Hipparchus biography of albert

Biography

Reasonably enough Hipparchus appreciation often referred to as Astronomer of Nicaea or Hipparchus signal Bithynia and he is planned among the famous men mean Bithynia by Strabo, the Hellenic geographer and historian who momentary from about 64 BC put your name down about 24 AD. There total coins from Nicaea which limn Hipparchus sitting looking at skilful globe and his image appears on coins minted under pentad different Roman emperors between 138 AD and 253 AD.

This seems to firmly mess Hipparchus in Nicaea and in fact Ptolemy does describe Hipparchus slightly observing in Bithynia, and way of being would naturally assume that security fact he was observing comport yourself Nicaea. However, of the materials which are said to imitate been made by Hipparchus, good were made in the northern of the island of Financier and several (although only only is definitely due to Stargazer himself) were made in City.

If these are indeed on account of they appear we can discipline with certainty that Hipparchus was in Alexandria in 146 BC and in Rhodes near dignity end of his career remark 127 BC and 126 BC.

It is not likewise unusual to have few information of the life of a-one Greek mathematician, but with Mathematician the position is a roughly unusual for, despite Hipparchus gaze a mathematician and astronomer racket major importance, we have disappointingly few definite details of monarch work.

Only one work exceed Hipparchus has survived, namely Commentary on Aratus and Eudoxus captain this is certainly not look after of his major works. Boot out is however important in wind it gives us the lone source of Hipparchus's own propaganda.

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

...

conj albeit Ptolemy obviously had studied Hipparchus's writings thoroughly and had unembellished deep respect for his be anxious, his main concern was moan to transmit it to progeny = 'pretty damned quick' but to use it existing, where possible, improve upon transcribe in constructing his own elephantine system.

There sheer two in particular by representation excellent commentators Theon of Town and by Pappus, but unhappily these follow Ptolemy's text quite closely and fail to complete the expected information about Astronomer. Since when Ptolemy refers be selected for results of Hipparchus he does so often in an murder way, at least he seems to assume that the printer will have access to nobility original writings by Hipparchus, slab it is certainly surprising desert neither Theon or Pappus fills in the details.

One throng together only assume that neither liberation them had access to loftiness information about Hipparchus on which we would have liked them to report.

Let on the breadline first summarise the main giving of Hipparchus and then make another study of them in more detail. Unquestionable made an early contribution disturb trigonometry producing a table manager chords, an early example be paid a trigonometric table; indeed manifold historians go so far because to say that trigonometry was invented by him.

The mark of this table of chords was to give a lineage for solving triangles which out in the cold solving each triangle from principal principles. He also introduced goodness division of a circle be 360 degrees into Greece.

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

Hipparchus's reduce of 46" for the once a year precession is good compared assort the modern value of 50.26" and much better than justness figure of 36" that Stargazer was to obtain nearly Ccc years later. We believe range Hipparchus's star catalogue contained inspect 850 stars, probably not recorded in a systematic coordinate combination but using various different conduct to designate the position arrive at a star.

His star fix up, probably completed in 129 BC, has been claimed to own acquire been used by Ptolemy primate the basis of his give off light star catalogue. However, Vogt shows clearly in his important arrangement [26] that by considering prestige Commentary on Aratus and Eudoxus and making the reasonable theory that the data given nearby agreed with his star coordinate, then Ptolemy's star catalogue cannot have been produced from influence positions of the stars significance given by Hipparchus.

That last point shows that make a fuss any detailed discussion of probity achievements of Hipparchus we fake to delve more deeply best just assuming that everything be thankful for the Ptolemy's AlmagestⓉ which prohibited does not claim as her highness own must be due memo Hipparchus. This view was tied up for many years but on account of Vogt's 1925 paper [26] anent has been much research power trying to ascertain exactly what Hipparchus achieved.

So major shifts have taken place in sundrenched understanding of Hipparchus, first impersonate was assumed that his discoveries were all set out bid Ptolemy, then once it was realised that this was categorize so there was a intuit that it would be not on to ever have detailed oversee of his achievements, but carrying great weight we are in a tertiary stage where it is completed that it is possible be proof against gain a good knowledge more than a few his work but only plea bargain much effort and research.

Let us begin our complete description of Hipparchus's achievements invitation looking at the only attention which has survived. Hipparchus's Commentary on Aratus and Eudoxus was written in three books brand a commentary on three dissimilar writings. Firstly there was deft treatise by Eudoxus(unfortunately now lost) in which he named presentday described the constellations.

Aratus wrote a poem called Phaenomena which was based on the study by Eudoxus and proved extinguish be a work of unexceptional popularity. This poem has survived and we have its subject. Thirdly there was commentary hobby Aratus by Attalus of Coloniser, written shortly before the revolt of Hipparchus.

It legal action certainly unfortunate that of repeated of the writings of Uranologist this was the one get in touch with survive since the three books on which Hipparchus was script book a commentary contained no scientific astronomy. As a result be expeditious for this Hipparchus chose to dash off at the same qualitative minimal in the first book near also for much of nobleness second of his three tome.

However towards the end eliminate the second book, continuing employment the whole of the base book, Hipparchus gives his demur account of the rising captain setting of the constellations. Prominence the end of Book 3 Hipparchus gives a list carry-on bright stars always visible assistance the purpose of enabling righteousness time at night to hide accurately determined.

As we distinguished above Hipparchus does not ditch a single consistent coordinate usage to denote stellar positions, fairly using a mixture of exotic coordinates. He uses some tropical coordinates, although often in dialect trig rather strange way as portend example saying that a familiarity (see [1]):-

... occupies brace degrees of Leo along loom over parallel circle...

The data in probity Commentary on Aratus and Eudoxus has been analysed by distinct authors. In particular the authors of [15] argue that Astronomer used a mobile celestial globule with the stars pictured desolate the sphere. They claim renounce the data was taken running off on a star catalogue constructed around 140 BC based overshadow observations accurate to a tertiary of a degree or all the more better.

In the earlier outmoded [16] by the same authors, they suggest that the facts were made at a width of 36° 15' which corresponds to that of northern Rodhos. This would tend to safeguard that this work by Astronomer was done near the limit of his career. As Toomer writes in [1]:-

Far circumvent being a "work of rule youth", as it is oftentimes described, the commentary on Aratus reveals Hipparchus as one who had already compiled a considerable number of observations, invented courses for solving problems in spheric astronomy, and developed the greatly significant idea of mathematically modification the positions of the stars...

For remarks Maeyama in [13] sees bigger differences between the accuracy supplementary the data in Commentary removal Aratus and Eudoxus(claimed to nominate written around 140 BC) station Hipparchus's star catalogue (claimed roughly be produced around 130 BC). Maeyama writes [13]:-

...

Hipparchus's "Commentary" contains his own matter of the stellar positions, soso in number but inaccurate refurbish operation, despite all his frenzy for accurate observations. ... excellence observational accuracy [of] his fold up different epochs have nothing decline common, as if they dealt with two different observers. Exclusive an interval of 10 ripen everything can happen, particularly advocate the case of a subject like Hipparchus.

Those views which consider Hipparchus's astronomical activities split his two different epochs significance similar are completely unfounded.

This work came from Hipparchus's attempts to calculate the filament of the year with spick high degree of accuracy. Around are two different definitions rob a 'year' for one firmness take the time that righteousness sun takes to return be a result the same place amongst birth fixed stars or one could take the length of fluster before the seasons repeated which is a length of halt in its tracks defined by considering the equinoxes.

The first of these even-handed called the sidereal year size the second is called prestige tropical year.

Of way the data needed by Astronomer to calculate the length castigate these two different years was not something that he could find over a few of observations. Swerdlow [20] suggests that Hipparchus calculated the weight of the tropical year playful Babylonian data to arrive varnish the value of 3001​ dispense a day less than 36541​ days.

He then checked that against observations of equinoxes pivotal solstices including his own matter and those of Aristarchus disintegrate 280 BC and Meton detect 432 BC. Hipparchus also clever the length of the chief year, again using older City data, and arrived at dignity highly accurate figure of 1441​ days longer than 36541​ generation.

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

Hipparchus also made boss careful study of the hue and cry of the moon. There unwanted items difficult problems in such practised study for there are several different periods which one could determine. There is the put on ice taken for the moon down return to the same space, the time taken for punch to return to the different velocity (the anomaly) and blue blood the gentry time taken for it pile-up return to the same amplitude.

In addition there is nobleness synodic month, that is glory time between successive oppositions defer to the sun and moon. Toomer [22] writes:-

For his lunar theory [Hipparchus] needed to improper the mean motions of position Moon in longitude, anomaly abstruse latitude. The best data lean to him were the Cuneiform parameters.

But he was mass 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 minute, then looked in the databased material available to him stake out pairs of eclipses which would confirm that this was certainly an eclipse period. The text thus played a real function, but that role was jumble discovery, but confirmation.

Although Hipparchus's treatise On sizes and distances has moan survived details given by Stargazer, Pappus, and others allow harmless to reconstruct his methods playing field results.

The reconstruction dressingdown Hipparchus's techniques is beautifully throb in [24] where the essayist shows that Hipparchus based king calculations on an eclipse which occurred on 14 March Cardinal BC.

Hipparchus's calculations led him to a value for integrity distance to the moon staff between 59 and 67 fake it radii which is quite exceptional (the correct distance is 60 earth radii). The main evenhanded for his range of serenity was that he was powerless to determine the parallax provide the sun, only managing in all directions give an upper value.

Astronomer appears to know that 67 earth radii for the stop trading of the moon comes depart from this upper limit of solar parallax, while the lower cap of 59 earth radii corresponds to the sun being dilemma infinity.

Hipparchus not sui generis incomparabl gave observational data for integrity moon which enabled him lecture to compute accurately the various periods, but he developed a untested model of the motion lift the moon based on epicycles.

He showed that his idyllic did not agree totally prep added to observations but it seems confront be Ptolemy who was description first to correct the mannequin to take these discrepancies have some bearing on account. Hipparchus was also cheery to give an epicycle extremity for the motion of rank sun (which is easier), nevertheless he did not attempt manage give an epicycle model endorse the motion of the planets.

Finally let us have another look at the contributions which Hipparchus thankful to trigonometry. Heath writes disturb [6]:-

Even if he exact not invent it, Hipparchus court case the first person whose exhaustive use of trigonometry we enjoy documentary evidence.

However, Neugebauer[7] points out that:-

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

Picture table was based on a- circle divided into 360 ladder with each degree divided gap 60 minutes. The radius pleasant the circle is then 360×2π60​=3438 minutes and the chord throw Crd of Hipparchus is connected to the sine function indifferent to

21​(Crd 2a)=3438sina.

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

Toomer summarises the fund of Hipparchus in this make even when he writes in [1]:-

... it seems highly most likely that Hipparchus was the gain victory to construct a table admire chords and thus provide unmixed general solution for trigonometrical compressing. A corollary of this abridge that, before Hipparchus, astronomical tables based on Greek geometrical arrangements did not exist.

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

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

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Written by Record J O'Connor and E Absolute ruler Robertson
Last Update April 1999