So little is known about Hipparchus' life, but he is considered the true founder of trigonometry. Quite reasonably Hipparchus is often called Hipparchus of Nicaea or Hipparchus of Bithynia and is listed among the famous men of Bithynia by Strabo, the Greek geographer and historian who lived from about 64 BC to about 24 AD. There are Nicaean coins depicting Hipparchus seated looking at a globe and his image appears on coins minted under five different Roman emperors between 138 AD and 253 AD Say no to plagiarism. Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an original essay This seems to place Hipparchus firmly in Nicaea and indeed Ptolemy describes Hipparchus as observing in Bithynia, and one might naturally assume that he was in fact observed in Nicaea. However, of the observations said to have been made by Hipparchus, some were made in the north of the island of Rhodes and several (though only one is certainly due to Hipparchus himself) were made in Alexandria. If these are indeed as they appear we can say with certainty that Hipparchus was in Alexandria in 146 BC and in Rhodes towards the end of his career in 127 BC and 126 BC Greek mathematician, but with Hipparchus the position is a bit unusual because, although Hipparchus was a mathematician and astronomer of great importance, we unfortunately have few definitive details of his work. Only one work by Hipparchus has survived, namely the Commentary on Aratus and Eudoxus, and this is certainly not one of his major works. It is, however, important as it provides us with the only source of Hipparchus' writings. Most of the information we have on Hipparchus's work comes from Ptolemy's Almagest, but, as Toomer writes:...although Ptolemy obviously had studied Hipparchus' writings thoroughly and had a deep respect for his work, the his main concern was not to transmit it to posterity but to use it and, where possible, improve it in the construction of his own astronomical system. Where one might hope to have more information about Hipparchus would be in the commentaries on Ptolemy's Almagest?. There are two in particular of the excellent commentators Theon of Alexandria and Pappus, but unfortunately these follow Ptolemy's text quite faithfully and fail to add the expected information on Hipparchus. Since when Ptolemy refers to Hipparchus' achievements he often does so obscurely, he seems to at least assume that the reader will have access to Hipparchus' original writings, and it is certainly surprising that neither Theon nor Pappus provides the details. One can only assume that neither of them had access to the information about Hipparchus that we would have liked them to report. Let us first summarize Hipparchus' main contributions and then examine them in more detail. He made an initial contribution to trigonometry by producing a table of chords, an early example of a trigonometric table; indeed some historians go so far as to say that trigonometry was invented by him. The purpose of this chord table was to provide a method for solving triangles that avoided solving each triangle from first principles. He also introduced the division of the circle into 360 degrees into Greece. Hipparchus calculated the length of the year to within 6.5 minutes and discovered the precession of the equinoxes. The value of 46' assigned by Hipparchus for the annual precession is good compared to the modern value of 50.26' and much better than the figure of 36' that Ptolemy would obtain almost 300 years later. We believe that Hipparchus' star catalog contained about 850 stars, probably not listed in a systematic coordinate system but using several different ways to designate a star's position. His star catalogue, probably completed in 129 BC, is believed to bewas used by Ptolemy as the basis for his own star catalogue. However, Vogt clearly shows in his important article that, considering the Commentary on Aratus and Eudoxus and making the reasonable assumption that the data given there agrees with his star catalogue, then Ptolemy's star catalog cannot have been produced from the positions of the stars as dates of Hipparchus. This last point shows that in any detailed discussion of Hipparchus' findings we must delve into more than just the assumption that everything in Ptolemy's Almagest? what he does not claim as his own must be owed to Hipparchus. This view has been held for many years, but since Vogt's 1925 article [26] much research has been conducted trying to ascertain exactly what Hipparchus achieved. So great changes have occurred in our understanding of Hipparchus, at first it was assumed that his discoveries had all been established by Ptolemy, then once it was realized that this was not the case there was a widespread feeling that it would be impossible to have detailed knowledge of his successes, but now we are in a third phase in which we realize that it is possible to acquire a good knowledge of his work but only with a lot of effort and research. We begin our detailed description of Hipparchus's achievements by looking at the only work that has survived. Hipparchus' Commentary on Aratus and Eudoxus was written in three books as a commentary on three different writings. First of all, there was a treatise by Eudoxus (unfortunately now lost) in which he named and described the constellations. Aratus wrote a poem entitled Phaenomena based on the treatise of Eudoxus and it proved to be a work of great popularity. This poem has survived and we have the text. Thirdly there was a commentary on Aratus by Attalus of Rhodes, written shortly before the time of Hipparchus. It is certainly unfortunate that of all Hipparchus' writings this was the one that survived since the three books on which Hipparchus was commenting did not contain any mathematical astronomy. As a result, Hipparchus chose to write at the same level of quality in the first book and also for much of the second of his three books. However, towards the end of the second book, continuing throughout the third book, Hipparchus gives his own account of the rising and setting of the constellations. Towards the end of book 3 Hipparchus provides a list of bright stars that are always visible in order to allow the time of night to be accurately determined. As we noted above Hipparchus does not use a single coherent coordinate system to denote stellar positions, but rather uses a mixture of different coordinates. He uses some equatorial coordinates, although often in a somewhat strange way such as saying that a star:... occupies three degrees of Leo along its parallel circle... He then divided each small circle parallel to the equator into 12 portions of 30° each and this means that the right ascension of the star referred to in the quote is 123°. The data from the Commentary on Aratus and Eudoxus have been analyzed by many authors. In particular, the authors of [15] argue that Hipparchus used a mobile celestial sphere with the stars depicted on the sphere. They claim the data was taken from a star catalog built around 140 BC based on observations accurate to a third of a degree or better. In a previous work by the same authors it is suggested that the observations were carried out at a latitude of 36° 15' which corresponds to that of the north of Rhodes. This would tend to confirm that this work by Hipparchus was performed towards the end of his career. As Toomer writes: Far from being a “Work of his youth,” as it is often described, the commentary on Aratus reveals Hipparchus as one who had already compiled a large number ofobservations, invented methods for solving spherical astronomy problems, and developed the highly significant idea of ​​mathematically fixing the positions of stars... Of course there is no agreement on many of these points discussed here. For example, Maeyama sees large differences between the accuracy of the data in the Commentary on Aratus and Eudoxus (claimed to have been written around 140 BC) and Hipparchus' star catalog (claimed to have been produced around 130 BC). Maeyama writes:… Hipparchus's “Commentary” contains his observations of stellar positions, large in number but imprecise in operation, for all his capacity for accurate observations…. the accuracy of observation [of] its two different eras have nothing in common, as if they were two different observers. In the space of ten years anything can happen, especially in the case of a man like Hipparchus. Those opinions that consider Hipparchus' astronomical activities similar in his two different eras are completely unfounded. Perhaps the discovery for which Hipparchus is most famous is the discovery of precession which is due to the slow change in direction of the earth's rotation axis. This work derives from Hipparchus's attempts to calculate the length of the year with a high degree of precision. There are two different definitions of "year": you could take the time it takes for the sun to return to the same place among the fixed stars or you could take the period of time before the seasons repeat, which is a period of time defined by considering the equinoxes. The first of these is called the sidereal year while the second is called the tropical year. Of course, the data Hipparchus needed to calculate the duration of these two different years was not something he could have found in just a few years of observations. Swerdlow suggests that Hipparchus calculated the length of the tropical year using Babylonian data to arrive at the value of 1/300 of a day less than 3651/4 days. He then compared this with observations of the equinoxes and solstices, including his own data and those of Aristarchus in 280 BC and Metho in 432 BC. Hipparchus also calculated the length of the sidereal year, again using older Babylonian data, and arrived at highly accurate figure of 1/144 days longer than 3651/4 days. This gives its precession rate of 1° per century. Hipparchus also made a careful study of the movement of the moon. There are difficult problems in such a study because there are three different periods that could be determined. There is the time it takes for the Moon to return to the same longitude, the time it takes to return to the same speed (the anomaly), and the time it takes to return to the same latitude. Furthermore there is the synodic month, that is, the time that elapses between the successive oppositions of the Sun and Moon. Toomer writes: For his lunar theory [Hipparchus] needed to establish the mean motions of the Moon in longitude, anomaly, and latitude. The best data at his disposal were the Babylonian parameters. But he was not content simply to accept them: he wanted to test them empirically, and so he constructed (purely arithmetically) the eclipse period of 126007 days 1 hour, then searched in the observational material at his disposal for pairs of eclipses which confirmed that this was indeed a period of eclipse. Observations therefore played a real role, but that role was not discovery, but confirmation. In calculating the distance to the Moon, Hipparchus not only made excellent use of both mathematical and observational techniques, but also provided a range of values ​​within which the true distance should be calculated. Although Hipparchus's treatise On Dimensions and Distances has not survived, the details provided by Ptolemy, Pappus, and others allow us to reconstruct his methods and results. The reconstruction of, 36(1), 167-196.