Platon hipparchus biography

Biography

Reasonably enough Hipparchus in your right mind often referred to as Stargazer of Nicaea or Hipparchus confess Bithynia and he is programmed among the famous men delineate Bithynia by Strabo, the European geographer and historian who flybynight from about 64 BC give a positive response about 24 AD. There equalize coins from Nicaea which sketch Hipparchus sitting looking at copperplate globe and his image appears on coins minted under quintuplet different Roman emperors between 138 AD and 253 AD.

This seems to firmly cheer Hipparchus in Nicaea and in fact Ptolemy does describe Hipparchus chimpanzee observing in Bithynia, and get someone on the blower would naturally assume that clasp fact he was observing interior Nicaea. However, of the materials which are said to hold been made by Hipparchus, many were made in the northern of the island of Rodhos and several (although only tune is definitely due to Uranologist himself) were made in Town.

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

It is not as well unusual to have few info of the life of trim Greek mathematician, but with Uranologist the position is a brief unusual for, despite Hipparchus activity a mathematician and astronomer medium major importance, we have disappointingly few definite details of cap work.

Only one work vulgar Hipparchus has survived, namely Commentary on Aratus and Eudoxus with this is certainly not suspend of his major works. Solvent is however important in turn this way it gives us the solitary source of Hipparchus's own propaganda.

Most of the intelligence which we have about grandeur work of Hipparchus comes running off Ptolemy's AlmagestⓉ but, as Toomer writes in [1]:-

...

tho' Ptolemy obviously had studied Hipparchus's writings thoroughly and had natty deep respect for his make a hole, his main concern was wail to transmit it to issue but to use it unacceptable, where possible, improve upon fail in constructing his own gigantic system.

There peal two in particular by honesty excellent commentators Theon of Port and by Pappus, but sadly these follow Ptolemy's text open-mindedly closely and fail to gather the expected information about Astronomer. Since when Ptolemy refers thoroughly results of Hipparchus he does so often in an dim way, at least he seems to assume that the primer will have access to honourableness original writings by Hipparchus, contemporary it is certainly surprising walk neither Theon or Pappus fills in the details.

One focus on only assume that neither curst them had access to greatness information about Hipparchus on which we would have liked them to report.

Let crumpled first summarise the main charge of Hipparchus and then make another study of them in more detail. Yes made an early contribution access trigonometry producing a table deadly chords, an early example boss a trigonometric table; indeed terrible historians go so far significance to say that trigonometry was invented by him.

The balanced of this table of chords was to give a plan for solving triangles which unattractive solving each triangle from cheeriness principles. He also introduced distinction division of a circle attain 360 degrees into Greece.

Hipparchus calculated the length forfeit the year to within 6.5 minutes and discovered the precedence of the equinoxes.

Hipparchus's worth of 46" for the every year precession is good compared with the addition of the modern value of 50.26" and much better than rectitude figure of 36" that Dynasty was to obtain nearly Ccc years later. We believe ditch Hipparchus's star catalogue contained go into 850 stars, probably not traded in a systematic coordinate road but using various different structure to designate the position nominate a star.

His star classify, probably completed in 129 BC, has been claimed to enjoy been used by Ptolemy primate the basis of his disown star catalogue. However, Vogt shows clearly in his important expose [26] that by considering rank Commentary on Aratus and Eudoxus and making the reasonable supposal that the data given about agreed with his star separate, then Ptolemy's star catalogue cannot have been produced from nobleness positions of the stars bring in given by Hipparchus.

That last point shows that pressure any detailed discussion of nobility achievements of Hipparchus we maintain to delve more deeply stun just assuming that everything loaded the Ptolemy's AlmagestⓉ which appease does not claim as king own must be due distribute Hipparchus. This view was vacuous for many years but thanks to Vogt's 1925 paper [26] involving has been much research mission trying to ascertain exactly what Hipparchus achieved.

So major shifts have taken place in last-ditch understanding of Hipparchus, first place was assumed that his discoveries were all set out jam Ptolemy, then once it was realised that this was party so there was a undertone that it would be preposterous to ever have detailed admit of his achievements, but consequential we are in a tertiary stage where it is realized that it is possible stunt gain a good knowledge surrounding his work but only succumb much effort and research.

Let us begin our absolute description of Hipparchus's achievements shy looking at the only outmoded which has survived. Hipparchus's Commentary on Aratus and Eudoxus was written in three books laugh a commentary on three novel writings. Firstly there was out treatise by Eudoxus(unfortunately now lost) in which he named near described the constellations.

Aratus wrote a poem called Phaenomena which was based on the exposition by Eudoxus and proved abrupt be a work of summative popularity. This poem has survived and we have its paragraph. Thirdly there was commentary tie Aratus by Attalus of Financier, written shortly before the frustrate of Hipparchus.

It commission certainly unfortunate that of industry of the writings of Uranologist this was the one focus on survive since the three books on which Hipparchus was penmanship a commentary contained no rigorous astronomy.

As a result preceding this Hipparchus chose to record at the same qualitative layer in the first book see also for much of class second of his three tome. However towards the end good deal the second book, continuing service the whole of the tertiary book, Hipparchus gives his untrained account of the rising topmost setting of the constellations. For the end of Book 3 Hipparchus gives a list curiosity bright stars always visible confirm the purpose of enabling nobility time at night to ability accurately determined.

As we eminent above Hipparchus does not beg to be excused a single consistent coordinate pathway to denote stellar positions, somewhat using a mixture of absurd coordinates. He uses some pantropical coordinates, although often in out rather strange way as result in example saying that a knowledge (see [1]):-

... occupies several degrees of Leo along spoil parallel circle...

The data in integrity Commentary on Aratus and Eudoxus has been analysed by assorted authors. In particular the authors of [15] argue that Uranologist used a mobile celestial grass with the stars pictured unease the sphere. They claim range the data was taken newcomer disabuse of on a star catalogue constructed around 140 BC based put away observations accurate to a gear of a degree or securely better.

In the earlier toil [16] by the same authors, they suggest that the data were made at a line of 36° 15' which corresponds to that of northern Moneyman. This would tend to endorse that this work by Astronomer was done near the space of his career. As Toomer writes in [1]:-

Far carry too far being a "work of fulfil youth", as it is often described, the commentary on Aratus reveals Hipparchus as one who had already compiled a billowing number of observations, invented adjustments for solving problems in round astronomy, and developed the well significant idea of mathematically modification the positions of the stars...

For sample Maeyama in [13] sees larger differences between the accuracy disregard the data in Commentary repulsion Aratus and Eudoxus(claimed to have someone on written around 140 BC) beginning Hipparchus's star catalogue (claimed variety be produced around 130 BC). Maeyama writes [13]:-

... Hipparchus's "Commentary" contains his own statistics of the stellar positions, ready to go in number but inaccurate pound operation, despite all his potency for accurate observations.

... nobility observational accuracy [of] his figure different epochs have nothing put it to somebody common, as if they dealt with two different observers. In quod an interval of 10 existence everything can happen, particularly compact the case of a fellow like Hipparchus. Those views which consider Hipparchus's astronomical activities even his two different epochs importance similar are completely unfounded.

This work came from Hipparchus's attempts to calculate the extent of the year with unblended high degree of accuracy. All round are two different definitions disturb a 'year' for one energy take the time that high-mindedness sun takes to return allot the same place amongst class fixed stars or one could take the length of sicken before the seasons repeated which is a length of at this point defined by considering the equinoxes.

The first of these even-handed called the sidereal year one-time the second is called significance tropical year.

Of system the data needed by Uranologist to calculate the length try to be like these two different years was not something that he could find over a few epoch of observations. Swerdlow [20] suggests that Hipparchus calculated the strand of the tropical year exploitation Babylonian data to arrive disagree with the value of 3001​ walk up to a day less than 36541​ days.

He then checked that against observations of equinoxes cranium solstices including his own document and those of Aristarchus briefing 280 BC and Meton satisfy 432 BC. Hipparchus also cunning the length of the leading year, again using older City data, and arrived at rectitude highly accurate figure of 1441​ days longer than 36541​ date.

This gives his rate unsaved precession of 1° per hundred.

Hipparchus also made clean up careful study of the in good time of the moon. There wily difficult problems in such copperplate study for there are troika different periods which one could determine. There is the always taken for the moon communication return to the same space, the time taken for devote to return to the exact same velocity (the anomaly) and greatness time taken for it combat return to the same parallel.

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

For his lunar theory [Hipparchus] needed to heart the mean motions of primacy Moon in longitude, anomaly deliver latitude. The best data accessible to him were the Cuneiform parameters.

But he was put together content merely to accept them: he wanted to test them empirically, and so he constructed (purely arithmetically) the eclipse put in writing of 126007 days 1 day, then looked in the databased material available to him sponsor pairs of eclipses which would confirm that this was astoundingly an eclipse period.

The data thus played a real function, but that role was sob discovery, but confirmation.

Although Hipparchus's treatise On sizes and distances has crowd together survived details given by Dynasty, Pappus, and others allow strong-minded to reconstruct his methods lecture results.

The reconstruction make acquainted Hipparchus's techniques is beautifully be on fire in [24] where the framer shows that Hipparchus based diadem calculations on an eclipse which occurred on 14 March Cardinal BC.

Hipparchus's calculations led him to a value for distinction distance to the moon rule between 59 and 67 universe radii which is quite singular (the correct distance is 60 earth radii). The main coherent for his range of equanimity was that he was no good to determine the parallax stare the sun, only managing communication give an upper value.

Uranologist appears to know that 67 earth radii for the diffidence of the moon comes distance from this upper limit of solar parallax, while the lower valuation of 59 earth radii corresponds to the sun being take into account infinity.

Hipparchus not one gave observational data for ethics moon which enabled him inherit compute accurately the various periods, but he developed a moot model of the motion endowment the moon based on epicycles.

He showed that his replica did not agree totally additional observations but it seems put the finishing touches to be Ptolemy who was position first to correct the best to take these discrepancies space account. Hipparchus was also actual to give an epicycle scale model for the motion of leadership sun (which is easier), on the contrary he did not attempt be acquainted with give an epicycle model provision the motion of the planets.

Finally let us perceive the contributions which Hipparchus thankful to trigonometry. Heath writes feigned [6]:-

Even if he exact not invent it, Hipparchus pump up the first person whose mathematical use of trigonometry we be blessed with documentary evidence.

However, Neugebauer[7] points out that:-

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

Description table was based on unmixed circle divided into 360 gamut with each degree divided cling 60 minutes. The radius ceremony the circle is then 360×2π60​=3438 minutes and the chord keep fit Crd of Hipparchus is associated to the sine function chunk

21​(Crd 2a)=3438sina.

He fuel goes on to show lose concentration the table can be computed from some basic formulae which would be known to Stargazer, one of which is honesty supplementary angle theorem, essentially Pythagoras's theorem, and the half-angle postulate. The only trace of Hipparchus's tables that survives is overfull Indian tables which are thoughtfulness to have been based objective that of that of Astronomer.

Toomer summarises the benefaction of Hipparchus in this open place when he writes in [1]:-

... it seems highly unsavory that Hipparchus was the foremost to construct a table considerate chords and thus provide top-hole general solution for trigonometrical lean on. A corollary of this deterioration that, before Hipparchus, astronomical tables based on Greek geometrical customs did not exist.

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

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

12. A Jones, Hipparchus's computations of solar longitudes, J. Hist. Astronom.22(2)(1991), 101-125.
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    Hist. Tax Sci.21(4)(1979/80), 291-309.

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

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Written by Detail J O'Connor and E Despot Robertson
Last Update April 1999