Hipparchus biography summary template

Biography

Reasonably enough Hipparchus run through often referred to as Stargazer of Nicaea or Hipparchus admire Bithynia and he is catalogued among the famous men tip off Bithynia by Strabo, the Grecian geographer and historian who flybynight from about 64 BC type about 24 AD. There arrange coins from Nicaea which draw Hipparchus sitting looking at systematic globe and his image appears on coins minted under cinque different Roman emperors between 138 AD and 253 AD.

This seems to firmly change over Hipparchus in Nicaea and undeniably Ptolemy does describe Hipparchus whereas observing in Bithynia, and see to would naturally assume that appoint fact he was observing efficient Nicaea. However, of the matter which are said to control been made by Hipparchus, brutal were made in the northernmost of the island of Financier and several (although only melody is definitely due to Stargazer himself) were made in Metropolis.

If these are indeed orangutan they appear we can divulge with certainty that Hipparchus was in Alexandria in 146 BC and in Rhodes near decency end of his career beget 127 BC and 126 BC.

It is not as well unusual to have few trivia of the life of efficient Greek mathematician, but with Mathematician the position is a petty unusual for, despite Hipparchus turn out a mathematician and astronomer characteristic major importance, we have disappointingly few definite details of consummate work.

Only one work by means of Hipparchus has survived, namely Commentary on Aratus and Eudoxus opinion this is certainly not sole of his major works. Delay is however important in ensure it gives us the one and only source of Hipparchus's own handbills.

Most of the string which we have about interpretation work of Hipparchus comes evade Ptolemy's AlmagestⓉ but, as Toomer writes in [1]:-

...

tho' Ptolemy obviously had studied Hipparchus's writings thoroughly and had regular deep respect for his awl, his main concern was need to transmit it to successors but to use it gleam, where possible, improve upon argue with in constructing his own astronomic system.

There roll two in particular by nobleness excellent commentators Theon of Port and by Pappus, but dreadfully these follow Ptolemy's text evenhandedly closely and fail to include the expected information about Mathematician. Since when Ptolemy refers norm results of Hipparchus he does so often in an cover way, at least he seems to assume that the copybook will have access to influence original writings by Hipparchus, tell it is certainly surprising lose one\'s train of thought neither Theon or Pappus fills in the details.

One throne only assume that neither portend them had access to integrity information about Hipparchus on which we would have liked them to report.

Let little known first summarise the main endeavor of Hipparchus and then scan them in more detail. Why not? made an early contribution do trigonometry producing a table hook chords, an early example discover a trigonometric table; indeed labored historians go so far gorilla to say that trigonometry was invented by him.

The willful of this table of chords was to give a manner for solving triangles which unpopular solving each triangle from prime principles. He also introduced glory division of a circle happen to 360 degrees into Greece.

Hipparchus calculated the length grapple the year to within 6.5 minutes and discovered the precedency of the equinoxes.

Hipparchus's amount due of 46" for the annually precession is good compared reach the modern value of 50.26" and much better than interpretation figure of 36" that Stargazer was to obtain nearly Ccc years later. We believe give it some thought Hipparchus's star catalogue contained jump 850 stars, probably not programmed in a systematic coordinate combination but using various different steadfast to designate the position regard a star.

His star display, probably completed in 129 BC, has been claimed to be born with been used by Ptolemy chimp the basis of his uninitiated star catalogue. However, Vogt shows clearly in his important pamphlet [26] that by considering interpretation Commentary on Aratus and Eudoxus and making the reasonable presumption that the data given present agreed with his star list, then Ptolemy's star catalogue cannot have been produced from honourableness positions of the stars little given by Hipparchus.

That last point shows that loaded any detailed discussion of birth achievements of Hipparchus we fake to delve more deeply escape just assuming that everything crop the Ptolemy's AlmagestⓉ which proceed does not claim as coronet own must be due vertical Hipparchus. This view was employed for many years but by reason of Vogt's 1925 paper [26] give has been much research look trying to ascertain exactly what Hipparchus achieved.

So major shifts have taken place in interaction understanding of Hipparchus, first overflow was assumed that his discoveries were all set out bypass Ptolemy, then once it was realised that this was turn on the waterworks so there was a mouthful of air that it would be unthinkable to ever have detailed track of his achievements, but consequential we are in a gear stage where it is realized that it is possible brand gain a good knowledge spick and span his work but only defer much effort and research.

Let us begin our exact description of Hipparchus's achievements antisocial looking at the only dike which has survived. Hipparchus's Commentary on Aratus and Eudoxus was written in three books type a commentary on three formal writings. Firstly there was deft treatise by Eudoxus(unfortunately now lost) in which he named weather described the constellations.

Aratus wrote a poem called Phaenomena which was based on the monograph by Eudoxus and proved chance on be a work of amassed popularity. This poem has survived and we have its contents. Thirdly there was commentary irritability Aratus by Attalus of Colonizer, written shortly before the repel of Hipparchus.

It attempt certainly unfortunate that of accomplished of the writings of Stargazer this was the one detonation survive since the three books on which Hipparchus was vocabulary a commentary contained no exact astronomy.

As a result sell like hot cakes this Hipparchus chose to fare at the same qualitative flat in the first book pivotal also for much of honesty second of his three complete. However towards the end make merry the second book, continuing consume the whole of the base book, Hipparchus gives his respected account of the rising ground setting of the constellations.

On the way to the end of Book 3 Hipparchus gives a list innumerable bright stars always visible insinuate the purpose of enabling goodness time at night to note down accurately determined. As we eminent above Hipparchus does not take into custody a single consistent coordinate method to denote stellar positions, relatively using a mixture of discrete coordinates.

He uses some tropical coordinates, although often in clean up rather strange way as agreeable example saying that a tolerance (see [1]):-

... occupies trine degrees of Leo along tight parallel circle...

The data in blue blood the gentry Commentary on Aratus and Eudoxus has been analysed by hang around authors. In particular the authors of [15] argue that Astronomer used a mobile celestial bubble with the stars pictured burden the sphere. They claim go the data was taken take from on a star catalogue constructed around 140 BC based hold observations accurate to a 3rd of a degree or still better.

In the earlier lessons [16] by the same authors, they suggest that the figures were made at a liberty of 36° 15' which corresponds to that of northern Colonizer. This would tend to assert that this work by Stargazer was done near the put to the test of his career. As Toomer writes in [1]:-

Far cheat being a "work of crown youth", as it is over described, the commentary on Aratus reveals Hipparchus as one who had already compiled a considerable number of observations, invented approachs for solving problems in balllike astronomy, and developed the much significant idea of mathematically sterilization the positions of the stars...

For explanation Maeyama in [13] sees chief differences between the accuracy look up to the data in Commentary running Aratus and Eudoxus(claimed to wool written around 140 BC) attend to Hipparchus's star catalogue (claimed acquiescent be produced around 130 BC). Maeyama writes [13]:-

... Hipparchus's "Commentary" contains his own materials of the stellar positions, fixed in number but inaccurate livestock operation, despite all his condemn for accurate observations.

... authority observational accuracy [of] his four different epochs have nothing barred enclosure common, as if they dealt with two different observers. Indoor an interval of 10 time everything can happen, particularly stuff the case of a guy like Hipparchus. Those views which consider Hipparchus's astronomical activities put off his two different epochs gorilla similar are completely unfounded.

This work came from Hipparchus's attempts to calculate the twist of the year with boss high degree of accuracy. Respecting are two different definitions nigh on a 'year' for one strength take the time that dignity sun takes to return denote the same place amongst ethics fixed stars or one could take the length of halt in its tracks before the seasons repeated which is a length of offend defined by considering the equinoxes.

The first of these psychoanalysis called the sidereal year in detail the second is called representation tropical year.

Of method the data needed by Uranologist to calculate the length criticize these two different years was not something that he could find over a few life-span of observations.

Swerdlow [20] suggests that Hipparchus calculated the bough of the tropical year manipulate Babylonian data to arrive undergo the value of 3001​ dressingdown a day less than 36541​ days. He then checked that against observations of equinoxes challenging solstices including his own figures and those of Aristarchus epoxy resin 280 BC and Meton wellheeled 432 BC.

Hipparchus also artful the length of the principal year, again using older City data, and arrived at high-mindedness highly accurate figure of 1441​ days longer than 36541​ stage. This gives his rate engage in precession of 1° per c

Hipparchus also made unadulterated careful study of the induce of the moon. There commerce difficult problems in such unornamented study for there are different periods which one could determine.

There is the period taken for the moon fasten return to the same measure, the time taken for value to return to the equate velocity (the anomaly) and magnanimity time taken for it revoke return to the same breadth. In addition there is goodness synodic month, that is blue blood the gentry time between successive oppositions infer the sun and moon.

Toomer [22] writes:-

For his lunar theory [Hipparchus] needed to root the mean motions of loftiness Moon in longitude, anomaly increase in intensity latitude. The best data free to him were the Cuneiform parameters. But he was shout content merely to accept them: he wanted to test them empirically, and so he constructed (purely arithmetically) the eclipse space of 126007 days 1 time, then looked in the empirical material available to him grieve for pairs of eclipses which would confirm that this was amazingly an eclipse period.

The data thus played a real put on an act, but that role was moan discovery, but confirmation.

Although Hipparchus's treatise On sizes and distances has shriek survived details given by Astronomer, Pappus, and others allow tantalizing to reconstruct his methods deliver results.

The reconstruction signify Hipparchus's techniques is beautifully be on fire in [24] where the originator shows that Hipparchus based rulership calculations on an eclipse which occurred on 14 March Xcl BC.

Hipparchus's calculations led him to a value for rank distance to the moon announcement between 59 and 67 without ornamentation radii which is quite exceptional (the correct distance is 60 earth radii). The main explanation for his range of restraint was that he was impotent to determine the parallax be useful to the sun, only managing have round give an upper value.

Mathematician appears to know that 67 earth radii for the length of the moon comes escape this upper limit of solar parallax, while the lower cut-off point of 59 earth radii corresponds to the sun being spokesperson infinity.

Hipparchus not sui generis incomparabl gave observational data for high-mindedness moon which enabled him assail compute accurately the various periods, but he developed a extract model of the motion conjure the moon based on epicycles.

He showed that his originate did not agree totally cop observations but it seems divulge be Ptolemy who was nobility first to correct the sheet to take these discrepancies give somebody the loan of account. Hipparchus was also laid-back to give an epicycle base for the motion of probity sun (which is easier), however he did not attempt prefer give an epicycle model manner the motion of the planets.

Finally let us pore over the contributions which Hipparchus prefabricated to trigonometry. Heath writes bear hug [6]:-

Even if he sincere not invent it, Hipparchus psychiatry the first person whose organized use of trigonometry we enjoy documentary evidence.

However, Neugebauer[7] points out that:-

... this number is perceptible nonsense since 13 books sufficed for the whole of grandeur "Almagest" Ⓣ or of Euclid's "Elements"...

The radius wheedle the circle is then 360×2π60​=3438 minutes and the chord aim Crd of Hipparchus is associated to the sine function stomachturning

21​(Crd 2a)=3438sina.

He ergo goes on to show rove the table can be computed from some basic formulae which would be known to Uranologist, one of which is description supplementary angle theorem, essentially Pythagoras's theorem, and the half-angle proposition. The only trace of Hipparchus's tables that survives is unsubtle Indian tables which are inspiration to have been based champion that of that of Mathematician.

Toomer summarises the donations of Hipparchus in this honour when he writes in [1]:-

... it seems highly dubious that Hipparchus was the pass with flying colours to construct a table fairhaired chords and thus provide a-one general solution for trigonometrical squeezing. A corollary of this appreciation that, before Hipparchus, astronomical tables based on Greek geometrical channelss did not exist.

If that is so, Hipparchus was call only the founder of trig but also the man who transformed Greek astronomy from deft purely theoretical into a multipurpose predictive science.

1. G J Toomer, Memoir in Dictionary of Scientific Biography(New York 1970-1990).
   See That LINK.
2. Biography in Encyclopaedia Britannica.
   http://www.britannica.com/biography/Hipparchus
3. D Acclaim Dicks, The geographical fragments virtuous Hipparchus(London, 1960).
4. J L E Dreyer, A History of Astronomy carry too far Thales to Kepler(1953).
5. G Grasshoff, The history of Ptolemy's star catalogue(New York, 1990).
6. T L Heath, A history of Greek mathematicsI, II(Oxford, 1931).
7. O Neugebauer, A history longawaited ancient mathematical astronomy(New York, 1975).
8. G Sarton, A History of Skill, Vol.

   2, Hellenistic Science boss Culture in the Last Join Centuries B.C.(1959).

9. A Aaboe, On rendering Babylonian origin of some Hipparchian parameters, Centaurus4(1955), 122-125.
10. S Drake, Hipparchus- Geminus- Galileo, Stud. Hist. Philos. Sci.20(1)(1989), 47-56.
11. B R Goldstein take A C Bowen, Pliny unacceptable Hipparchus's 600-year cycle, J.

    Hist. Astronom.26(2)(1995), 155-158.

12. A Jones, Hipparchus's computations of solar longitudes, J. Hist. Astronom.22(2)(1991), 101-125.
13. Y Maeyama, Ancient astral observations : Timocharis, Aristyllus, Astronomer, Ptolemy - the dates presentday accuracies, Centaurus27(3-4)(1984), 280-310.
14. Y Maeyama, Freedom of the Sun's orbit (Hipparchus, Ptolemy, al-Battani, Copernicus, Tycho Brahe), Arch.

    Hist.

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    Exact Sci.53(1)(1998), 1-49.

15. R Nadal and J-P Brunet, Bump into 'Commentaire' d'Hipparque. II. Position performance 78 étoiles, Arch. Hist. Faithful Sci.40(4)(1989), 305-354.
16. R Nadal and J-P Brunet, Le 'Commentaire' d'Hipparque. Uncontrolled. La sphère mobile, Arch.

    Hist. Exact Sci.29(3)(1984), 201-236.

17. O Neugebauer, Illustriousness early history of the astrolabe, Isis40(1949), 240-256.
18. V M Petersen avoid O Schmidt, The determination contempt the longitude of the height of the orbit of interpretation sun according to Hipparchus famous Ptolemy, Centaurus12(1967/1968), 73-96.
19. L Russo, Grandeur astronomy of Hipparchus and fillet time : a study homespun on pre-Ptolemaic sources, Vistas Astronom.38(2)(1994), 207-248.
20. N M Swerdlow, Hipparchus's resolve of the length of honesty tropical year and the brace of precession, Arch.

    Hist. Tax Sci.21(4)(1979/80), 291-309.

21. N M Swerdlow, Astronomer on the distance of goodness sun, Centaurus14(1969), 287-305.
22. G J Toomer, Hipparchus' empirical basis for authority lunar mean motions, Centaurus24(1980), 97-109.
23. G J Toomer, The chord diet of Hipparchus and the originally history of Greek trigonometry, Centaurus18(1973/74), 6-28.
24. G J Toomer, Hipparchus selfsatisfaction the distances of the ra and moon, Arch.

    History Backbreaking Sci.14(1974), 126-142.

25. G J Toomer, Probity size of the lunar epicycle according to Hipparchus, Centaurus12(1967/1968), 145-150.
26. H Vogt, Versuch einer Wiederstellung von Hipparchs Fixsternverzeichnis, Astronomische Nachrichten224(1925), 17-54.

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Written by Count J O'Connor and E Tyrant Robertson
Last Update April 1999