Trigonometry developed in many parts of the world over thousands of years, but the mathematicians who are most credited with its discovery are Hipparchus, Menelaus and Ptolemy. That means, no further statement is allowed on these hundreds of stars. Since Nicolaus Copernicus (14731543) established his heliocentric model of the universe, the stars have provided a fixed frame of reference, relative to which the plane of the equator slowly shiftsa phenomenon referred to as the precession of the equinoxes, a wobbling of Earths axis of rotation caused by the gravitational influence of the Sun and Moon on Earths equatorial bulge that follows a 25,772-year cycle. You can observe all of the stars from the equator over the course of a year, although high- declination stars will be difficult to see so close to the horizon. [35] It was total in the region of the Hellespont (and in his birthplace, Nicaea); at the time Toomer proposes the Romans were preparing for war with Antiochus III in the area, and the eclipse is mentioned by Livy in his Ab Urbe Condita Libri VIII.2. According to Roman sources, Hipparchus made his measurements with a scientific instrument and he obtained the positions of roughly 850 stars. Ptolemy discussed this a century later at length in Almagest VI.6. [15] However, Franz Xaver Kugler demonstrated that the synodic and anomalistic periods that Ptolemy attributes to Hipparchus had already been used in Babylonian ephemerides, specifically the collection of texts nowadays called "System B" (sometimes attributed to Kidinnu).[16]. ? The traditional value (from Babylonian System B) for the mean synodic month is 29days; 31,50,8,20 (sexagesimal) = 29.5305941 days. The three most important mathematicians involved in devising Greek trigonometry are Hipparchus, Menelaus, and Ptolemy. How did Hipparchus contribute to trigonometry? [4][5] He was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. Aristarchus, Hipparchus and Archimedes after him, used this inequality without comment. 103,049 is the tenth SchrderHipparchus number, which counts the number of ways of adding one or more pairs of parentheses around consecutive subsequences of two or more items in any sequence of ten symbols. Ptolemy mentions that Menelaus observed in Rome in the year 98 AD (Toomer). Ptolemy characterized him as a lover of truth (philalths)a trait that was more amiably manifested in Hipparchuss readiness to revise his own beliefs in the light of new evidence. Steele J.M., Stephenson F.R., Morrison L.V. 1:28 Solving an Ancient Tablet's Mathematical Mystery Sidoli N. (2004). What is Aristarchus full name? Hipparchus of Nicaea was an Ancient Greek astronomer and mathematician. "The Size of the Lunar Epicycle According to Hipparchus. Ch. It is believed that he was born at Nicaea in Bithynia. Analysis of Hipparchus's seventeen equinox observations made at Rhodes shows that the mean error in declination is positive seven arc minutes, nearly agreeing with the sum of refraction by air and Swerdlow's parallax. In the first book, Hipparchus assumes that the parallax of the Sun is 0, as if it is at infinite distance. Hipparchus: The birth of trigonometry occurred in the chord tables of Hipparchus (c 190 - 120 BCE) who was born shortly after Eratosthenes died. Ptolemy made no change three centuries later, and expressed lengths for the autumn and winter seasons which were already implicit (as shown, e.g., by A. Aaboe). According to Pappus, he found a least distance of 62, a mean of 67+13, and consequently a greatest distance of 72+23 Earth radii. He didn't invent the sine and cosine functions, but instead he used the \chord" function, giving the length of the chord of the unit circle that subtends a given angle. This makes Hipparchus the founder of trigonometry. Knowledge of the rest of his work relies on second-hand reports, especially in the great astronomical compendium the Almagest, written by Ptolemy in the 2nd century ce. However, this does not prove or disprove anything because the commentary might be an early work while the magnitude scale could have been introduced later. [14], Hipparchus probably compiled a list of Babylonian astronomical observations; G. J. Toomer, a historian of astronomy, has suggested that Ptolemy's knowledge of eclipse records and other Babylonian observations in the Almagest came from a list made by Hipparchus. 43, No. It was also observed in Alexandria, where the Sun was reported to be obscured 4/5ths by the Moon. UNSW scientists have discovered the purpose of a famous 3700-year-old Babylonian clay tablet, revealing it is the world's oldest and most accurate trigonometric table. Hipparchus was not only the founder of trigonometry but also the man who transformed Greek astronomy from a purely theoretical into a practical predictive science. [47] Although the Almagest star catalogue is based upon Hipparchus's one, it is not only a blind copy but enriched, enhanced, and thus (at least partially) re-observed.[15]. The armillary sphere was probably invented only latermaybe by Ptolemy only 265 years after Hipparchus. (The true value is about 60 times. Hipparchus wrote a commentary on the Arateiahis only preserved workwhich contains many stellar positions and times for rising, culmination, and setting of the constellations, and these are likely to have been based on his own measurements. Hipparchus of Nicaea (c. 190 - c. 120 B.C.) How did Hipparchus discover and measure the precession of the equinoxes? Hipparchus's catalogue is reported in Roman times to have enlisted about 850 stars but Ptolemy's catalogue has 1025 stars. Did Hipparchus invent trigonometry? (1991). At school we are told that the shape of a right-angled triangle depends upon the other two angles. The distance to the moon is. It is not clear whether this would be a value for the sidereal year at his time or the modern estimate of approximately 365.2565 days, but the difference with Hipparchus's value for the tropical year is consistent with his rate of precession (see below). The modern words "sine" and "cosine" are derived from the Latin word sinus via mistranslation from Arabic (see Sine and cosine#Etymology).Particularly Fibonacci's sinus rectus arcus proved influential in establishing the term. [54] It was only in Hipparchus's time (2nd century BC) when this division was introduced (probably by Hipparchus's contemporary Hypsikles) for all circles in mathematics. How did Hipparchus discover trigonometry? Besides geometry, Hipparchus also used arithmetic techniques developed by the Chaldeans. Apparently it was well-known at the time. It is known to us from Strabo of Amaseia, who in his turn criticised Hipparchus in his own Geographia. It is unknown who invented this method. According to Theon, Hipparchus wrote a 12-book work on chords in a circle, since lost. Like others before and after him, he found that the Moon's size varies as it moves on its (eccentric) orbit, but he found no perceptible variation in the apparent diameter of the Sun. In this only work by his hand that has survived until today, he does not use the magnitude scale but estimates brightnesses unsystematically. In addition to varying in apparent speed, the Moon diverges north and south of the ecliptic, and the periodicities of these phenomena are different. He contemplated various explanationsfor example, that these stars were actually very slowly moving planetsbefore he settled on the essentially correct theory that all the stars made a gradual eastward revolution relative to the equinoxes. Astronomy test. Hipparchus's solution was to place the Earth not at the center of the Sun's motion, but at some distance from the center. Hipparchus also wrote critical commentaries on some of his predecessors and contemporaries. [29] (The maximum angular deviation producible by this geometry is the arcsin of 5+14 divided by 60, or approximately 5 1', a figure that is sometimes therefore quoted as the equivalent of the Moon's equation of the center in the Hipparchan model.). And the same individual attempted, what might seem presumptuous even in a deity, viz. I. [31] Speculating a Babylonian origin for the Callippic year is difficult to defend, since Babylon did not observe solstices thus the only extant System B year length was based on Greek solstices (see below). (See animation.). how did hipparchus discover trigonometry 29 Jun. He tabulated the chords for angles with increments of 7.5. (He similarly found from the 345-year cycle the ratio 4,267 synodic months = 4,573 anomalistic months and divided by 17 to obtain the standard ratio 251 synodic months = 269 anomalistic months.) His two books on precession, 'On the Displacement of the Solsticial and Equinoctial Points' and 'On the Length of the Year', are both mentioned in the Almagest of Ptolemy. In Raphael's painting The School of Athens, Hipparchus is depicted holding his celestial globe, as the representative figure for astronomy.[39]. That apparent diameter is, as he had observed, 360650 degrees. Hipparchus discovered the Earth's precession by following and measuring the movements of the stars, specifically Spica and Regulus, two of the brightest stars in our night sky. His contribution was to discover a method of using the . ), Greek astronomer and mathematician who made fundamental contributions to the advancement of astronomy as a mathematical science and to the foundations of trigonometry. Ch. Once again you must zoom in using the Page Up key. Let the time run and verify that a total solar eclipse did occur on this day and could be viewed from the Hellespont. The Greeks were mostly concerned with the sky and the heavens. An Australian mathematician has discovered that Babylonians may have used applied geometry roughly 1,500 years before the Greeks supposedly invented its foundations, according to a new study. Hipparchus was a famous ancient Greek astronomer who managed to simulate ellipse eccentricity by introducing his own theory known as "eccentric theory". : The now-lost work in which Hipparchus is said to have developed his chord table, is called Tn en kukli euthein (Of Lines Inside a Circle) in Theon of Alexandria's fourth-century commentary on section I.10 of the Almagest. The map segment, which was found beneath the text on a sheet of medieval parchment, is thought to be a copy of the long-lost star catalog of the second century B.C. Hipparchus also analyzed the more complicated motion of the Moon in order to construct a theory of eclipses. Not only did he make extensive observations of star positions, Hipparchus also computed lunar and solar eclipses, primarily by using trigonometry. 2 - Why did Copernicus want to develop a completely. Comparing both charts, Hipparchus calculated that the stars had shifted their apparent position by around two degrees. These models, which assumed that the apparent irregular motion was produced by compounding two or more uniform circular motions, were probably familiar to Greek astronomers well before Hipparchus. G J Toomer's chapter "Ptolemy and his Greek Predecessors" in "Astronomy before the Telescope", British Museum Press, 1996, p.81. Every year the Sun traces out a circular path in a west-to-east direction relative to the stars (this is in addition to the apparent daily east-to-west rotation of the celestial sphere around Earth). The lunar crater Hipparchus and the asteroid 4000 Hipparchus are named after him. He criticizes Hipparchus for making contradictory assumptions, and obtaining conflicting results (Almagest V.11): but apparently he failed to understand Hipparchus's strategy to establish limits consistent with the observations, rather than a single value for the distance. Hipparchus calculated the length of the year to within 6.5 minutes and discovered the precession of the equinoxes. This makes Hipparchus the founder of trigonometry. Alternate titles: Hipparchos, Hipparchus of Bithynia, Professor of Classics, University of Toronto. Trigonometry is discovered by an ancient greek mathematician Hipparchus in the 2 n d century BC. Many credit him as the founder of trigonometry. Like others before and after him, he also noticed that the Moon has a noticeable parallax, i.e., that it appears displaced from its calculated position (compared to the Sun or stars), and the difference is greater when closer to the horizon. His famous star catalog was incorporated into the one by Ptolemy and may be almost perfectly reconstructed by subtraction of two and two-thirds degrees from the longitudes of Ptolemy's stars. Hipparchus of Nicaea was a Greek Mathematician, Astronomer, Geographer from 190 BC. However, the timing methods of the Babylonians had an error of no fewer than eight minutes. He also introduced the division of a circle into 360 degrees into Greece. However, Strabo's Hipparchus dependent latitudes for this region are at least 1 too high, and Ptolemy appears to copy them, placing Byzantium 2 high in latitude.) His birth date (c.190BC) was calculated by Delambre based on clues in his work. He considered every triangle as being inscribed in a circle, so that each side became a chord. 1. Greek astronomer Hipparchus . (Parallax is the apparent displacement of an object when viewed from different vantage points). But the papyrus makes the date 26 June, over a day earlier than the 1991 paper's conclusion for 28 June. With his value for the eccentricity of the orbit, he could compute the least and greatest distances of the Moon too. "The Introduction of Dated Observations and Precise Measurement in Greek Astronomy" Archive for History of Exact Sciences Alexander Jones "Ptolemy in Perspective: Use and Criticism of his Work from Antiquity to the Nineteenth Century, Springer, 2010, p.36. He then analyzed a solar eclipse, which Toomer (against the opinion of over a century of astronomers) presumes to be the eclipse of 14 March 190BC. [41] This system was made more precise and extended by N. R. Pogson in 1856, who placed the magnitudes on a logarithmic scale, making magnitude 1 stars 100 times brighter than magnitude 6 stars, thus each magnitude is 5100 or 2.512 times brighter than the next faintest magnitude. Before him a grid system had been used by Dicaearchus of Messana, but Hipparchus was the first to apply mathematical rigor to the determination of the latitude and longitude of places on the Earth. The Moon would move uniformly (with some mean motion in anomaly) on a secondary circular orbit, called an, For the eccentric model, Hipparchus found for the ratio between the radius of the. So he set the length of the tropical year to 365+14 1300 days (= 365.24666 days = 365days 5hours 55min, which differs from the modern estimate of the value (including earth spin acceleration), in his time of approximately 365.2425 days, an error of approximately 6min per year, an hour per decade, and ten hours per century. It was disputed whether the star catalog in the Almagest is due to Hipparchus, but 19762002 statistical and spatial analyses (by R. R. Newton, Dennis Rawlins, Gerd Grasshoff,[44] Keith Pickering[45] and Dennis Duke[46]) have shown conclusively that the Almagest star catalog is almost entirely Hipparchan. The catalog was superseded only in the late 16th century by Brahe and Wilhelm IV of Kassel via superior ruled instruments and spherical trigonometry, which improved accuracy by an order of magnitude even before the invention of the telescope. Hipparchus adopted values for the Moons periodicities that were known to contemporary Babylonian astronomers, and he confirmed their accuracy by comparing recorded observations of lunar eclipses separated by intervals of several centuries. He also might have developed and used the theorem called Ptolemy's theorem; this was proved by Ptolemy in his Almagest (I.10) (and later extended by Carnot). True is only that "the ancient star catalogue" that was initiated by Hipparchus in the second century BC, was reworked and improved multiple times in the 265 years to the Almagest (which is good scientific practise until today). It was based on a circle in which the circumference was divided, in the normal (Babylonian) manner, into 360 degrees of 60 minutes, and the radius was measured in the same units; thus R, the radius, expressed in minutes, is This function is related to the modern sine function (for in degrees) by If he sought a longer time base for this draconitic investigation he could use his same 141 BC eclipse with a moonrise 1245 BC eclipse from Babylon, an interval of 13,645 synodic months = 14,8807+12 draconitic months 14,623+12 anomalistic months. Hipparchus could confirm his computations by comparing eclipses from his own time (presumably 27 January 141BC and 26 November 139BC according to [Toomer 1980]), with eclipses from Babylonian records 345 years earlier (Almagest IV.2; [A.Jones, 2001]). ?rk?s/; Greek: ????? "Hipparchus' Treatment of Early Greek Astronomy: The Case of Eudoxus and the Length of Daytime Author(s)". Bowen A.C., Goldstein B.R. Part 2 can be found here. Hipparchus produced a table of chords, an early example of a trigonometric table. [49] His two books on precession, On the Displacement of the Solstitial and Equinoctial Points and On the Length of the Year, are both mentioned in the Almagest of Claudius Ptolemy. Review of, "Hipparchus Table of Climata and Ptolemys Geography", "Hipparchos' Eclipse-Based Longitudes: Spica & Regulus", "Five Millennium Catalog of Solar Eclipses", "New evidence for Hipparchus' Star Catalog revealed by multispectral imaging", "First known map of night sky found hidden in Medieval parchment", "Magnitudes of Thirty-six of the Minor Planets for the first day of each month of the year 1857", "The Measurement Method of the Almagest Stars", "The Genesis of Hipparchus' Celestial Globe", Hipparchus "Table of Climata and Ptolemys Geography", "Hipparchus on the Latitude of Southern India", Eratosthenes' Parallel of Rhodes and the History of the System of Climata, "Ptolemys Latitude of Thule and the Map Projection in the Pre-Ptolemaic Geography", "Hipparchus, Plutarch, Schrder, and Hough", "On the shoulders of Hipparchus: A reappraisal of ancient Greek combinatorics", "X-Prize Group Founder to Speak at Induction", "A new determination of lunar orbital parameters, precession constant, and tidal acceleration from LLR measurements", "The Epoch of the Constellations on the Farnese Atlas and their Origin in Hipparchus's Lost Catalogue", Eratosthenes Parallel of Rhodes and the History of the System of Climata, "The accuracy of eclipse times measured by the Babylonians", "Lunar Eclipse Times Recorded in Babylonian History", Learn how and when to remove this template message, Biography of Hipparchus on Fermat's Last Theorem Blog, Os Eclipses, AsterDomus website, portuguese, Ancient Astronomy, Integers, Great Ratios, and Aristarchus, David Ulansey about Hipparchus's understanding of the precession, A brief view by Carmen Rush on Hipparchus' stellar catalog, "New evidence for Hipparchus' Star Catalogue revealed by multispectral imaging", Ancient Greek and Hellenistic mathematics, https://en.wikipedia.org/w/index.php?title=Hipparchus&oldid=1141264401, Short description is different from Wikidata, Articles with unsourced statements from September 2022, Articles with unsourced statements from March 2021, Articles containing Ancient Greek (to 1453)-language text, Wikipedia articles incorporating a citation from the 1911 Encyclopaedia Britannica with Wikisource reference, Wikipedia external links cleanup from May 2017, Creative Commons Attribution-ShareAlike License 3.0. [63], Jean Baptiste Joseph Delambre, historian of astronomy, mathematical astronomer and director of the Paris Observatory, in his history of astronomy in the 18th century (1821), considered Hipparchus along with Johannes Kepler and James Bradley the greatest astronomers of all time. With Hipparchuss mathematical model one could calculate not only the Suns orbital location on any date, but also its position as seen from Earth. In calculating latitudes of climata (latitudes correlated with the length of the longest solstitial day), Hipparchus used an unexpectedly accurate value for the obliquity of the ecliptic, 2340' (the actual value in the second half of the second centuryBC was approximately 2343'), whereas all other ancient authors knew only a roughly rounded value 24, and even Ptolemy used a less accurate value, 2351'.[53]. These must have been only a tiny fraction of Hipparchuss recorded observations. Our editors will review what youve submitted and determine whether to revise the article. He also discovered that the moon, the planets and the stars were more complex than anyone imagined. The result that two solar eclipses can occur one month apart is important, because this can not be based on observations: one is visible on the northern and the other on the southern hemisphereas Pliny indicatesand the latter was inaccessible to the Greek. Author of. His theory influence is present on an advanced mechanical device with code name "pin & slot". [65], Johannes Kepler had great respect for Tycho Brahe's methods and the accuracy of his observations, and considered him to be the new Hipparchus, who would provide the foundation for a restoration of the science of astronomy.[66]. They write new content and verify and edit content received from contributors. Eratosthenes (3rd century BC), in contrast, used a simpler sexagesimal system dividing a circle into 60 parts. to number the stars for posterity and to express their relations by appropriate names; having previously devised instruments, by which he might mark the places and the magnitudes of each individual star. Apparently his commentary Against the Geography of Eratosthenes was similarly unforgiving of loose and inconsistent reasoning. "Hipparchus on the distance of the sun. Ptolemy has even (since Brahe, 1598) been accused by astronomers of fraud for stating (Syntaxis, book 7, chapter 4) that he observed all 1025 stars: for almost every star he used Hipparchus's data and precessed it to his own epoch 2+23 centuries later by adding 240' to the longitude, using an erroneously small precession constant of 1 per century. Hipparchus seems to have been the first to exploit Babylonian astronomical knowledge and techniques systematically. As the first person to look at the heavens with the newly invented telescope, he discovered evidence supporting the sun-centered theory of Copernicus. This was the basis for the astrolabe. Hipparchus compiled a table of the chords of angles and made them available to other scholars. Trigonometry is a branch of math first created by 2nd century BC by the Greek mathematician Hipparchus. It was a four-foot rod with a scale, a sighting hole at one end, and a wedge that could be moved along the rod to exactly obscure the disk of Sun or Moon. It is unknown what instrument he used. Hipparchus (/ h p r k s /; Greek: , Hipparkhos; c. 190 - c. 120 BC) was a Greek astronomer, geographer, and mathematician.He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equinoxes. The formal name for the ESA's Hipparcos Space Astrometry Mission is High Precision Parallax Collecting Satellite, making a backronym, HiPParCoS, that echoes and commemorates the name of Hipparchus. Hipparchuss most important astronomical work concerned the orbits of the Sun and Moon, a determination of their sizes and distances from Earth, and the study of eclipses. The history of trigonometry and of trigonometric functions sticks to the general lines of the history of math. Hipparchus made observations of equinox and solstice, and according to Ptolemy (Almagest III.4) determined that spring (from spring equinox to summer solstice) lasted 9412 days, and summer (from summer solstice to autumn equinox) 92+12 days. "Associations between the ancient star catalogs". From modern ephemerides[27] and taking account of the change in the length of the day (see T) we estimate that the error in the assumed length of the synodic month was less than 0.2 second in the fourth centuryBC and less than 0.1 second in Hipparchus's time. 104". (1967). This is called its anomaly and it repeats with its own period; the anomalistic month. He did this by using the supplementary angle theorem, half angle formulas, and linear . Ptolemy later used spherical trigonometry to compute things such as the rising and setting points of the ecliptic, or to take account of the lunar parallax. 2 - Why did Ptolemy have to introduce multiple circles. He was an outspoken advocate of the truth, of scientific . This is a highly critical commentary in the form of two books on a popular poem by Aratus based on the work by Eudoxus. A solution that has produced the exact .mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}5,4585,923 ratio is rejected by most historians although it uses the only anciently attested method of determining such ratios, and it automatically delivers the ratio's four-digit numerator and denominator. Hipparchus discovered the table of values of the trigonometric ratios. Lived c. 210 - c. 295 AD. Nadal R., Brunet J.P. (1984). Some scholars do not believe ryabhaa's sine table has anything to do with Hipparchus's chord table. In the first, the Moon would move uniformly along a circle, but the Earth would be eccentric, i.e., at some distance of the center of the circle. How did Hipparchus discover trigonometry? Most of what is known about Hipparchus comes from Strabo's Geography and Pliny's Natural History in the first century; Ptolemy's second-century Almagest; and additional references to him in the fourth century by Pappus and Theon of Alexandria in their commentaries on the Almagest.[11]. (1974). Let us know if you have suggestions to improve this article (requires login). The first trigonometric table was apparently compiled by Hipparchus, who is consequently now known as "the father of trigonometry". Toomer (1980) argued that this must refer to the large total lunar eclipse of 26 November 139BC, when over a clean sea horizon as seen from Rhodes, the Moon was eclipsed in the northwest just after the Sun rose in the southeast. In geographic theory and methods Hipparchus introduced three main innovations. The geometry, and the limits of the positions of Sun and Moon when a solar or lunar eclipse is possible, are explained in Almagest VI.5. Hipparchus's ideas found their reflection in the Geography of Ptolemy. Hipparchus is the first astronomer known to attempt to determine the relative proportions and actual sizes of these orbits. Chords are nearly related to sines. He communicated with observers at Alexandria in Egypt, who provided him with some times of equinoxes, and probably also with astronomers at Babylon. It is known today that the planets, including the Earth, move in approximate ellipses around the Sun, but this was not discovered until Johannes Kepler published his first two laws of planetary motion in 1609. Anyway, Hipparchus found inconsistent results; he later used the ratio of the epicycle model (3122+12: 247+12), which is too small (60: 4;45 sexagesimal). were probably familiar to Greek astronomers well before Hipparchus. In essence, Ptolemy's work is an extended attempt to realize Hipparchus's vision of what geography ought to be. He was inducted into the International Space Hall of Fame in 2004. One of his two eclipse trios' solar longitudes are consistent with his having initially adopted inaccurate lengths for spring and summer of 95+34 and 91+14 days. He was then in a position to calculate equinox and solstice dates for any year. "Geographical Latitudes in Eratosthenes, Hipparchus and Posidonius". Hipparchus was in the international news in 2005, when it was again proposed (as in 1898) that the data on the celestial globe of Hipparchus or in his star catalog may have been preserved in the only surviving large ancient celestial globe which depicts the constellations with moderate accuracy, the globe carried by the Farnese Atlas. The first known table of chords was produced by the Greek mathematician Hipparchus in about 140 BC. Earlier Greek astronomers and mathematicians were influenced by Babylonian astronomy to some extent, for instance the period relations of the Metonic cycle and Saros cycle may have come from Babylonian sources (see "Babylonian astronomical diaries"). 2 (1991) pp. Parallax lowers the altitude of the luminaries; refraction raises them, and from a high point of view the horizon is lowered. . His results appear in two works: Per megethn ka apostmtn ("On Sizes and Distances") by Pappus and in Pappus's commentary on the Almagest V.11; Theon of Smyrna (2nd century) mentions the work with the addition "of the Sun and Moon". His other reputed achievements include the discovery and measurement of Earth's precession, the compilation of the first known comprehensive star catalog from the western world, and possibly the invention of the astrolabe, as well as of the armillary sphere that he may have used in creating the star catalogue. Hipparchus, also spelled Hipparchos, (born, Nicaea, Bithynia [now Iznik, Turkey]died after 127 bce, Rhodes? As shown in a 1991 After Hipparchus the next Greek mathematician known to have made a contribution to trigonometry was Menelaus. How did Hipparchus discover trigonometry? Hipparchus insists that a geographic map must be based only on astronomical measurements of latitudes and longitudes and triangulation for finding unknown distances. Therefore, it is possible that the radius of Hipparchus's chord table was 3600, and that the Indians independently constructed their 3438-based sine table."[21]. Hipparchus's long draconitic lunar period (5,458 months = 5,923 lunar nodal periods) also appears a few times in Babylonian records. He is also famous for his incidental discovery of the. Isaac Newton and Euler contributed developments to bring trigonometry into the modern age.