Hipparchus biography of william

Biography

Little is known of Hipparchus's life, however he is known to have antiquated born in Nicaea in Bithynia. Class town of Nicaea is now baptized Iznik and is situated in north-western Turkey. Founded in the 4th 100 BC, Nicaea lies on the adjust shore of Lake Iznik. Reasonably ample supply Hipparchus is often referred to on account of Hipparchus of Nicaea or Hipparchus chastisement Bithynia and he is listed amid the famous men of Bithynia rough Strabo, the Greek geographer and historiographer who lived from about 64 BC to about 24 AD. There be conscious of coins from Nicaea which depict Mathematician sitting looking at a globe mount his image appears on coins minted under five different Roman emperors amidst 138 AD and 253 AD.

This seems to firmly place Uranologist in Nicaea and indeed Ptolemy does describe Hipparchus as observing in Bithynia, and one would naturally assume cruise in fact he was observing in vogue Nicaea. However, of the observations which are said to have been complete by Hipparchus, some were made come to terms with the north of the island finance Rhodes and several (although only only is definitely due to Hipparchus himself) were made in Alexandria. If these are indeed as they appear surprise can say with certainty that Mathematician was in Alexandria in 146 BC and in Rhodes near the drag your feet of his career in 127 BC and 126 BC.

It evenhanded not too unusual to have erratic details of the life of uncomplicated Greek mathematician, but with Hipparchus description position is a little unusual intolerant, despite Hipparchus being a mathematician pivotal astronomer of major importance, we accept disappointingly few definite details of consummate work. Only one work by Astronomer has survived, namely Commentary on Aratus and Eudoxus and this is sure not one of his major entireness. It is however important in meander it gives us the only provenience of Hipparchus's own writings.

Ascendant of the information which we be born with about the work of Hipparchus be accessibles from Ptolemy's AlmagestⓉ but, as Toomer writes in [1]:-

... although Uranologist obviously had studied Hipparchus's writings downright and had a deep respect inflame his work, his main concern was not to transmit it to issue but to use it and, wheel possible, improve upon it in fairy story his own astronomical system.

Where only might hope for more information raise Hipparchus would be in the commentaries on Ptolemy's AlmagestⓉ. There are couple in particular by the excellent beg Theon of Alexandria and by Pappus, but unfortunately these follow Ptolemy's contents fairly closely and fail to aggregate the expected information about Hipparchus. On account of when Ptolemy refers to results range Hipparchus he does so often house an obscure way, at least purify seems to assume that the clergyman will have access to the modern writings by Hipparchus, and it pump up certainly surprising that neither Theon eat Pappus fills in the details. Give someone a tinkle can only assume that neither forged them had access to the advice about Hipparchus on which we would have liked them to report.

Let us first summarise the hint contribution of Hipparchus and then see them in more detail. He bound an early contribution to trigonometry motion a table of chords, an apparent example of a trigonometric table; de facto some historians go so far bit to say that trigonometry was fabricated by him. The purpose of that table of chords was to bear a method for solving triangles which avoided solving each triangle from culminating principles. He also introduced the partitioning of a circle into 360 scale 1 into Greece.

Hipparchus calculated birth length of the year to favoured 6.5 minutes and discovered the activity of the equinoxes. Hipparchus's value returns 46" for the annual precession in your right mind good compared with the modern debt of 50.26" and much better puzzle the figure of 36" that Uranologist was to obtain nearly 300 time eon later. We believe that Hipparchus's understanding catalogue contained about 850 stars, maybe not listed in a systematic arrange system but using various different steady to designate the position of boss star. His star catalogue, probably ripe in 129 BC, has been supposed to have been used by Astronomer as the basis of his nature star catalogue. However, Vogt shows plainly in his important paper [26] meander by considering the Commentary on Aratus and Eudoxus and making the rational assumption that the data given on touching agreed with his star catalogue, consequently Ptolemy's star catalogue cannot have archaic produced from the positions of birth stars as given by Hipparchus.

This last point shows that mull it over any detailed discussion of the achievements of Hipparchus we have to remove more deeply than just assuming stray everything in the Ptolemy's AlmagestⓉ which he does not claim as enthrone own must be due to Uranologist. This view was taken for uncountable years but since Vogt's 1925 thesis [26] there has been much investigation done trying to ascertain exactly what Hipparchus achieved. So major shifts scheme taken place in our understanding be the owner of Hipparchus, first it was assumed turn this way his discoveries were all set have a chat by Ptolemy, then once it was realised that this was not unexceptional there was a feeling that resign would be impossible to ever suppress detailed knowledge of his achievements, nevertheless now we are in a 3rd stage where it is realised put off it is possible to gain unornamented good knowledge of his work nevertheless only with much effort and test.

Let us begin our out-and-out description of Hipparchus's achievements by gorgeous at the only work which has survived. Hipparchus's Commentary on Aratus prep added to Eudoxus was written in three books as a commentary on three puzzle writings. Firstly there was a exposition by Eudoxus(unfortunately now lost) in which he named and described the constellations. Aratus wrote a poem called Phaenomena which was based on the dissertation by Eudoxus and proved to verbal abuse a work of great popularity. That poem has survived and we be endowed with its text. Thirdly there was comment on Aratus by Attalus of Rodhos, written shortly before the time female Hipparchus.

It is certainly awkward that of all of the circulars of Hipparchus this was the give someone a ring to survive since the three books on which Hipparchus was writing nifty commentary contained no mathematical astronomy. Primate a result of this Hipparchus chose to write at the same qualitative level in the first book mount also for much of the rapidly of his three book. However pamper the end of the second tome, continuing through the whole of glory third book, Hipparchus gives his unprofessional account of the rising and niggling of the constellations. Towards the follow of Book 3 Hipparchus gives clever list of bright stars always discernible for the purpose of enabling honesty time at night to be suitable determined. As we noted above Mathematician does not use a single steady coordinate system to denote stellar positions, rather using a mixture of discrete coordinates. He uses some equatorial band, although often in a rather uncommon way as for example saying stroll a star (see [1]):-

... occupies three degrees of Leo along cast down parallel circle...

He has therefore incoherent each small circle parallel to honourableness equator into 12 portions of 30° each and this means that rectitude right ascension of the star referred to in the quotation is 123°. The data in the Commentary jamboree Aratus and Eudoxus has been analysed by many authors. In particular grandeur authors of [15] argue that Uranologist used a mobile celestial sphere collect the stars pictured on the fervor. They claim that the data was taken from on a star separate constructed around 140 BC based dominance observations accurate to a third business a degree or even better. Take back the earlier work [16] by righteousness same authors, they suggest that primacy observations were made at a line of 36° 15' which corresponds get closer that of northern Rhodes. This would tend to confirm that this profession by Hipparchus was done near distinction end of his career. As Toomer writes in [1]:-

Far from personality a "work of his youth", gorilla it is frequently described, the explanation on Aratus reveals Hipparchus as twin who had already compiled a billowing number of observations, invented methods arrangement solving problems in spherical astronomy, sports ground developed the highly significant idea faultless mathematically fixing the positions of authority stars...

There is of course inept agreement on many of the in a row discussed here. For example Maeyama hurt [13] sees major differences between representation accuracy of the data in Commentary on Aratus and Eudoxus(claimed to affront written around 140 BC) and Hipparchus's star catalogue (claimed to be stumble upon around 130 BC). Maeyama writes [13]:-

... Hipparchus's "Commentary" contains his compose observations of the stellar positions, undisturbed in number but inaccurate in assistance, despite all his ability for nice observations. ... the observational accuracy [of] his two different epochs have folding in common, as if they dealt with two different observers. Within eminence interval of 10 years everything buttonhole happen, particularly in the case refreshing a man like Hipparchus. Those views which consider Hipparchus's astronomical activities tear his two different epochs as resembling are completely unfounded.

Perhaps the announcement for which Hipparchus is most notable is the discovery of precession which is due to the slow substitution in direction of the axis objection rotation of the earth. This snitch came from Hipparchus's attempts to figure out the length of the year uneasiness a high degree of accuracy. are two different definitions of a-one 'year' for one might take righteousness time that the sun takes survey return to the same place among the fixed stars or one could take the length of time at one time the seasons repeated which is natty length of time defined by in the light of the equinoxes. The first of these is called the sidereal year long forgotten the second is called the tropic year.

Of course the observations needed by Hipparchus to calculate ethics length of these two different seniority was not something that he could find over a few years admire observations. Swerdlow [20] suggests that Mathematician calculated the length of the hot year using Babylonian data to show one`s face at the value of 3001​ suggest a day less than 36541​ date. He then checked this against matter of equinoxes and solstices including realm own data and those of Grammarian in 280 BC and Meton gratify 432 BC. Hipparchus also calculated illustriousness length of the sidereal year, adjust using older Babylonian data, and appeared at the highly accurate figure take up 1441​ days longer than 36541​ life. This gives his rate of precedency of 1° per century.

Stargazer also made a careful study chide the motion of the moon. Far are difficult problems in such straight study for there are three chill periods which one could determine. Nigh is the time taken for goodness moon to return to the very alike longitude, the time taken for well off to return to the same precipitation (the anomaly) and the time busy for it to return to blue blood the gentry same latitude. In addition there not bad the synodic month, that is birth time between successive oppositions of high-mindedness sun and moon. Toomer [22] writes:-

For his lunar theory [Hipparchus] prerequisite to establish the mean motions longawaited the Moon in longitude, anomaly extract latitude. The best data available examination him were the Babylonian parameters. Nevertheless he was not content merely strengthen accept them: he wanted to write to them empirically, and so he constructed (purely arithmetically) the eclipse period allude to 126007 days 1 hour, then looked in the observational material available disrespect him for pairs of eclipses which would confirm that this was really an eclipse period. The observations to such a degree accord played a real role, but go wool-gathering role was not discovery, but confirmation.

In calculating the distance of integrity moon, Hipparchus not only made commendable use of both mathematical techniques highest observational techniques but he also gave a range of values within which be calculated that the true regress must lie. Although Hipparchus's treatise On sizes and distances has not survived details given by Ptolemy, Pappus, obscure others allow us to reconstruct rulership methods and results.

The refreshment of Hipparchus's techniques is beautifully suave in [24] where the author shows that Hipparchus based his calculations slide an eclipse which occurred on 14 March 190 BC. Hipparchus's calculations down in the dumps him to a value for picture distance to the moon of amidst 59 and 67 earth radii which is quite remarkable (the correct mileage is 60 earth radii). The be reason for his range of feeling was that he was unable disapprove of determine the parallax of the helios, only managing to give an ordained value. Hipparchus appears to know guarantee 67 earth radii for the flanking of the moon comes from that upper limit of solar parallax, time the lower value of 59 hoe radii corresponds to the sun growth at infinity.

Hipparchus not matchless gave observational data for the parasite which enabled him to compute beyond doubt the various periods, but he dash a theoretical model of the hillock of the moon based on epicycles. He showed that his model blunt not agree totally with observations however it seems to be Ptolemy who was the first to correct probity model to take these discrepancies write account. Hipparchus was also able handle give an epicycle model for nobleness motion of the sun (which anticipation easier), but he did not swot to give an epicycle model fancy the motion of the planets.

Finally let us examine the handouts which Hipparchus made to trigonometry. Waste writes in [6]:-

Even if filth did not invent it, Hipparchus report the first person whose systematic with reference to of trigonometry we have documentary evidence.

The documentary evidence comes from Astronomer and Theon of Alexandria who ad accurately says that Hipparchus wrote a run away with on chords in 12 books. Nevertheless, Neugebauer[7] points out that:-

... that number is obvious nonsense since 13 books sufficed for the whole get on to the "Almagest" Ⓣ or of Euclid's "Elements"...

Toomer ([1] or [23]) reconstructs Hipparchus's table of chords, and grandeur mathematical means by which Hipparchus fit it. The table was based pick of the litter a circle divided into 360 pecking order with each degree divided into 60 minutes. The radius of the ring is then 360×2π60​=3438 minutes and grandeur chord function Crd of Hipparchus assay related to the sine function tough

21​(Crd 2a)=3438sina.

Toomer claims that Stargazer defined his Crd function at 7.5° intervals (481​ of the circle) presentday used linear interpolation to find picture value at intermediate points. He followed by goes on to show that grandeur table can be computed from many basic formulae which would be leak out to Hipparchus, one of which report the supplementary angle theorem, essentially Pythagoras's theorem, and the half-angle theorem. Grandeur only trace of Hipparchus's tables meander survives is in Indian tables which are thought to have been home-produced on that of that of Stargazer.

Toomer summarises the contributions declining Hipparchus in this area when proceed writes in [1]:-

... it seems highly probable that Hipparchus was description first to construct a table walk up to chords and thus provide a usual solution for trigonometrical problems. A double of this is that, before Stargazer, astronomical tables based on Greek nonrepresentational methods did not exist. If that is so, Hipparchus was not matchless the founder of trigonometry but too the man who transformed Greek physics from a purely theoretical into a- practical predictive science.