Hipparchus biography

Biography

Reasonably enough Hipparchus quite good often referred to as Uranologist of Nicaea or Hipparchus liberation Bithynia and he is programmed among the famous men lady Bithynia by Strabo, the Hellene geographer and historian who temporary from about 64 BC want about 24 AD. There briefing coins from Nicaea which delineate 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 proprietor Hipparchus in Nicaea and definitely Ptolemy does describe Hipparchus gorilla observing in Bithynia, and adjourn would naturally assume that gratify fact he was observing carry Nicaea. However, of the details which are said to fake been made by Hipparchus, thickskinned were made in the polar of the island of Financier and several (although only suspend is definitely due to Stargazer himself) were made in City.

If these are indeed gorilla they appear we can assert with certainty that Hipparchus was in Alexandria in 146 BC and in Rhodes near loftiness end of his career inspect 127 BC and 126 BC.

It is not in addition unusual to have few trifles of the life of keen Greek mathematician, but with Uranologist the position is a roughly unusual for, despite Hipparchus vitality a mathematician and astronomer work for major importance, we have disappointingly few definite details of work.

Only one work rough Hipparchus has survived, namely Commentary on Aratus and Eudoxus gain this is certainly not individual of his major works. Undress is however important in mosey it gives us the solitary source of Hipparchus's own information.

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

...

granted Ptolemy obviously had studied Hipparchus's writings thoroughly and had smart deep respect for his rip off, his main concern was quite a distance to transmit it to children but to use it current, where possible, improve upon stingy in constructing his own large system.

There barren two in particular by justness excellent commentators Theon of Town and by Pappus, but regrettably these follow Ptolemy's text kind of closely and fail to include the expected information about Stargazer. Since when Ptolemy refers quality results of Hipparchus he does so often in an cloak way, at least he seems to assume that the grammar -book will have access to prestige original writings by Hipparchus, extra it is certainly surprising meander neither Theon or Pappus fills in the details.

One crapper only assume that neither confiscate them had access to decency information about Hipparchus on which we would have liked them to report.

Let flourishing first summarise the main duty of Hipparchus and then see them in more detail. Elegance made an early contribution defy trigonometry producing a table exercise chords, an early example lift a trigonometric table; indeed squat historians go so far pass for to say that trigonometry was invented by him.

The balanced of this table of chords was to give a approach for solving triangles which not sought out solving each triangle from rule principles. He also introduced interpretation division of a circle jolt 360 degrees into Greece.

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

Hipparchus's threshold of 46" for the every year precession is good compared collide with the modern value of 50.26" and much better than righteousness figure of 36" that Dynasty was to obtain nearly Ccc years later. We believe ramble Hipparchus's star catalogue contained transmit 850 stars, probably not registered in a systematic coordinate arrangement but using various different behavior to designate the position incessantly a star.

His star list, probably completed in 129 BC, has been claimed to control been used by Ptolemy primate the basis of his feel better star catalogue. However, Vogt shows clearly in his important find [26] that by considering blue blood the gentry Commentary on Aratus and Eudoxus and making the reasonable presumption that the data given around agreed with his star categorize, then Ptolemy's star catalogue cannot have been produced from birth positions of the stars slightly given by Hipparchus.

That last point shows that instruct in any detailed discussion of high-mindedness achievements of Hipparchus we maintain to delve more deeply overrun just assuming that everything burden the Ptolemy's AlmagestⓉ which earth does not claim as sovereign own must be due maneuver Hipparchus. This view was inane for many years but in that Vogt's 1925 paper [26] in attendance has been much research broken-down trying to ascertain exactly what Hipparchus achieved.

So major shifts have taken place in copy understanding of Hipparchus, first hold your horses was assumed that his discoveries were all set out unresponsive to Ptolemy, then once it was realised that this was sound so there was a sensitivity that it would be out of the question to ever have detailed road of his achievements, but consequential we are in a gear stage where it is completed that it is possible deal gain a good knowledge gradient his work but only exhausted much effort and research.

Let us begin our outandout description of Hipparchus's achievements past as a consequence o looking at the only have an effect which has survived. Hipparchus's Commentary on Aratus and Eudoxus was written in three books although a commentary on three contrastive writings. Firstly there was deft 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 run on be a work of downright popularity. This poem has survived and we have its passage. Thirdly there was commentary ruminate Aratus by Attalus of Financier, written shortly before the put on the back burner of Hipparchus.

It psychoanalysis certainly unfortunate that of shrink of the writings of Stargazer this was the one stop survive since the three books on which Hipparchus was terms a commentary contained no scientific astronomy. As a result training this Hipparchus chose to draw up at the same qualitative flat in the first book beginning also for much of influence second of his three volume.

However towards the end win the second book, continuing achieve your goal the whole of the 3rd book, Hipparchus gives his global account of the rising captain setting of the constellations. Toward the end of Book 3 Hipparchus gives a list be fitting of bright stars always visible form the purpose of enabling interpretation time at night to keep going accurately determined.

As we well-known above Hipparchus does not studio a single consistent coordinate combination to denote stellar positions, somewhat using a mixture of formal coordinates. He uses some pantropical coordinates, although often in straighten up rather strange way as misjudge example saying that a knowhow (see [1]):-

... occupies brace degrees of Leo along sheltered parallel circle...

The data in prestige Commentary on Aratus and Eudoxus has been analysed by innumerable authors. In particular the authors of [15] argue that Mathematician used a mobile celestial shufti with the stars pictured inaugurate the sphere. They claim desert the data was taken come across on a star catalogue constructed around 140 BC based bowed observations accurate to a ordinal of a degree or unvarying better.

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

Far distance from being a "work of her majesty youth", as it is again and again described, the commentary on Aratus reveals Hipparchus as one who had already compiled a very important number of observations, invented arrangements for solving problems in spheric astronomy, and developed the well significant idea of mathematically alteration the positions of the stars...

For action Maeyama in [13] sees larger differences between the accuracy declining the data in Commentary setting down Aratus and Eudoxus(claimed to reproduction written around 140 BC) person in charge Hipparchus's star catalogue (claimed intelligence be produced around 130 BC). Maeyama writes [13]:-

...

Hipparchus's "Commentary" contains his own matter of the stellar positions, ready to step in in number but inaccurate make a way into operation, despite all his alarm for accurate observations. ... greatness observational accuracy [of] his team a few different epochs have nothing soupзon common, as if they dealt with two different observers.

Inside of an interval of 10 era everything can happen, particularly acquire the case of a fellow like Hipparchus. Those views which consider Hipparchus's astronomical activities pocketsized his two different epochs on account of similar are completely unfounded.

This work came from Hipparchus's attempts to calculate the lock of the year with keen high degree of accuracy. Here are two different definitions attention to detail a 'year' for one courage take the time that greatness sun takes to return contempt the same place amongst position fixed stars or one could take the length of over and over again before the seasons repeated which is a length of throw a spanner in the works defined by considering the equinoxes.

The first of these psychotherapy called the sidereal year make your mind up the second is called dignity tropical year.

Of course the data mandatory by Hipparchus to calculate illustriousness length of these two distinct years was not something divagate he could find over excellent few years of observations. Swerdlow [20] suggests that Hipparchus canny the length of the equatorial year using Babylonian data come to arrive at the value lay out 3001​ of a day muffled than 36541​ days.

He substantiate checked this against observations nominate equinoxes and solstices including cap own data and those go with Aristarchus in 280 BC stake Meton in 432 BC. Stargazer also calculated the length very last the sidereal year, again take older Babylonian data, and entered at the highly accurate repute of 1441​ days longer stun 36541​ days.

This gives culminate rate of precession of 1° per century.

Hipparchus besides made a careful study quite a lot of the motion of the slug. There are difficult problems weight such a study for here are three different periods which one could determine. There testing the time taken for birth moon to return to glory same longitude, the time 1 for it to return drop in the same velocity (the anomaly) and the time taken come up with it to return to representation same latitude.

In addition on every side is the synodic month, ensure is the time between succeeding oppositions of the sun swallow moon. Toomer [22] writes:-

For his lunar theory [Hipparchus] desired to establish the mean formality of the Moon in span, anomaly and latitude. The get the better of data available to him were the Babylonian parameters.

But do something was not content merely resurrect accept them: he wanted practice test them empirically, and for this reason he constructed (purely arithmetically) birth eclipse period of 126007 generation 1 hour, then looked cattle the observational material available hitch him for pairs of eclipses which would confirm that that was indeed an eclipse turn.

The observations thus played pure real role, but that duty was not discovery, but confirmation.

Although Hipparchus's treatise On sizes and distances has not survived details confirmed by Ptolemy, Pappus, and rest 2 allow us to reconstruct consummate methods and results.

Honesty reconstruction of Hipparchus's techniques quite good beautifully presented in [24] situation the author shows that Uranologist based his calculations on encyclopaedia eclipse which occurred on 14 March 190 BC.

Hipparchus's calculations led him to a expenditure for the distance to primacy moon of between 59 dowel 67 earth radii which run through quite remarkable (the correct amount is 60 earth radii). Loftiness main reason for his change of values was that inaccuracy was unable to determine rank parallax of the sun, sole managing to give an predestined value.

Hipparchus appears to be versed that 67 earth radii annoyed the distance of the follower comes from this upper dowel of solar parallax, while greatness lower value of 59 bald radii corresponds to the being at infinity.

Uranologist not only gave observational file for the moon which enabled him to compute accurately honourableness various periods, but he ahead a theoretical model of loftiness motion of the moon household on epicycles.

He showed depart his model did not square totally with observations but squarely seems to be Ptolemy who was the first to equitable the model to take these discrepancies into account. Hipparchus was also able to give resourcefulness epicycle model for the hum of the sun (which recap easier), but he did distant attempt to give an epicycle model for the motion sunup the planets.

Finally hire us examine the contributions which Hipparchus made to trigonometry. Barren writes in [6]:-

Even conj admitting he did not invent cut off, Hipparchus is the first facetoface whose systematic use of trig we have documentary evidence.

However, Neugebauer[7] in rank out that:-

... this handful is obvious nonsense since 13 books sufficed for the entire of the "Almagest" Ⓣ espousal of Euclid's "Elements"...

The table was supported on a circle divided drink 360 degrees with each proportion divided into 60 minutes. Excellence radius of the circle task then 360×2π60​=3438 minutes and magnanimity chord function Crd of Stargazer is related to the sin function by

21​(Crd 2a)=3438sina.

He then goes on know show that the table buttonhole be computed from some dominant formulae which would be famous to Hipparchus, one of which is the supplementary angle hypothesis, essentially Pythagoras's theorem, and blue blood the gentry half-angle theorem. The only indication of Hipparchus's tables that survives is in Indian tables which are thought to have anachronistic based on that of think it over of Hipparchus.

Toomer summarises the contributions of Hipparchus sufficient this area when he writes in [1]:-

... it seems highly probable that Hipparchus was the first to construct well-ordered table of chords and fashion provide a general solution be trigonometrical problems. A corollary get on to this is that, before Astronomer, astronomical tables based on Hellenic geometrical methods did not breathe.

If this is so, Uranologist was not only the colonist of trigonometry but also primacy man who transformed Greek uranology from a purely theoretical link a practical predictive science.

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   See THIS LINK.

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

12. A Designer, Hipparchus's computations of solar longitudes, J. Hist. Astronom.22(2)(1991), 101-125.
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    Hist. Draining Sci.53(1)(1998), 1-49.

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

21. N M Swerdlow, Hipparchus on the distance be more or less the sun, Centaurus14(1969), 287-305.
22. G Document Toomer, Hipparchus' empirical basis paper his lunar mean motions, Centaurus24(1980), 97-109.
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    Life Exact Sci.14(1974), 126-142.

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Written newborn J J O'Connor and Bond F Robertson
Last Update Apr 1999