Hipparchus of Nicaea (/hɪˈpɑːrkəs/; Greek: Ἵππαρχος, Hipparkhos; c. 190 – c. 120 BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry[1] but is most famous for his incidental discovery of precession of the equinoxes.[2]

Hipparchus was born in Nicaea, Bithynia (now İznik, 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 by Meton of Athens (5th century BC), Timocharis, Aristyllus, Aristarchus of Samos and Eratosthenes, among others.[4] 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.

Hipparchos 1.jpeg
Born c. 190 BC
Nicaea, Kingdom of Bithynia
Died c. 120 BC
Rhodes, Roman Republic

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.[5]

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,[6] 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.[7] 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[8] in the more ambitious 2005 paper, thus no specialists in the area accept its widely publicized speculation.[9]

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;[10] he goes on to say that Newton may have been influenced by them.[11] According to one book review, both of these claims have been rejected by other scholars.[12]

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.[13][14]

Babylonian sources

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.[15] 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).[16]

Hipparchus's long draconitic lunar period (5,458 months = 5,923 lunar nodal periods) also appears a few times in Babylonian records.[17] 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 5,458/5,923 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 BC eclipse with a Babylonian eclipse of 720 BC to find the less accurate ratio 7160 synodic months = 7,770 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 BC eclipse with a moonrise 1245 BC eclipse from Babylon, an interval of 13,645 synodic months = 14,8807 1/2 draconitic months ≈ 14,623 1/2 anomalistic months. Dividing by 5/2 produces 5458 synodic months = 5923 precisely.[18] 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 BC, 600 years before his era, the tables were actually good back to before the eclipse in question because as only recently noted[19] their use in reverse is no more difficult than forwards.

Geometry, trigonometry, and other mathematical techniques



He described the chord table in a work, now lost, called Tōn en kuklōi eutheiōn (Of Lines Inside a Circle) by Theon of Alexandria in his 4th-century commentary on the Almagest I.10; some claim his table may have survived in astronomical treatises in India, for instance the Surya Siddhanta. Trigonometry was a significant innovation, because it allowed Greek astronomers to solve any triangle, and made it possible to make quantitative astronomical models and predictions using their preferred geometric techniques.[20]








Lunar and solar theory


Motion of the Moon


Hipparchus could confirm his computations by comparing eclipses from his own time (presumably 27 January 141 BC and 26 November 139 BC according to [Toomer 1980]), with eclipses from Babylonian records 345 years earlier (Almagest IV.2; [A.Jones, 2001]). Already al-Biruni (Qanun VII.2.II) and Copernicus (de revolutionibus IV.4) noted that the period of 4,267 moons is actually about 5 minutes longer than the value for the eclipse period that Ptolemy attributes to Hipparchus. However, the timing methods of the Babylonians had an error of no less than 8 minutes.[27] Modern scholars agree that Hipparchus rounded the eclipse period to the nearest hour, and used it to confirm the validity of the traditional values, rather than try to derive an improved value from his own observations. From modern ephemerides[28] and taking account of the change in the length of the day (see ΔT) we estimate that the error in the assumed length of the synodic month was less than 0.2 seconds in the 4th century BC and less than 0.1 seconds in Hipparchus's time.

Orbit of the Moon



Hipparchus devised a geometrical method to find the parameters from three positions of the Moon, at particular phases of its anomaly. In fact, he did this separately for the eccentric and the epicycle model. Ptolemy describes the details in the Almagest IV.11. Hipparchus used two sets of three lunar eclipse observations, which he carefully selected to satisfy the requirements. The eccentric model he fitted to these eclipses from his Babylonian eclipse list: 22/23 December 383 BC, 18/19 June 382 BC, and 12/13 December 382 BC. The epicycle model he fitted to lunar eclipse observations made in Alexandria at 22 September 201 BC, 19 March 200 BC, and 11 September 200 BC.



Apparent motion of the Sun


Recent expert translation and analysis by Anne Tihon of papyrus P. Fouad 267 A has confirmed the 1991 finding cited above that Hipparchus obtained a summer solstice in 158 BC But the papyrus makes the date June 26, over a day earlier than the 1991 paper's conclusion for June 28. The earlier study's §M found that Hipparchus did not adopt June 26 solstices until 146 BC when he founded the orbit of the sun which Ptolemy later adopted. Dovetailing these data suggests Hipparchus extrapolated the 158 BC June 26 solstice from his 145 solstice 12 years later a procedure that would cause only minuscule error. The papyrus also confirmed that Hipparchus had used Callippic solar motion in 158 BC, a new finding in 1991 but not attested directly until P. Fouad 267 A. Another table on the papyrus is perhaps for sidereal motion and a third table is for Metonic tropical motion, using a previously unknown year of 365 1/4 – 1/309 days. This was presumably found[31] by dividing the 274 years from 432 to 158 BC, into the corresponding interval of 100077 days and 14 3/4 hours between Meton's sunrise and Hipparchus's sunset solstices.

At the end of his career, Hipparchus wrote a book called Peri eniausíou megéthous ("On the Length of the Year") about his results. The established value for the tropical year, introduced by Callippus in or before 330 BC was 365 + 1/4 days.[32] Speculating a Babylonian origin for the Callippic year is hard to defend, since Babylon did not observe solstices thus the only extant System B year length was based on Greek solstices (see below). Hipparchus's equinox observations gave varying results, but he himself points out (quoted in Almagest III.1(H195)) that the observation errors by himself and his predecessors may have been as large as 1/4 day. He used old solstice observations, and determined a difference of about one day in about 300 years. So he set the length of the tropical year to 365 + 1/4 - 1/300 days (= 365.24666... days = 365 days 5 hours 55 min, which differs from the actual value (modern estimate, including earth spin acceleration) in his time of about 365.2425 days, an error of about 6 min per year, an hour per decade, 10 hours per century.



Orbit of the Sun


Distance, parallax, size of the Moon and the Sun







Hipparchus thus had the problematic result that his minimum distance (from book 1) was greater than his maximum mean distance (from book 2). He was intellectually honest about this discrepancy, and probably realized that especially the first method is very sensitive to the accuracy of the observations and parameters. (In fact, modern calculations show that the size of the 189 BC solar eclipse at Alexandria must have been closer to 9/10ths and not the reported 4/5ths, a fraction more closely matched by the degree of totality at Alexandria of eclipses occurring in 310 and 129 BC which were also nearly total in the Hellespont and are thought by many to be more likely possibilities for the eclipse Hipparchus used for his computations.)



See [Toomer 1974] for a more detailed discussion.





Astronomical instruments and astrometry



Equatorial ring
Equatorial ring of Hipparchus's time.




Star catalog

Hipparchus by Raphael
Hipparchus holding his celestial globe, in Raphael's The School of Athens (c. 1510)

Late in his career (possibly about 135 BC) Hipparchus compiled his star catalog, the original of which does not survive. He also constructed a celestial globe depicting the constellations, based on his observations. His interest in the fixed stars may have been inspired by the observation of a supernova (according to Pliny), or by his discovery of precession, according to Ptolemy, who says that Hipparchus could not reconcile his data with earlier observations made by Timocharis and Aristillus. For more information see Discovery of precession. In Raphael's painting The School of Athens, Hipparchus is depicted holding his celestial globe, as the representative figure for astronomy.[37]



As with most of his work, Hipparchus's star catalog was adopted and perhaps expanded by Ptolemy. Delambre, in 1817, cast doubt on Ptolemy's work. It was disputed whether the star catalog in the Almagest is due to Hipparchus, but 1976–2002 statistical and spatial analyses (by R. R. Newton, Dennis Rawlins, Gerd Grasshoff,[38] Keith Pickering[39] and Dennis Duke[40]) have shown conclusively that the Almagest star catalog is almost entirely Hipparchan. Ptolemy has even (since Brahe, 1598) been accused by astronomers of fraud for stating (Syntaxis, book 7, chapter 4) that he observed all 1025 stars: for almost every star he used Hipparchus's data and precessed it to his own epoch ​2 23 centuries later by adding 2°40' to the longitude, using an erroneously small precession constant of 1° per century.


Stellar magnitude

Hipparchus ranked stars in three magnitude very general classes according to their brightness but he did not assign a numerical brightness value to any star. The magnitude system ranging from 1 (brightest) to 6 (faintest) was established by Ptolemy. That system by Ptolemy is effectively still in use today, though extended and made more precise through the introduction of a logarithmic scale by N. R. Pogson in 1856.

Precession of the equinoxes (146–127 BC)



Hipparchus's treatise "Against the Geography of Eratosthenes" in three books is not preserved.[44] Most of our knowledge of it comes from Strabo, according to whom Hipparchus thoroughly and often unfairly criticized Eratosthenes mainly for internal contradictions and inaccuracy in determining positions of geographical localities. Hipparchus insists that a geographic map must be based only on astronomical measurements of latitudes and longitudes and triangulation for finding unknown distances. In geographic theory and methods Hipparchus introduced three main innovations.[45] He was the first to use the grade grid, to determine geographic latitude from star observations, and not only from the sun’s altitude, a method known long before him, and to suggest that geographic longitude could be determined by means of simultaneous observations of lunar eclipses in distant places. In the practical part of his work, the so-called "table of climata", Hipparchus listed latitudes for several tens of localities. In particular, he improved Eratosthenes' values for the latitudes of Athens, Sicily, and southern extremity of India.[46] In calculating latitudes of climata (latitudes correlated with the length of the longest solstitial day), Hipparchus used an unexpectedly accurate value for the obliquity of the ecliptic, 23°40′ (the actual value in the second half of the 2nd century BC was approximately 23°43′), whereas all other ancient authors knew only a roughly rounded value 24°, and even Ptolemy used a less accurate value, 23°51′.[47] Hipparchus opposed the view generally accepted in the Hellenistic period that the Atlantic and Indian Oceans and the Caspian Sea are parts of a single ocean. At the same time he extends the limits of the oikoumene, i.e. the inhabited part of the land, up to the equator and the Arctic Circle.[48] Hipparchus’ ideas found their reflection in the Geography of Ptolemy. In essence, Ptolemy's work is an extended attempt to realize Hipparchus’ vision of what geography ought to be.





Editions and translations


  1. ^ C. M. Linton (2004). From Eudoxus to Einstein: a history of mathematical astronomy. Cambridge University Press. p. 52. ISBN 0-521-82750-7.
  2. ^ G J Toomer's chapter "Ptolemy and his Greek Predecessors" in "Astronomy before the Telescope", British Museum Press, 1996, p. 81.
  4. ^ Jones, Alexander Raymond (2017). Hipparchus. Encyclopedia Brittanica, Inc. Retrieved 25 August 2017.
  6. ^ "Hipparchus of Nicea". Ancient History Encyclopedia. Retrieved June 2016. Check date values in: |access-date= (help)
  13. ^ Stanley, Richard P. (1997), "Hipparchus, Plutarch, Schröder, and Hough" (PDF), The American Mathematical Monthly, 104 (4): 344–350, doi:10.2307/2974582, MR 1450667
  14. ^ Acerbi, F. (2003), "On the shoulders of Hipparchus: A reappraisal of ancient Greek combinatorics" (PDF), Archive for History of Exact Sciences, 57: 465–502, doi:10.1007/s00407-003-0067-0, archived from the original (PDF) on 21 July 2011
  17. ^ Aaboe, Asger (1955), "On the Babylonian origin of some Hipparchian parameters", Centaurus, 4 (2): 122–125, Bibcode:1955Cent....4..122A, doi:10.1111/j.1600-0498.1955.tb00619.x. On p. 124, Aaboe identifies the Hipparchian equation 5458 syn. mo. = 5923 drac. mo. with the equation of 1,30,58 syn. mo. = 1,38,43 drac. mo. (written in sexagesimal) which he cites to p. 73. of Neugebauer's Astronomical Cuneiform Texts, London 1955.
  18. ^ Pro & con arguments are given at DIO volume 11 number 1 article 3 sections C & D.
  19. ^ See demonstration of reverse use of Hipparchus's table for the 1245 BCE eclipse.
  20. ^ Toomer, "The Chord Table of Hipparchus" (1973).
  23. ^ Dennis Rawlins, "Hipparchos' Eclipse-Based Longitudes: Spica & Regulus", DIO 16 (2009).
  24. ^ Detailed dissents on both values are presented in DIO volume 11 number 1 articles 1 & 3 and DIO volume 20 article 3 section L. See also these analyses' summary.
  25. ^ These figures are for dynamical time, not the solar time of Hipparchus's era. E.g., the true 4267 year interval was nearer 126,007 days plus a little over a 1/2 hour.
  26. ^ Footnote 18 of DIO 6 (1996).
  27. ^ Stephenson & Fatoohi 1993; Steele et al. 1997
  28. ^ Chapront et al. 2002
  30. ^ Toomer, 1967
  31. ^ Explained at equation 25 of a recent investigation, paper #2.
  35. ^ Ibid, note 14; Jones 2001
  36. ^ http://eclipse.gsfc.nasa.gov/SEcat5/SE-0199--0100.html, #04310, Fred Espenak, NASA/GSFC
  37. ^ Swerdlow, N. M. (August 1992), "The Enigma of Ptolemy's Catalogue of Stars", Journal for the History of Astronomy, 23: 173–183, Bibcode:1992JHA....23..173S, doi:10.1177/002182869202300303
  39. ^ "Keith Pickering" (PDF). Retrieved 6 August 2012.
  41. ^ Benson Bobrick, The Fated Sky, Simon & Schuster, 2005, p 151
  43. ^ Alexander Jones "Ptolemy in Perspective: Use and Criticism of his Work from Antiquity to the Nineteenth Century, Springer, 2010, p.36.



Further reading

  • Ptolemy (1984). Ptolemy's Almagest. G.J. Toomer, trans. New York: Springer-Verlag. ISBN 0-387-91220-7.

External links



Celestial bodies

Star catalog

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