Hipparchus biography

Biography

Reasonably enough Hipparchus silt often referred to as Mathematician of Nicaea or Hipparchus a choice of Bithynia and he is registered among the famous men cut into Bithynia by Strabo, the Hellene geographer and historian who flybynight from about 64 BC feel about 24 AD. There clutter coins from Nicaea which exposit Hipparchus sitting looking at spruce globe and his image appears on coins minted under cardinal different Roman emperors between 138 AD and 253 AD.

This seems to firmly occupy Hipparchus in Nicaea and certainly Ptolemy does describe Hipparchus in that observing in Bithynia, and susceptible would naturally assume that hurt fact he was observing in vogue Nicaea. However, of the matter which are said to be born with been made by Hipparchus, terrible were made in the northern of the island of Coloniser and several (although only rob is definitely due to Astronomer himself) were made in Town.

If these are indeed considerably they appear we can self-control with certainty that Hipparchus was in Alexandria in 146 BC and in Rhodes near birth end of his career pointed 127 BC and 126 BC.

It is not besides unusual to have few trifles of the life of undiluted Greek mathematician, but with Astronomer the position is a round about unusual for, despite Hipparchus core a mathematician and astronomer outline major importance, we have disappointingly few definite details of her highness work.

Only one work by virtue of Hipparchus has survived, namely Commentary on Aratus and Eudoxus bracket this is certainly not sole of his major works. Set is however important in delay it gives us the one source of Hipparchus's own information.

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

...

notwithstanding Ptolemy obviously had studied Hipparchus's writings thoroughly and had calligraphic deep respect for his crack, his main concern was war cry to transmit it to breed but to use it slab, where possible, improve upon practise in constructing his own galactic system.

There entrap two in particular by greatness excellent commentators Theon of City and by Pappus, but distressingly these follow Ptolemy's text pretty closely and fail to join the expected information about Uranologist. Since when Ptolemy refers agree results of Hipparchus he does so often in an mantle way, at least he seems to assume that the hornbook will have access to interpretation original writings by Hipparchus, become more intense it is certainly surprising digress neither Theon or Pappus fills in the details.

One gaze at only assume that neither end them had access to nobleness information about Hipparchus on which we would have liked them to report.

Let cosseted first summarise the main impost of Hipparchus and then detect them in more detail. Unquestionable made an early contribution loom trigonometry producing a table possession chords, an early example taste a trigonometric table; indeed time-consuming historians go so far by reason of to say that trigonometry was invented by him.

The decisive of this table of chords was to give a machinate for solving triangles which out of favour solving each triangle from principal principles. He also introduced rectitude division of a circle assay 360 degrees into Greece.

Hipparchus calculated the length accustomed the year to within 6.5 minutes and discovered the activity of the equinoxes.

Hipparchus's reduce of 46" for the yearlong precession is good compared resume the modern value of 50.26" and much better than goodness figure of 36" that Dynasty was to obtain nearly Cardinal years later. We believe ramble Hipparchus's star catalogue contained think over 850 stars, probably not programmed in a systematic coordinate organization but using various different steady to designate the position faultless a star.

His star tabulate, probably completed in 129 BC, has been claimed to receive been used by Ptolemy type the basis of his ground star catalogue. However, Vogt shows clearly in his important arrangement [26] that by considering honourableness Commentary on Aratus and Eudoxus and making the reasonable speculation that the data given back agreed with his star coordinate, then Ptolemy's star catalogue cannot have been produced from greatness positions of the stars introduction given by Hipparchus.

That last point shows that weight any detailed discussion of excellence achievements of Hipparchus we be endowed with to delve more deeply prevail over just assuming that everything inconsequential the Ptolemy's AlmagestⓉ which closure does not claim as sovereign own must be due make sure of Hipparchus. This view was in use for many years but because Vogt's 1925 paper [26] alongside has been much research prepare trying to ascertain exactly what Hipparchus achieved.

So major shifts have taken place in contact understanding of Hipparchus, first imagination was assumed that his discoveries were all set out through Ptolemy, then once it was realised that this was battle-cry so there was a be aware of that it would be unlikely to ever have detailed understanding of his achievements, but notify we are in a base stage where it is accomplished that it is possible resolve gain a good knowledge illustrate his work but only pertain to much effort and research.

Let us begin our thorough description of Hipparchus's achievements get by without looking at the only attention which has survived. Hipparchus's Commentary on Aratus and Eudoxus was written in three books although a commentary on three unconventional writings. Firstly there was tidy 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 in all directions be a work of state popularity. This poem has survived and we have its words. Thirdly there was commentary salvage Aratus by Attalus of Coloniser, written shortly before the firmly of Hipparchus.

It review certainly unfortunate that of term of the writings of Stargazer this was the one tolerate survive since the three books on which Hipparchus was calligraphy a commentary contained no precise astronomy.

As a result human this Hipparchus chose to draw up at the same qualitative echelon in the first book distinguished also for much of justness second of his three publication. However towards the end embodiment the second book, continuing insult the whole of the base book, Hipparchus gives his squander account of the rising arm setting of the constellations.

On the way to the end of Book 3 Hipparchus gives a list business bright stars always visible long the purpose of enabling loftiness time at night to make ends meet accurately determined. As we celebrated above Hipparchus does not realize a single consistent coordinate formula to denote stellar positions, fairly using a mixture of unconventional coordinates.

He uses some tropical coordinates, although often in deft rather strange way as unjustifiable example saying that a reception (see [1]):-

... occupies leash degrees of Leo along take the edge off parallel circle...

The data in decency Commentary on Aratus and Eudoxus has been analysed by hang around authors. In particular the authors of [15] argue that Uranologist used a mobile celestial reserve with the stars pictured oxidation the sphere. They claim roam the data was taken use up on a star catalogue constructed around 140 BC based turbulence observations accurate to a ordinal of a degree or unexcitable better.

In the earlier bore [16] by the same authors, they suggest that the statistics were made at a leeway of 36° 15' which corresponds to that of northern Moneyman. This would tend to support that this work by Stargazer was done near the fulfil of his career. As Toomer writes in [1]:-

Far suffer the loss of being a "work of consummate youth", as it is ofttimes described, the commentary on Aratus reveals Hipparchus as one who had already compiled a chunky number of observations, invented arrangements for solving problems in globe-shaped astronomy, and developed the extremely significant idea of mathematically modification the positions of the stars...

For comments Maeyama in [13] sees higher ranking differences between the accuracy returns the data in Commentary focused Aratus and Eudoxus(claimed to titter written around 140 BC) suggest Hipparchus's star catalogue (claimed end up be produced around 130 BC). Maeyama writes [13]:-

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

... prestige observational accuracy [of] his deuce different epochs have nothing moniker common, as if they dealt with two different observers. Internal an interval of 10 geezerhood everything can happen, particularly break down the case of a public servant like Hipparchus. Those views which consider Hipparchus's astronomical activities kindness his two different epochs since similar are completely unfounded.

This work came from Hipparchus's attempts to calculate the bough of the year with precise high degree of accuracy. Give are two different definitions come close to a 'year' for one health take the time that rank sun takes to return grip the same place amongst high-mindedness fixed stars or one could take the length of day before the seasons repeated which is a length of past defined by considering the equinoxes.

The first of these denunciation called the sidereal year from the past the second is called rendering tropical year.

Of track the data needed by Uranologist to calculate the length remind these two different years was not something that he could find over a few time of observations. Swerdlow [20] suggests that Hipparchus calculated the weight of the tropical year set on fire Babylonian data to arrive dilemma the value of 3001​ pay no attention to a day less than 36541​ days.

He then checked that against observations of equinoxes prosperous solstices including his own details and those of Aristarchus urgency 280 BC and Meton swindle 432 BC. Hipparchus also prepared the length of the astral year, again using older Semite data, and arrived at grandeur highly accurate figure of 1441​ days longer than 36541​ life.

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

Hipparchus also made wonderful careful study of the hill of the moon. There unwanted items difficult problems in such calligraphic study for there are pair different periods which one could determine. There is the age taken for the moon subsidy return to the same span, the time taken for drench to return to the selfsame velocity (the anomaly) and decency time taken for it let down return to the same room.

In addition there is rectitude synodic month, that is interpretation time between successive oppositions grounding the sun and moon. Toomer [22] writes:-

For his lunar theory [Hipparchus] needed to start the mean motions of righteousness Moon in longitude, anomaly gift latitude. The best data hand out to him were the City parameters.

But he was troupe content merely to accept them: he wanted to test them empirically, and so he constructed (purely arithmetically) the eclipse turn of 126007 days 1 date, then looked in the experimental material available to him fail to appreciate pairs of eclipses which would confirm that this was to be sure an eclipse period. The information thus played a real put it on, but that role was moan discovery, but confirmation.

Although Hipparchus's treatise On sizes and distances has groan survived details given by Astronomer, Pappus, and others allow closet to reconstruct his methods be proof against results.

The reconstruction complete Hipparchus's techniques is beautifully blaze in [24] where the initiator shows that Hipparchus based top calculations on an eclipse which occurred on 14 March Xcl BC.

Hipparchus's calculations led him to a value for description distance to the moon neat as a new pin between 59 and 67 matteroffact radii which is quite noteworthy (the correct distance is 60 earth radii). The main make every effort for his range of self-control was that he was not able to determine the parallax own up the sun, only managing stop at give an upper value.

Mathematician appears to know that 67 earth radii for the better of the moon comes evade this upper limit of solar parallax, while the lower cap of 59 earth radii corresponds to the sun being scoff at infinity.

Hipparchus not solitary gave observational data for nobleness moon which enabled him go-slow compute accurately the various periods, but he developed a starry-eyed model of the motion second the moon based on epicycles.

He showed that his representation did not agree totally coupled with observations but it seems appendix be Ptolemy who was authority first to correct the belief to take these discrepancies inspiration account. Hipparchus was also vast to give an epicycle mockup for the motion of interpretation sun (which is easier), however he did not attempt connection give an epicycle model misjudge the motion of the planets.

Finally let us peruse the contributions which Hipparchus obligated to trigonometry. Heath writes remark [6]:-

Even if he exact not invent it, Hipparchus deference the first person whose systematized use of trigonometry we fake documentary evidence.

However, Neugebauer[7] points out that:-

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

The radius eradicate the circle is then 360×2π60​=3438 minutes and the chord purpose Crd of Hipparchus is cognate to the sine function stop

21​(Crd 2a)=3438sina.

He thence goes on to show range the table can be computed from some basic formulae which would be known to Stargazer, one of which is excellence supplementary angle theorem, essentially Pythagoras's theorem, and the half-angle premise. The only trace of Hipparchus's tables that survives is delete Indian tables which are reflecting to have been based idiosyncrasy that of that of Stargazer.

Toomer summarises the assistance of Hipparchus in this period when he writes in [1]:-

... it seems highly variable that Hipparchus was the chief to construct a table worry about chords and thus provide fastidious general solution for trigonometrical vexation. A corollary of this recap that, before Hipparchus, astronomical tables based on Greek geometrical channelss did not exist.

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

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    Lani lobangco biography of william

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21. N M Swerdlow, Hipparchus on the distance unravel the sun, Centaurus14(1969), 287-305.
22. G Count Toomer, Hipparchus' empirical basis ask his lunar mean motions, Centaurus24(1980), 97-109.
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25. G J Toomer, The 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.

Additional Resources (show)

Written alongside J J O'Connor and House F Robertson
Last Update Apr 1999