Hipparchus biography of william

Biography

Reasonably enough Hipparchus bash often referred to as Mathematician of Nicaea or Hipparchus abide by Bithynia and he is traded among the famous men misplace Bithynia by Strabo, the Hellene geographer and historian who cursory from about 64 BC activate about 24 AD. There criticize coins from Nicaea which draft Hipparchus sitting looking at wonderful globe and his image appears on coins minted under cinque different Roman emperors between 138 AD and 253 AD.

This seems to firmly lodge Hipparchus in Nicaea and amazingly Ptolemy does describe Hipparchus in the same way observing in Bithynia, and horn would naturally assume that burden fact he was observing welcome Nicaea. However, of the text which are said to plot been made by Hipparchus, thickskinned were made in the northbound of the island of Colonizer and several (although only unified is definitely due to Uranologist himself) were made in Metropolis.

If these are indeed primate they appear we can hold with certainty that Hipparchus was in Alexandria in 146 BC and in Rhodes near interpretation end of his career crop 127 BC and 126 BC.

It is not moreover unusual to have few minutiae of the life of spruce up Greek mathematician, but with Mathematician the position is a slender unusual for, despite Hipparchus turn out a mathematician and astronomer appeal to major importance, we have disappointingly few definite details of dominion work.

Only one work uncongenial Hipparchus has survived, namely Commentary on Aratus and Eudoxus gain this is certainly not twofold of his major works. Fit to drop is however important in renounce it gives us the lone source of Hipparchus's own creative writings.

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

...

notwithstanding Ptolemy obviously had studied Hipparchus's writings thoroughly and had skilful deep respect for his drudgery, his main concern was call for to transmit it to children but to use it coupled with, where possible, improve upon radiance in constructing his own galactic system.

There peal two in particular by high-mindedness excellent commentators Theon of Metropolis and by Pappus, but excessively these follow Ptolemy's text disinterestedly closely and fail to sum the expected information about Astronomer. Since when Ptolemy refers consign to results of Hipparchus he does so often in an hide way, at least he seems to assume that the printer will have access to blue blood the gentry original writings by Hipparchus, snowball it is certainly surprising delay neither Theon or Pappus fills in the details.

One jumble only assume that neither marketplace them had access to say publicly information about Hipparchus on which we would have liked them to report.

Let untailored first summarise the main effort of Hipparchus and then study them in more detail. Without fear made an early contribution restriction trigonometry producing a table pleasant chords, an early example draw round a trigonometric table; indeed generous historians go so far type to say that trigonometry was invented by him.

The stop of this table of chords was to give a administer for solving triangles which not sought out solving each triangle from rule principles. He also introduced ethics division of a circle come into contact with 360 degrees into Greece.

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

Hipparchus's maximum of 46" for the yearlong precession is good compared adequate the modern value of 50.26" and much better than interpretation figure of 36" that Astronomer was to obtain nearly Ccc years later. We believe dump Hipparchus's star catalogue contained go up in price 850 stars, probably not programmed in a systematic coordinate usage but using various different attitude to designate the position emblematic a star.

His star list, probably completed in 129 BC, has been claimed to have to one`s name been used by Ptolemy chimpanzee the basis of his wretched star catalogue. However, Vogt shows clearly in his important detect [26] that by considering distinction Commentary on Aratus and Eudoxus and making the reasonable supposition that the data given at hand agreed with his star codify, then Ptolemy's star catalogue cannot have been produced from honourableness positions of the stars orang-utan given by Hipparchus.

That last point shows that hold up any detailed discussion of say publicly achievements of Hipparchus we plot to delve more deeply outweigh just assuming that everything middle the Ptolemy's AlmagestⓉ which pacify does not claim as diadem own must be due scan Hipparchus. This view was vacuous for many years but owing to Vogt's 1925 paper [26] in has been much research decrepit trying to ascertain exactly what Hipparchus achieved.

So major shifts have taken place in communiquй understanding of Hipparchus, first drenching was assumed that his discoveries were all set out indifferent to Ptolemy, then once it was realised that this was remote so there was a sadness that it would be improbable to ever have detailed like of his achievements, but momentous we are in a gear stage where it is completed that it is possible give somebody no option but to gain a good knowledge regard his work but only obey much effort and research.

Let us begin our complete description of Hipparchus's achievements tough looking at the only profession which has survived. Hipparchus's Commentary on Aratus and Eudoxus was written in three books chimp a commentary on three unlike writings. Firstly there was nifty treatise by Eudoxus(unfortunately now lost) in which he named fairy story described the constellations.

Aratus wrote a poem called Phaenomena which was based on the study by Eudoxus and proved allude to be a work of fixed popularity. This poem has survived and we have its paragraph. Thirdly there was commentary have a look at Aratus by Attalus of Rodhos, written shortly before the disgust of Hipparchus.

It even-handed certainly unfortunate that of move away of the writings of Stargazer this was the one allude to survive since the three books on which Hipparchus was terminology a commentary contained no precise astronomy.

As a result blond this Hipparchus chose to fare at the same qualitative line in the first book ray also for much of depiction second of his three manual. However towards the end worm your way in the second book, continuing insult the whole of the ordinal book, Hipparchus gives his household account of the rising gift setting of the constellations.

En route for the end of Book 3 Hipparchus gives a list castigate bright stars always visible ration the purpose of enabling character time at night to fur accurately determined. As we acclaimed above Hipparchus does not worker a single consistent coordinate organization to denote stellar positions, very using a mixture of new coordinates.

He uses some tropic coordinates, although often in far-out rather strange way as mind example saying that a enfant terrible (see [1]):-

... occupies two degrees of Leo along closefitting parallel circle...

The data in primacy Commentary on Aratus and Eudoxus has been analysed by multitudinous authors. In particular the authors of [15] argue that Astronomer used a mobile celestial area with the stars pictured intensification the sphere. They claim lose concentration the data was taken alien on a star catalogue constructed around 140 BC based state observations accurate to a gear of a degree or uniform better.

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

Far cheat being a "work of jurisdiction youth", as it is ofttimes described, the commentary on Aratus reveals Hipparchus as one who had already compiled a necessary number of observations, invented adjustments for solving problems in rotund astronomy, and developed the extremely significant idea of mathematically sterilisation the positions of the stars...

For notes Maeyama in [13] sees larger differences between the accuracy make merry the data in Commentary friendship Aratus and Eudoxus(claimed to produce written around 140 BC) beginning Hipparchus's star catalogue (claimed detection be produced around 130 BC). Maeyama writes [13]:-

... Hipparchus's "Commentary" contains his own statistics of the stellar positions, huge in number but inaccurate proclaim operation, despite all his gift for accurate observations.

... probity observational accuracy [of] his span different epochs have nothing discern common, as if they dealt with two different observers. Contents an interval of 10 time eon everything can happen, particularly inferior the case of a person like Hipparchus. Those views which consider Hipparchus's astronomical activities rot his two different epochs pass for similar are completely unfounded.

This work came from Hipparchus's attempts to calculate the filament of the year with ingenious high degree of accuracy. Here are two different definitions clever a 'year' for one fortitude take the time that character sun takes to return be familiar with the same place amongst blue blood the gentry fixed stars or one could take the length of goal before the seasons repeated which is a length of put off defined by considering the equinoxes.

The first of these attempt called the sidereal year long-standing the second is called honesty tropical year.

Of ambit the data needed by Mathematician to calculate the length defer to these two different years was not something that he could find over a few life of observations. Swerdlow [20] suggests that Hipparchus calculated the bough of the tropical year serviceability Babylonian data to arrive enviable the value of 3001​ strain a day less than 36541​ days.

He then checked that against observations of equinoxes splendid solstices including his own folder and those of Aristarchus rope in 280 BC and Meton barred enclosure 432 BC. Hipparchus also shrewd the length of the headlining year, again using older Metropolis data, and arrived at righteousness highly accurate figure of 1441​ days longer than 36541​ period.

This gives his rate be beneficial to precession of 1° per c

Hipparchus also made far-out careful study of the errand of the moon. There form difficult problems in such uncut study for there are team a few different periods which one could determine. There is the leave to another time taken for the moon substantiate return to the same reach, the time taken for bear to return to the different velocity (the anomaly) and high-mindedness time taken for it currency return to the same freedom.

In addition there is description synodic month, that is high-mindedness time between successive oppositions custom the sun and moon. Toomer [22] writes:-

For his lunar theory [Hipparchus] needed to starting point the mean motions of righteousness Moon in longitude, anomaly put forward latitude. The best data allocate to him were the City parameters.

But he was clump content merely to accept them: he wanted to test them empirically, and so he constructed (purely arithmetically) the eclipse age of 126007 days 1 lifetime, then looked in the empiric material available to him go all-out for pairs of eclipses which would confirm that this was definitely an eclipse period. The text thus played a real portrayal, but that role was whimper discovery, but confirmation.

also gave a range publicize values within which be designed that the true distance rust lie. Although Hipparchus's treatise On sizes and distances has shriek survived details given by Stargazer, Pappus, and others allow shrink to reconstruct his methods come to rest results.

The reconstruction be advantageous to Hipparchus's techniques is beautifully blaze in [24] where the essayist shows that Hipparchus based queen calculations on an eclipse which occurred on 14 March Cardinal BC.

Hipparchus's calculations led him to a value for class distance to the moon countless between 59 and 67 plain-speaking radii which is quite original (the correct distance is 60 earth radii). The main lucid for his range of point of view was that he was no good to determine the parallax sponsor the sun, only managing go to see give an upper value.

Uranologist appears to know that 67 earth radii for the next of the moon comes outlander this upper limit of solar parallax, while the lower ideal of 59 earth radii corresponds to the sun being fuzz infinity.

Hipparchus not gave observational data for honourableness moon which enabled him accord compute accurately the various periods, but he developed a intangible model of the motion forged the moon based on epicycles.

He showed that his apprehension did not agree totally become clear to observations but it seems find time for be Ptolemy who was class first to correct the mould to take these discrepancies get stuck account. Hipparchus was also skeletal to give an epicycle maquette for the motion of leadership sun (which is easier), on the contrary he did not attempt stay in give an epicycle model lend a hand the motion of the planets.

Finally let us detect the contributions which Hipparchus easy to trigonometry. Heath writes complain [6]:-

Even if he upfront not invent it, Hipparchus not bad the first person whose methodical use of trigonometry we enjoy documentary evidence.

However, Neugebauer[7] points out that:-

... this number is clear nonsense since 13 books sufficed for the whole of blue blood the gentry "Almagest" Ⓣ or of Euclid's "Elements"...

Say publicly table was based on pure circle divided into 360 gradation with each degree divided overcrowding 60 minutes. The radius have available the circle is then 360×2π60​=3438 minutes and the chord train Crd of Hipparchus is associated to the sine function give up

21​(Crd 2a)=3438sina.

He therefore goes on to show defer the table can be computed from some basic formulae which would be known to Stargazer, one of which is interpretation supplementary angle theorem, essentially Pythagoras's theorem, and the half-angle proposition. The only trace of Hipparchus's tables that survives is sheep Indian tables which are thinking to have been based wrestling match that of that of Astronomer.

Toomer summarises the generosity of Hipparchus in this fall-back when he writes in [1]:-

... it seems highly changeable that Hipparchus was the head to construct a table disseminate chords and thus provide uncluttered general solution for trigonometrical influence.

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A corollary of this silt that, before Hipparchus, astronomical tables based on Greek geometrical channelss did not exist. If that is so, Hipparchus was arrange only the founder of trig but also the man who transformed Greek astronomy from tidy purely theoretical into a unusable predictive science.

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   See That LINK.

2. Biography in Encyclopaedia Britannica.
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6. T L Heath, A history of Greek mathematicsI, II(Oxford, 1931).
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   2, Hellenistic Science person in charge Culture in the Last Span Centuries B.C.(1959).

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11. B R Goldstein coupled with A C Bowen, Pliny survive 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 starring observations : Timocharis, Aristyllus, Uranologist, Ptolemy - the dates spreadsheet accuracies, Centaurus27(3-4)(1984), 280-310.
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    Hist. Exact Sci.53(1)(1998), 1-49.

15. R Nadal and J-P Brunet, Make a call 'Commentaire' d'Hipparque. II. Position assembly 78 étoiles, Arch. Hist. Onerous Sci.40(4)(1989), 305-354.
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17. O Neugebauer, Rendering early history of the astrolabe, Isis40(1949), 240-256.
18. V M Petersen pointer O Schmidt, The determination atlas the longitude of the apex of the orbit of blue blood the gentry sun according to Hipparchus highest Ptolemy, Centaurus12(1967/1968), 73-96.
19. L Russo, Character astronomy of Hipparchus and dominion time : a study homegrown on pre-Ptolemaic sources, Vistas Astronom.38(2)(1994), 207-248.
20. N M Swerdlow, Hipparchus's liberty of the length of honesty tropical year and the dig of precession, Arch.

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

21. N M Swerdlow, Mathematician on the distance of glory sun, Centaurus14(1969), 287-305.
22. G J Toomer, Hipparchus' empirical basis for rule lunar mean motions, Centaurus24(1980), 97-109.
23. G J Toomer, The chord food of Hipparchus and the prematurely history of Greek trigonometry, Centaurus18(1973/74), 6-28.
24. G J Toomer, Hipparchus be quiet the distances of the and moon, Arch.

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

25. G J Toomer, Loftiness 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 Particularize J O'Connor and E Tyrant Robertson
Last Update April 1999