Hipparchus
| Hipparchus | |
|---|---|
 |
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| Born | c. 190 BC Nicaea, Kingdom of Bithynia |
| Died | c. 120 BC Rhodes, Roman Republic |
| Occupation | |
Hipparchus was born in Nicaea, Bithynia (now Iznik, Turkey), and probably died on the island of Rhodes. He is known to have been a working astronomer at least from 162 to 127 BC.[3] Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity. He was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. For this he certainly made use of the observations and perhaps the mathematical techniques accumulated over centuries by the Babylonians and other people from Mesopotamia. He developed trigonometry and constructed trigonometric tables, and he solved several problems of spherical trigonometry. With his solar and lunar theories and his trigonometry, he may have been the first to develop a reliable method to predict solar eclipses. His other reputed achievements include the discovery and measurement of Earth's precession, the compilation of the first comprehensive star catalog of the western world, and possibly the invention of the astrolabe, also of the armillary sphere, which he used during the creation of much of the star catalogue.
Contents
Life and work
Relatively little of Hipparchus's direct work survives into modern times. Although he wrote at least fourteen books, only his commentary on the popular astronomical poem by Aratus was preserved by later copyists. Most of what is known about Hipparchus comes from Strabo's Geography and Pliny's Natural History in the 1st century; Ptolemy's 2nd-century Almagest; and additional references to him in the 4th century by Pappus of Alexandria and Theon of Alexandria in their commentaries on the Almagest.[4]There is a strong tradition that Hipparchus was born in Nicaea (Greek Νίκαια), in the ancient district of Bithynia (modern-day Iznik in province Bursa), in what today is the country Turkey.
The exact dates of his life are not known, but Ptolemy attributes to him astronomical observations in the period from 147–127 BC, and some of these are stated as made in Rhodes; earlier observations since 162 BC might also have been made by him. His birth date (c. 190 BC) was calculated by Delambre based on clues in his work. Hipparchus must have lived some time after 127 BC because he analyzed and published his observations from that year. Hipparchus obtained information from Alexandria as well as Babylon, but it is not known when or if he visited these places. He is believed to have died on the island of Rhodes, where he seems to have spent most of his later life.
It is not known what Hipparchus's economic means were nor how he supported his scientific activities. His appearance is likewise unknown: there are no contemporary portraits. In the 2nd and 3rd centuries coins were made in his honour in Bithynia that bear his name and show him with a globe; this supports the tradition that he was born there.
Hipparchus is thought to be the first to calculate a heliocentric system,[5] but he abandoned his work because the calculations showed the orbits were not perfectly circular as believed to be mandatory by the science of the time. As an astronomer of antiquity his influence, supported by ideas from Aristotle, held sway for nearly 2000 years, until the heliocentric model of Copernicus.
Hipparchus's only preserved work is Τῶν Ἀράτου καὶ Εὐδόξου φαινομένων ἐξήγησις ("Commentary on the Phaenomena of Eudoxus and Aratus"). This is a highly critical commentary in the form of two books on a popular poem by Aratus based on the work by Eudoxus.[6] Hipparchus also made a list of his major works, which apparently mentioned about fourteen books, but which is only known from references by later authors. His famous star catalog was incorporated into the one by Ptolemy, and may be almost perfectly reconstructed by subtraction of two and two thirds degrees from the longitudes of Ptolemy's stars. The first trigonometric table was apparently compiled by Hipparchus, who is now consequently known as "the father of trigonometry".
Modern speculation
Hipparchus was in the international news in 2005, when it was again proposed (as in 1898) that the data on the celestial globe of Hipparchus or in his star catalog may have been preserved in the only surviving large ancient celestial globe which depicts the constellations with moderate accuracy, the globe carried by the Farnese Atlas. There are a variety of mis-steps[7] in the more ambitious 2005 paper, thus no specialists in the area accept its widely publicized speculation.[8]Lucio Russo has said that Plutarch, in his work On the Face in the Moon, was reporting some physical theories that we consider to be Newtonian and that these may have come originally from Hipparchus;[9] he goes on to say that Newton may have been influenced by them.[10] According to one book review, both of these claims have been rejected by other scholars.[11]
A line in Plutarch's Table Talk states that Hipparchus counted 103049 compound propositions that can be formed from ten simple propositions. 103049 is the tenth Schröder–Hipparchus number, which counts the number of ways of adding one or more pairs of parentheses around consecutive subsequences of two or more items in any sequence of ten symbols. This has led to speculation that Hipparchus knew about enumerative combinatorics, a field of mathematics that developed independently in modern mathematics.[12][13]
Babylonian sources
Further information: Babylonian astronomy
Earlier Greek astronomers and mathematicians were influenced by
Babylonian astronomy to some extent, for instance the period relations
of the Metonic cycle and Saros cycle may have come from Babylonian sources (see "Babylonian astronomical diaries"). Hipparchus seems to have been the first to exploit Babylonian astronomical knowledge and techniques systematically.[14] Except for Timocharis and Aristillus, he was the first Greek known to divide the circle in 360 degrees of 60 arc minutes (Eratosthenes before him used a simpler sexagesimal system dividing a circle into 60 parts). He also used the Babylonian unit pechus ("cubit") of about 2° or 2.5°.Hipparchus probably compiled a list of Babylonian astronomical observations; G. J. Toomer, a historian of astronomy, has suggested that Ptolemy's knowledge of eclipse records and other Babylonian observations in the Almagest came from a list made by Hipparchus. Hipparchus's use of Babylonian sources has always been known in a general way, because of Ptolemy's statements. However, Franz Xaver Kugler demonstrated that the synodic and anomalistic periods that Ptolemy attributes to Hipparchus had already been used in Babylonian ephemerides, specifically the collection of texts nowadays called "System B" (sometimes attributed to Kidinnu).[15]
Hipparchus's long draconitic lunar period (5458 months = 5923 lunar nodal periods) also appears a few times in Babylonian records.[16] But the only such tablet explicitly dated is post-Hipparchus so the direction of transmission is not settled by the tablets.
Hipparchus's draconitic lunar motion cannot be solved by the lunar-four arguments that are sometimes proposed to explain his anomalistic motion. A solution that has produced the exact 5458/5923 ratio is rejected by most historians though it uses the only anciently attested method of determining such ratios, and it automatically delivers the ratio's four-digit numerator and denominator. Hipparchus initially used (Almagest 6.9) his 141 B. C. E. eclipse with a Babylonian eclipse of 720 B. C. E. to find the less accurate ratio 7160 synodic months = 7770 draconitic months, simplified by him to 716 = 777 through division by 10. (He similarly found from the 345-year cycle the ratio 4267 synodic months = 4573 anomalistic months and divided by 17 to obtain the standard ratio 251 synodic months = 269 anomalistic months.) If he sought a longer time base for this draconitic investigation he could use his same 141 B. C. E. eclipse with a moonrise 1245 B. C. E. eclipse from Babylon, an interval of 13645 synodic months = 148807 1/2 draconitic months ≈ 14623 1/2 anomalistic months. Dividing by 5/2 produces 5458 synodic months = 5923 precisely.[17] The obvious main objection is that the early eclipse is unattested though that is not surprising in itself and there is no consensus on whether Babylonian observations were recorded this remotely. Though Hipparchus's tables formally went back only to 747 B. C. E., 600 years before his era, the tables were actually good back to before the eclipse in question because as only recently noted[18] their use in reverse is no more difficult than forwards.
Geometry, trigonometry, and other mathematical techniques
Hipparchus was recognized as the first mathematician known to have possessed a trigonometric table, which he needed when computing the eccentricity of the orbits of the Moon and Sun. He tabulated values for the chord function, which gives the length of the chord for each angle. He did this for a circle with a circumference of 21600 and a radius (rounded) of 3438 units: this circle has a unit length of 1 arc minute along its perimeter. He tabulated the chords for angles with increments of 7.5°. In modern terms, the chord of an angle equals the radius times twice the sine of half of the angle, i.e.:- chord(A) = r(2 sin(A/2)).
For his chord table Hipparchus must have used a better approximation for π than the one from Archimedes of between 3 + 1/7 and 3 + 10/71; perhaps he had the one later used by Ptolemy: 3;8:30 (sexagesimal) (Almagest VI.7); but it is not known if he computed an improved value himself.
But some scholars do not believe Arayabhatta's Sin table has anything to do with Hipparchus's chord table which does not exist today. Some scholars do not agree with this hypothesis that Hipparchus constructed a chord table. Bo. C Klintberg states "With mathematical reconstructions and philosophical arguments I show that Toomer's 1973 paper never contained any conclusive evidence for his claims that Hipparchus had a 3438'-based chord table, and that the Indians used that table to compute their sine tables. Recalculating Toomer's reconstructions with a 3600' radius – i.e. the radius of the chord table in Ptolemy's Almagest, expressed in 'minutes' instead of 'degrees' – generates Hipparchan-like ratios similar to those produced by a 3438' radius. It is therefore possible that the radius of Hipparchus's chord table was 3600', and that the Indians independently constructed their 3438'-based sine table." [20]
Hipparchus could construct his chord table using the Pythagorean theorem and a theorem known to Archimedes. He also might have developed and used the theorem in plane geometry called Ptolemy's theorem, because it was proved by Ptolemy in his Almagest (I.10) (later elaborated on by Carnot).
Hipparchus was the first to show that the stereographic projection is conformal, and that it transforms circles on the sphere that do not pass through the center of projection to circles on the plane. This was the basis for the astrolabe.
Besides geometry, Hipparchus also used arithmetic techniques developed by the Chaldeans. He was one of the first Greek mathematicians to do this, and in this way expanded the techniques available to astronomers and geographers.
There are several indications that Hipparchus knew spherical trigonometry, but the first surviving text of it is that of Menelaus of Alexandria in the 1st century, who on that basis is now commonly credited with its discovery. (Previous to the finding of the proofs of Menelaus a century ago, Ptolemy was credited with the invention of spherical trigonometry.) Ptolemy later used spherical trigonometry to compute things like the rising and setting points of the ecliptic, or to take account of the lunar parallax. Hipparchus may have used a globe for these tasks, reading values off coordinate grids drawn on it, or he may have made approximations from planar geometry, or perhaps used arithmetical approximations developed by the Chaldeans. He might have used spherical trigonometry.
Aubrey Diller has shown that the clima calculations which Strabo preserved from Hipparchus were performed by spherical trigonometry with the sole accurate obliquity known to have been used by ancient astronomers, 23°40'. All thirteen clima figures agree with Diller's proposal.[21] Further confirming his contention is the finding that the big errors in Hipparchus's longitude of Regulus and both longitudes of Spica agree to a few minutes in all three instances with a theory that he took the wrong sign for his correction for parallax when using eclipses for determining stars' positions.
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