen cen turies later, and was just as unsuccessful. Late in life, Apollonius left Alexandria for Pergamum, a city in western Asia Minor which at this time had a library second only to that of Alexandria. He was the last topflight mathe matician of the ancient world. [50] HIPPARCHUS (hih-pahrikus) Greek astronomer
northwest Turkey), about 190 b .
. Died: about 120 b . c . Hipparchus was the greatest of the Greek astronomers as Archimedes [47] was the greatest of the Greek mathe maticians, and, like Archimedes, Hip parchus was unusual in that he did not work at Alexandria, although he may have been educated there. He set up his observatory at Rhodes, an island in the southeastern Aegean, and invented many of the instruments used in naked-eye as tronomy for the next seventeen cen turies. Hipparchus carried on the work of Aristarchus [41] measuring the size and distance of the sun and moon. He not only made use of Aristarchus’ lunar eclipse method, but also determined the moon’s parallax. We all experience parallax when we note the apparent shift of the position of a near object com pared with a far one when we change our own position. (From a train window we can see the trees nearby move against the background of the trees farther off.) The angle through which the near ob ject shifts depends both upon the size of your own change of position and upon the distance of the near object. If you know the amount by which you have shifted, you can calculate the distance of the object. To do this, you must know the ratios of the sides of a right triangle for the various angles the sides make with the hypotenuse. The theory was known and some mathematicians man aged to work with such ratios. Hip parchus, however, was the first to work out an accurate table of such ratios
[50] HIPPARCHUS HIPPARCHUS
and is therefore usually considered the founder of trigonometry. By measuring the position of the moon against the stars under appropriately changing conditions, the moon’s parallax can be determined and its distance calcu lated. He found that distance to be thirty times the diameter of the earth, which is correct. If anyone had used the value for the earth’s diameter as determined by Eratosthenes [48], the moon would be shown to be about a quarter million miles from the earth. Unfortunately no other heavenly body is as close to the earth as the moon, and none, therefore, shows so large a paral lax. Before the invention of the tele scope, no other heavenly body showed a parallax large enough to be measured. The moon, therefore, remained the only heavenly body with a known distance from the earth for nineteen centuries after Hipparchus. In 134 b . c . Hipparchus observed a star in the constellation Scorpio of which he could find no record in previous observa tions. This was a serious matter. Nowa days we know that stars, ordinarily too faint to be seen with the naked eye, do occasionally explode, increase in brightness, and become visible, but in Greek times no such thing was imagined. Instead there was the definite belief that the heavens were permanent and un changeable. Hipparchus could not easily tell whether this star was an example of the contrary because of the unsystematic nature of previous observations. He de cided then that future astronomers would not suffer similar difficulties if a new star should appear and proceeded to record the exact positions of a little over a thousand of the brighter stars. This was the first accurate star map and far outclassed the earlier efforts of Eudoxus [27] and Eratosthenes. In order to make his map he plotted the position of each star according to its latitude (angular distance north or south of the equator) and longitude (angular distance east or west of some arbitrary point). It was an easy analogy to plot positions on the earth’s surface in the same way. Latitude and longitude had been used on maps before, notably by Dicaearchus [33] a century and a half before, but with Hipparchus they be came the organized gridwork that they have remained to this day. Hipparchus’ star map led to another important discovery, for in comparing his observations with those he could find among the reports of his predecessors, he found a uniform shift from west to east. He could account for this by supposing that the north celestial pole moved in a slow circle in the sky, completing one cycle in 26,700 years. This meant the equinox arrived a trifling bit earlier each year and the effect was called the “precession of the equinoxes.” It was not until the time of Copernicus [127] that it was shown that the reason for this mo tion was a slow wobble of the earth upon its axis, rather than the star’s movement. And it required Newton [231] eighteen centuries after Hip parchus to explain the cause of the precession. Hipparchus was also the first to divide the stars into classes depending on their brightness. The twenty brightest stars of the sky are of “first magnitude.” Then, in order of decreasing brightness there are second, third, fourth, and fifth mag nitudes, while those of the sixth magni tude are just visible to the naked eye. This system has been kept (although refined and extended) to the present day. Hipparchus’ most ambitious achieve ment, however, was to work out a new scheme of the universe, replacing that of Eudoxus. The work of Callippus [32] and Aristotle [29] had filled the heavens with a large number of spheres and the system had become unwieldy. Hip parchus therefore tackled the matter from a fresh viewpoint, one that had been suggested, but not developed, by Apollonius [49] a half century before. Hipparchus reduced the number of heavenly spheres within the outermost starry celestial vault to seven, one for each of the planets. The individual planet, however, was not actually part of the sphere. It was part of a smaller sphere and it was the center of that smaller sphere that was on the main sphere. The planet moved in a circle as the small sphere turned, and it also 34 [50] HIPPARCHUS POSEIDONIUS
moved along in a larger circle as the center of the small sphere turned as part of the large sphere. The large sphere was the “deferent,” the small sphere the “epi cycle.”
By adjusting the speeds of the two spheres, by piling smaller epicycle upon larger epicycle, the actual motion of the planet could be duplicated. Hipparchus also helped matters by introducing the notion of the eccentric; that is, the sug gestion that a planet did not move about the earth’s center, but about a fictitious point in space that was near the earth’s center, and this fictitious point in turn revolved about the earth’s center. The Hipparchian scheme of the uni verse was highly complicated but it pre served the axioms of Plato and Aristotle, to the effect that the earth was the un moving center of the universe, and that the planets moved in combinations of circles.
Actually it might seem as though the Aristarchean view of the planets revolv ing about the sun was much simpler in concept and that it ought to have won out. This is not so. In the first place it was hard to think of the whole earth flying through space (unless you are taught it is so when you are a child and will believe anything). In addition the Hipparchian scheme was useful and the Aristarchean was not. The changing po sition of the planets was important for ritualistic reasons and in astrology, and what Hipparchus had done was to pro duce a mathematical system for calcu lating the positions of the planets at any given future time. His scheme of epicycles, deferents, and eccentrics helped him perform his calculations, like the construction lines drawn on geometric figures to help ar rive at the proof of a theorem. Looking back at it now, we realize there was no reason to think the “construction lines” were real, but for some sixteen centuries astronomers insisted on thinking they were. Whether the construction lines were real or not, however, Hipparchus’ methods of calculating planetary posi tions worked. On the other hand, the views of Aris tarchus in which the planets circled the sun were merely a pretty picture. The system was not, to our knowledge, worked out mathematically to yield pre dictions of planetary positions. Therefore the scheme was not useful. When Copernicus finally did work out the mathematics of the Aristarchean uni verse, the Hipparchian universe was doomed. [51] SELEUCUS (see-lyoo'kus) Greek astronomer Born: Seleucia (on the Tigris River), about 190 B.c. Died: date unknown A contemporary of Hipparchus [50], Seleucus was far the inferior, but he was the one astronomer of note who cham pioned the notions of Aristarchus [41] concerning the position of the sun at the center of the planetary system. Hip parchus, with his earth-centered system, won out temporarily (if eighteen cen turies can be considered temporary), but it was Seleucus who was right just the same.
Seleucus groped toward an explanation of the tides, feeling that the moon was responsible and noting that the tides did not come at the same time or in the same manner in different parts of the world. He was hampered here by his re fusal to accept Eratosthenes’ [48] view that the earth’s oceans formed a single, interconnected body of water. In this case, he joined Hipparchus in being wrong. Because Seleucus lived in Babylonia, he was commonly called a Chaldean or Babylonian, but he was probably part Greek in descent at least. [52] POSEIDONIUS (pos-ih-doh'nee-us) Greek philosopher
B.C.
Died: ab o ut
50 b . c . Poseidonius was a Stoic philosopher who studied at Athens, later headed a school at Rhodes and had great and influential friends among the Romans.
[52] POSEIDONIUS LUCRETIUS
Cicero and Pompey were among his pu pils. Some of his scientific researches were valuable, for he, like Pytheas [39] two and a half centuries earlier, believed the moon caused the tides and he trav eled west to the Atlantic Ocean to study them. He also worked out a size for the sun that was larger (and therefore closer to the truth) than that proposed by any other ancient astronomer, even Aris tarchus [41], and was the first astrono mer to take into account the refraction of the atmosphere in making his obser vations. He tried, like Aristotle [29] and Eratosthenes [48] before him, to take all knowledge for his province but was less successful, partly because of the accumu lation of knowledge in the two centuries since Aristotle. However, his real importance in his tory lies in an erroneous determination he made. He repeated the work of Eratosthenes in determining the size of the earth. He used the position of the star Canopus in place of the sun, which was, indeed, an improvement over Eratosthenes. Poseidonius, however, ap parently neglected, in this case, to allow for the shift in the star’s position with atmospheric refraction of light and he therefore obtained the too-low figure of eighteen thousand miles for the earth’s circumference. (It is also possible that Strabo [56], the only source we have for this, for Poseidonius’ own works have not survived, misquoted him a half cen tury later.) However that might be, Ptolemy [64] accepted the lower figure in preference to Eratosthenes’ value, and the world of scholarship went along with that decision until the beginning of modem times. Columbus [121], for instance, was en couraged to sail westward from Spain because he believed the lower value and thought Asia lay only three or four thou sand miles westward. Had he known that Eratosthenes was correct and that it lay twelve thousand miles westward, he would probably never have dreamed of sailing, and if he had, he would certainly have got no one to finance him. In addition Poseidonius helped popu larize the doctrines of astrology (that planetary positions influence human affairs) and make them respectable. Plato [24] was mystical enough to lean in that direction, but astronomers such as Eudoxus [27] had opposed it. With Poseidonius, astrology won and its perni cious influence over true astronomy was to endure seventeen centuries, into the time of Kepler [169]. [53] LUCRETIUS (lyoo-kree'shee-us); in full, TITUS LUCRETIUS CARUS Roman philosopher and poet Born: Rome, about 95 b . c .
ab o u t 55
b . c . From 200 b .
. onward, Rome domi nated the Mediterranean world politi cally, militarily, and economically, but never intellectually. Leadership in sci ence was left in Greek hands to the very end of ancient times. When Roman thinkers did concern themselves with sci ence, it was as transmitters rather than as originators. Lucretius was the best of these. He was a convinced and ardent follower of Epicurus [35], In his book De Natura
published in 56 b .
., he expounded a mechanistic Epicurean view of the uni verse in a long poem. Lucretius held that all things were composed of atoms, quite in line with the theories of Democritus [20], and this he carried to the ultimate extreme. Even such immaterial objects as the mind and soul, said Lucretius, are made up of atoms, which are, however, finer than the atoms making up gross material things.
Lucretius did not deny the existence of gods, but held that they too were com posed of atoms and that they did not concern themselves with the affairs of men. Nor did he believe in a life hereaf ter, but considered death the prelude to peaceful nothingness and therefore not to be feared. Lucretius envisaged an evolutionary universe, one that developed slowly to its present state, physically, biologically, and sociologically—quite a modem view. He was the first to divide human history, for
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