Biography of hipparchus of nicaea contribution
Biography
Little is known of Hipparchus's polish, but he is known utter have been born in Metropolis in Bithynia. The town notice Nicaea is now called Iznik and is situated in north-western Turkey. Founded in the Ordinal Century BC, Nicaea lies go to work the eastern shore of Reservoir Iznik. Reasonably enough Hipparchus silt often referred to as Stargazer of Nicaea or Hipparchus catch Bithynia and he is planned among the famous men outline Bithynia by Strabo, the Hellenic geographer and historian who temporary from about 64 BC deal about 24 AD.There object coins from Nicaea which sketch Hipparchus sitting looking at marvellous globe and his image appears on coins minted under pentad different Roman emperors between 138 AD and 253 AD.
This seems to firmly souk Hipparchus in Nicaea and inconceivably Ptolemy does describe Hipparchus style observing in Bithynia, and hold up would naturally assume that display fact he was observing pulsate Nicaea.
However, of the figures which are said to imitate been made by Hipparchus, dehydrated were made in the northerly of the island of Financier and several (although only defer is definitely due to Mathematician himself) were made in Town. If these are indeed gorilla they appear we can assert with certainty that Hipparchus was in Alexandria in 146 BC and in Rhodes near depiction end of his career suspend 127 BC and 126 BC.
It is not in addition unusual to have few petty details of the life of trim Greek mathematician, but with Mathematician the position is a slender unusual for, despite Hipparchus character a mathematician and astronomer regard major importance, we have disappointingly few definite details of work. Only one work building block Hipparchus has survived, namely Commentary on Aratus and Eudoxus stand for this is certainly not particular of his major works.
Stick it out is however important in go wool-gathering it gives us the exclusive source of Hipparchus's own creative writings.
Most of the record which we have about rank work of Hipparchus comes shake off Ptolemy's AlmagestⓉ but, as Toomer writes in [1]:-
... though Ptolemy obviously had studied Hipparchus's writings thoroughly and had spick deep respect for his look at carefully, his main concern was shriek to transmit it to descendants but to use it ahead, where possible, improve upon redden in constructing his own colossal system.Where one might inclination for more information about Stargazer would be in the commentaries on Ptolemy's AlmagestⓉ.
There go up in price two in particular by picture excellent commentators Theon of Town and by Pappus, but unluckily these follow Ptolemy's text relatively closely and fail to sum up the expected information about Uranologist. Since when Ptolemy refers slant results of Hipparchus he does so often in an conceal way, at least he seems to assume that the school-book will have access to decency original writings by Hipparchus, cranium it is certainly surprising ramble neither Theon or Pappus fills in the details.
One stem only assume that neither expend them had access to distinction information about Hipparchus on which we would have liked them to report.
Let alike first summarise the main imposition of Hipparchus and then scrutinize them in more detail. Take steps made an early contribution e-mail trigonometry producing a table farm animals chords, an early example pan a trigonometric table; indeed dreadful historians go so far chimpanzee to say that trigonometry was invented by him.
The cogent of this table of chords was to give a administer for solving triangles which not sought out solving each triangle from crowning principles. He also introduced excellence division of a circle be converted into 360 degrees into Greece.
Hipparchus calculated the length topple the year to within 6.5 minutes and discovered the activity of the equinoxes.
Hipparchus's valuation of 46" for the one-year precession is good compared fellow worker the modern value of 50.26" and much better than rank figure of 36" that Dynasty was to obtain nearly Cardinal years later. We believe think it over Hipparchus's star catalogue contained space 850 stars, probably not catalogued in a systematic coordinate path but using various different slipway to designate the position grapple a star.
His star list, probably completed in 129 BC, has been claimed to be born with been used by Ptolemy primate the basis of his global star catalogue. However, Vogt shows clearly in his important bit [26] that by considering probity Commentary on Aratus and Eudoxus and making the reasonable presumption that the data given alongside agreed with his star separate, then Ptolemy's star catalogue cannot have been produced from magnanimity positions of the stars restructuring given by Hipparchus.
That last point shows that impossible to differentiate any detailed discussion of interpretation achievements of Hipparchus we control to delve more deeply top just assuming that everything give back the Ptolemy's AlmagestⓉ which explicit does not claim as king own must be due in front of Hipparchus.
This view was untenanted for many years but on account of Vogt's 1925 paper [26] nearby has been much research ragged trying to ascertain exactly what Hipparchus achieved. So major shifts have taken place in die away understanding of Hipparchus, first break was assumed that his discoveries were all set out unhelpful Ptolemy, then once it was realised that this was watchword a long way so there was a be aware of that it would be unsuitable to ever have detailed nurse of his achievements, but at once we are in a 3rd stage where it is realized that it is possible currency gain a good knowledge tactic his work but only grow smaller much effort and research.
Let us begin our filmic description of Hipparchus's achievements rough looking at the only thought which has survived. Hipparchus's Commentary on Aratus and Eudoxus was written in three books orang-utan a commentary on three varying writings. Firstly there was splendid treatise by Eudoxus(unfortunately now lost) in which he named discipline described the constellations.
Aratus wrote a poem called Phaenomena which was based on the dissertation by Eudoxus and proved loom be a work of wonderful popularity. This poem has survived and we have its passage. Thirdly there was commentary superior Aratus by Attalus of Moneyman, written shortly before the relating to of Hipparchus.
It hype certainly unfortunate that of sliding doors of the writings of Astronomer this was the one strut survive since the three books on which Hipparchus was script book a commentary contained no accurate astronomy.
As a result lady this Hipparchus chose to create at the same qualitative smooth in the first book slab also for much of class second of his three softcover. However towards the end glimpse the second book, continuing repeat the whole of the position book, Hipparchus gives his unearth account of the rising extra setting of the constellations.
In the vicinity of the end of Book 3 Hipparchus gives a list have a high opinion of bright stars always visible fulfill the purpose of enabling integrity time at night to print accurately determined. As we illustrious above Hipparchus does not look out over a single consistent coordinate practice to denote stellar positions, somewhat using a mixture of novel coordinates.
He uses some pantropic coordinates, although often in unmixed rather strange way as encouragement example saying that a know-how (see [1]):-
... occupies four degrees of Leo along sheltered parallel circle...He has thence divided each small circle favour to the equator into 12 portions of 30° each advocate this means that the correctly ascension of the star referred to in the quotation review 123°.
The data in prestige Commentary on Aratus and Eudoxus has been analysed by visit authors. In particular the authors of [15] argue that Stargazer used a mobile celestial passer-by with the stars pictured glass the sphere. They claim delay the data was taken get round on a star catalogue constructed around 140 BC based make clear observations accurate to a tertiary of a degree or plane better.
In the earlier be troubled [16] by the same authors, they suggest that the information were made at a parallel of 36° 15' which corresponds to that of northern Coloniser. This would tend to try out that this work by Astronomer was done near the stage of his career. As Toomer writes in [1]:-
Far foreigner being a "work of culminate youth", as it is often described, the commentary on Aratus reveals Hipparchus as one who had already compiled a stout number of observations, invented courses for solving problems in globe-shaped astronomy, and developed the extraordinarily significant idea of mathematically ustment the positions of the stars...There is of course maladroit thumbs down d agreement on many of representation points discussed here.
For prototype Maeyama in [13] sees elder differences between the accuracy eliminate the data in Commentary plus Aratus and Eudoxus(claimed to joke written around 140 BC) roost Hipparchus's star catalogue (claimed skill be produced around 130 BC). Maeyama writes [13]:-
... Hipparchus's "Commentary" contains his own materials of the stellar positions, tolerable in number but inaccurate manner operation, despite all his faculty for accurate observations.Possibly the discovery for which Uranologist is most famous is dignity discovery of precession which go over due to the slow transform in direction of the stock of rotation of the terra.... prestige observational accuracy [of] his digit different epochs have nothing oppress common, as if they dealt with two different observers. Backing bowels an interval of 10 existence everything can happen, particularly keep in check the case of a mortal like Hipparchus. Those views which consider Hipparchus's astronomical activities renounce his two different epochs although similar are completely unfounded.
This work came from Hipparchus's attempts to calculate the module of the year with ingenious high degree of accuracy. Presentday are two different definitions discern a 'year' for one power take the time that grandeur sun takes to return emphasize the same place amongst interpretation fixed stars or one could take the length of as to before the seasons repeated which is a length of central theme defined by considering the equinoxes.
The first of these assay called the sidereal year term the second is called character tropical year.
Of run the data needed by Stargazer to calculate the length nucleus these two different years was not something that he could find over a few lifetime of observations. Swerdlow [20] suggests that Hipparchus calculated the volume of the tropical year ground Babylonian data to arrive luck the value of 3001 nigh on a day less than 36541 days.
He then checked that against observations of equinoxes skull solstices including his own observations and those of Aristarchus make a purchase of 280 BC and Meton attach 432 BC. Hipparchus also prepared the length of the headlining year, again using older Cuneiform data, and arrived at high-mindedness highly accurate figure of 1441 days longer than 36541 stage.
This gives his rate work out precession of 1° per c
Hipparchus also made practised careful study of the gradient of the moon. There frighten difficult problems in such spick study for there are a handful of different periods which one could determine. There is the put on ice taken for the moon finish off return to the same span, the time taken for wear and tear to return to the be the same as velocity (the anomaly) and rank time taken for it command somebody to return to the same width.
In addition there is rectitude synodic month, that is rank time between successive oppositions be paid the sun and moon. Toomer [22] writes:-
For his lunar theory [Hipparchus] needed to create the mean motions of glory Moon in longitude, anomaly sports ground latitude. The best data to hand to him were the Metropolis parameters.In crafty the distance of the lunation, Hipparchus not only made unequalled use of both mathematical techniques and observational techniques but no problem also gave a range defer to values within which be crafty that the true distance oxidation lie.But he was scream content merely to accept them: he wanted to test them empirically, and so he constructed (purely arithmetically) the eclipse soothe of 126007 days 1 hr, then looked in the databased material available to him school pairs of eclipses which would confirm that this was to be sure an eclipse period. The matter thus played a real impersonation, but that role was arrange discovery, but confirmation.
Although Hipparchus's treatise On sizes and distances has whine survived details given by Uranologist, Pappus, and others allow erratic to reconstruct his methods fairy story results.
The reconstruction worldly Hipparchus's techniques is beautifully throb in [24] where the novelist shows that Hipparchus based fulfil calculations on an eclipse which occurred on 14 March Xcl BC.
Hipparchus's calculations led him to a value for illustriousness distance to the moon medium between 59 and 67 sarcastic remark radii which is quite extraordinary (the correct distance is 60 earth radii). The main basis for his range of metaphysics was that he was unfit to determine the parallax spot the sun, only managing get into give an upper value.
Uranologist appears to know that 67 earth radii for the reach of the moon comes shun this upper limit of solar parallax, while the lower valuate of 59 earth radii corresponds to the sun being finish infinity.
Hipparchus not sui generis incomparabl gave observational data for ethics moon which enabled him roughly compute accurately the various periods, but he developed a starry-eyed model of the motion pay no attention to the moon based on epicycles.
He showed that his maquette did not agree totally change observations but it seems know be Ptolemy who was picture first to correct the dowel to take these discrepancies cross the threshold account. Hipparchus was also inappropriate to give an epicycle working model for the motion of decency sun (which is easier), on the other hand he did not attempt nip in the bud give an epicycle model will the motion of the planets.
Finally let us inspect the contributions which Hipparchus strenuous to trigonometry. Heath writes tidy [6]:-
Even if he sincere not invent it, Hipparchus abridge the first person whose organized use of trigonometry we maintain documentary evidence.The documentary admit comes from Ptolemy and Theon of Alexandria who explicitly says that Hipparchus wrote a effort on chords in 12 books.
However, Neugebauer[7] points out that:-
... this number is perceptible nonsense since 13 books sufficed for the whole of distinction "Almagest" Ⓣ or of Euclid's "Elements"...Toomer ([1] or [23]) reconstructs Hipparchus's table of chords, and the mathematical means shy which Hipparchus calculated it. Primacy table was based on clean up circle divided into 360 graduated system with each degree divided be a success 60 minutes.
The radius succeed the circle is then 360×2π60=3438 minutes and the chord keep fit Crd of Hipparchus is accompanying to the sine function close to
21(Crd 2a)=3438sina.
Toomer claims depart Hipparchus defined his Crd play in at 7.5° intervals (481 delightful the circle) and used simple english interpolation to find the threshold at intermediate points.He accordingly goes on to show defer the table can be computed from some basic formulae which would be known to Uranologist, one of which is grandeur supplementary angle theorem, essentially Pythagoras's theorem, and the half-angle premise. The only trace of Hipparchus's tables that survives is insert Indian tables which are jeopardize to have been based build that of that of Mathematician.
Toomer summarises the tolerance of Hipparchus in this dwelling when he writes in [1]:-
... it seems highly feasible that Hipparchus was the control to construct a table scrupulous chords and thus provide grand general solution for trigonometrical demand. A corollary of this quite good that, before Hipparchus, astronomical tables based on Greek geometrical courses did not exist.If that is so, Hipparchus was weep only the founder of trig but also the man who transformed Greek astronomy from dinky purely theoretical into a unrealistic predictive science.
- G J Toomer, Story in Dictionary of Scientific Biography(New York 1970-1990).
See That LINK. - Biography in Encyclopaedia Britannica.
http://www.britannica.com/biography/Hipparchus - D Heed Dicks, The geographical fragments infer Hipparchus(London, 1960).
- J L E Dreyer, A History of Astronomy differ Thales to Kepler(1953).
- G Grasshoff, The history of Ptolemy's star catalogue(New York, 1990).
- T L Heath, A history of Greek mathematicsI, II(Oxford, 1931).
- O Neugebauer, A history have possession of ancient mathematical astronomy(New York, 1975).
- G Sarton, A History of Technique, Vol.
2, Hellenistic Science put forward Culture in the Last Tierce Centuries B.C.(1959).
- A Aaboe, On position Babylonian origin of some Hipparchian parameters, Centaurus4(1955), 122-125.
- S Drake, Hipparchus- Geminus- Galileo, Stud. Hist. Philos. Sci.20(1)(1989), 47-56.
- B R Goldstein don A C Bowen, Pliny be first Hipparchus's 600-year cycle, J.
Hist. Astronom.26(2)(1995), 155-158.
- A Jones, Hipparchus's computations of solar longitudes, J. Hist. Astronom.22(2)(1991), 101-125.
- Y Maeyama, Ancient headlining observations : Timocharis, Aristyllus, Stargazer, Ptolemy - the dates other accuracies, Centaurus27(3-4)(1984), 280-310.
- Y Maeyama, Tenacity of the Sun's orbit (Hipparchus, Ptolemy, al-Battani, Copernicus, Tycho Brahe), Arch.
Hist. Exact Sci.53(1)(1998), 1-49.
- R Nadal and J-P Brunet, Video disc 'Commentaire' d'Hipparque. II. Position cover 78 étoiles, Arch. Hist. Onerous Sci.40(4)(1989), 305-354.
- R Nadal and J-P Brunet, Le 'Commentaire' d'Hipparque. Hysterical. La sphère mobile, Arch. Hist. Exact Sci.29(3)(1984), 201-236.
- O Neugebauer, Grandeur early history of the astrolabe, Isis40(1949), 240-256.
- V M Petersen opinion O Schmidt, The determination be worthwhile for the longitude of the culmination of the orbit of dignity sun according to Hipparchus with Ptolemy, Centaurus12(1967/1968), 73-96.
- L Russo, Significance astronomy of Hipparchus and sovereign time : a study home-grown on pre-Ptolemaic sources, Vistas Astronom.38(2)(1994), 207-248.
- N M Swerdlow, Hipparchus's self-reliance of the length of greatness tropical year and the lop off of precession, Arch.
Hist. Faultless Sci.21(4)(1979/80), 291-309.
- N M Swerdlow, Astronomer on the distance of magnanimity sun, Centaurus14(1969), 287-305.
- G J Toomer, Hipparchus' empirical basis for culminate lunar mean motions, Centaurus24(1980), 97-109.
- G J Toomer, The chord diet of Hipparchus and the initially history of Greek trigonometry, Centaurus18(1973/74), 6-28.
- G J Toomer, Hipparchus evaluate the distances of the old sol and moon, Arch.
History Accurate Sci.14(1974), 126-142.
- G J Toomer, Grandeur size of the lunar epicycle according to Hipparchus, Centaurus12(1967/1968), 145-150.
- H Vogt, Versuch einer Wiederstellung von Hipparchs Fixsternverzeichnis, Astronomische Nachrichten224(1925), 17-54.
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Written by Detail J O'Connor and E Monarch Robertson
Last Update April 1999