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HIPPARCHUS was born at Nicæa in Bithynia, and from his astronomical observations it appears that he was living in the interval 160-125 B.C. His observations appear to have been almost entirely taken from the island of Rhodes. Whatever communication he had with Alexandria, there is no evidence that he resided there.
Of the numerous astronomical memoirs which he is recorded to have written, the only one that is extant is his commentary on the poem of Aratus, recording the observations of Eudoxus. Hipparchus was probably young when he wrote this work: it does not mention any of the discoveries that have made him famous. Pliny, writing in the first century A.D., speaks of him with enthusiasm, as a man whom it was impossible to over-praise, and mentions especially his audacious enterprise of constructing a map of the stars. Ptolemy, in the following century, calls him a laborious searcher after truth, and makes continual references to his results. But in the great historical work of Delambre, it was for the first time shown in detail that Ptolemy had acknowledged but a small instalment of his debt; and that the immense reputation enjoyed by him through the times of Arabian and medieval astronomy rested in great part on the discoveries of Hipparchus.
These discoveries are numerous; but the two most important of them, the institution of Trigonometry and the establishment of the precession of the equinoxes, are, as Comte has pointed out, intimately connected with each other. He found, by comparing his own observations of the stars with those made 150 years previously by Aristillus and Timocharis, that their positions as measured perpendicular to the equator and parallel with a fixed point in it (i.e. their declinations and right ascensions), showed notable variation of an apparently irregular kind. The case altered, however, when the two positions of the star were referred not to the equator, but to the ecliptic. Measured perpendicularly to the ecliptic the position of the star--in other words, its latitude--had not changed; but the measurements parallel to the ecliptic, that is to say its longitude, showed a variation amounting to a degree and a half in the period examined. This remarkable phenomenon was geometrically represented by supposing the intersections of the equator with the ecliptic--in other words, the equinoctial points--to alter their positions yearly in a direction opposite to that of the sun's path. They were said to retrograde, so that the equinoxes occurred every year somewhat earlier than would be the case if they remained stationary. The conversion of declinations and right ascensions into latitudes and longitudes shows that Hipparchus had the power of solving the spherical triangle produced by the intersections of the equator and the ecliptic with a meridian; in a word, that he was aquainted with the principles of spherical trigonometry.
But for the further discoveries of Hipparchus on the solar and lunar motions, plane, as well as spherical, trigonometry was needed. We know from Ptolemy that he constructed in twelve books a table of chords. Archimedes half a century before him had inserted in a circle a rectilinear figure of 96 sides. But far more precision than this was needed if angular magnitude was to be brought within the range of arithmetical computation. Taking the radius of the circle as equivalent to 60 units, each unit further divisible into sixty, and so onwards on the sexagesimal scale, he constructed a table showing the numerical value of all chords. The mode of doing this is fully explained in the Almagest of Ptolemy; and it is probable that the method of Hipparchus was similar. It rested on a theorem that, in every four-sided figure inscribed in a circle, the rectangle formed by the diagonals is equal to the two rectangles formed by the opposite sides. Here, then, was an equation between six chords: and, by considering the cases in which some chords were already known, it became possible to calculate the rest. Where one of the diagonals was a diameter, and the other was a perpendicular let fall upon it, the relation between the chord of the arc and the chord of half the arc was not difficult to determine. Knowing already the value of such chords as the diameter, corresponding to the arc of 180°, of the side of the hexagon, which was the chord of 60°, of the chords of 72°, and 36°, the sides respectively of the pentagon and decagon, it now became easy to proceed further by bisection. Ultimately the table included all arcs from half a degree upwards, proceeding by intervals of half a degree. For intermediate values, the thirtieth part of the chord was added for each minute, as a sufficient approximation.
Plane trigonometry was essential for the researches of Hipparchus into the solar and lunar motions. By previous astronomers it was supposed that the sun's motion in the ecliptic was uniform. Hipparchus observed that from the vernal equinox to the summer solstice 94½ days elapsed; 92½ days from this solstice to the autumnal equinox--a correspondingly shorter time, therefore, in the two periods between autumn and spring. That this estimate of the period from vernal to autumnal equinox was a half a day too long is a secondary error due to imperfect instruments. He represented this unequal velocity by supposing the earth placed excentrically in the orbit described by the sun. He valued the degree of this excentricity at one twenty-fourth of the radius, a slightly excessive estimate; and calculated the longitudes of the position at which the sun was nearest to or farthest from the earth (perigee and apogee). The length of the year from vernal equinox to vernal equinox he estimated, more accurately than before by 5 hours 55 minutes and 12 seconds; the true amount is about 6 minutes less.
The motion of the Moon offered a more difficult problem. The motion of this body is unequal both in latitude and longitude. The points of slowest and quickest movement correspond to all parts of the zodiac in succession. Theocratic astronomers had found that, in a period of 223 intervals between one full moon and the next, eclipses recurred in similar order. By careful observation of eclipses, the only precise mode available for ascertaining the moon's position, and by comparison with former observations, Hipparchus, aided always by his calculus, defined the inclination of the moon's orbit to the ecliptic, the amount of the moon's daily motion in the heavens, the motion of her perigee, and also that of her nodes (intersection of her orbit with the ecliptic).
The result of these investigations was that solar and lunar tables could now be formed, defining with much precision the position of the sun and moon in the heavens on any future day. Astronomy began to approach the ideal goal of all scientific research,--prevision.
The Catalogue of Stars formed by Hipparchus, with the longitude and latitude of each accurately defined, must not be passed over. He was led to this by his early work on the poem of Aratus, in which the position of the stars named is very loosely given. Ptolemy, centuries afterwards, gave his own catalogue, purporting to be the result of independent observations. Closely examined, it proves to be the Catalogue of Hipparchus, with an addition to the longitude of each star of Hipparchus' estimate for precession. This estimate is now known to be too slight: and if Ptolemy had made genuine observations of his own he would have discovered the error.
Hipparchus may be regarded as the founder of scientific astronomy. The note of this science is the combination of precise observation with that power of indirectly measuring magnitudes which constitutes the science of mathematics. The records of theocratic astronomy could lead at best to empirical laws, from which rude guesses at the future could be made, frequently falsified by the event. The observations of Hipparchus were made with instruments hardly superior to theirs, and falling short a hundredfold of the precision of a modern observatory. But they were made by a great intellect fortified by geometrical science. Hence they reached the aim by which true science is distinguished from historical or literary erudition, the power of accurately forecasting the future.
It should not be forgotten that Hipparchus, continuing the work begun by Pytheas and Eratosthenes, did much in the application of Astronomy to Geography. He constructed parallels of latitude at intervals of about four degrees through the extent of land known, or conceived, as existing on the earth's surface, from the Arctic circle southwards to within 12 degrees of the equator. He also attempted to fix the meridian of the principal cities of the Mediterranean.
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| This biography is
reprinted from The New Calendar of Great Men. Ed. Frederic
Harrison. London: Macmillan and Co., 1920. |
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