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His results were the best so far: the actual mean distance of the Moon is 60.3 Earth radii, within his limits from Hipparchus's second book. Author of. Hipparchus is sometimes called the "father of astronomy",[7][8] a title first conferred on him by Jean Baptiste Joseph Delambre.[9]. Hipparchus produced a table of chords, an early example of a trigonometric table. Hipparchus must have lived some time after 127BC because he analyzed and published his observations from that year. How did Hipparchus discover trigonometry? [33] His other triplet of solar positions is consistent with 94+14 and 92+12 days,[34] an improvement on the results (94+12 and 92+12 days) attributed to Hipparchus by Ptolemy, which a few scholars still question the authorship of. From where on Earth could you observe all of the stars during the course of a year? One evening, Hipparchus noticed the appearance of a star where he was certain there had been none before. Isaac Newton and Euler contributed developments to bring trigonometry into the modern age. [58] According to one book review, both of these claims have been rejected by other scholars. He used old solstice observations and determined a difference of approximately one day in approximately 300 years. Hipparchus may also have used other sets of observations, which would lead to different values. Hipparchus was the first to show that the stereographic projection is conformal, and that it transforms circles on the sphere that do not pass through the center of projection to circles on the plane. He had immense in geography and was one of the most famous astronomers in ancient times. Hipparchus, also spelled Hipparchos, (born, Nicaea, Bithynia [now Iznik, Turkey]died after 127 bce, Rhodes? He was intellectually honest about this discrepancy, and probably realized that especially the first method is very sensitive to the accuracy of the observations and parameters. Hipparchus calculated the length of the year to within 6.5 minutes and discovered the precession of the equinoxes. He also introduced the division of a circle into 360 degrees into Greece. How did Hipparchus discover and measure the precession of the equinoxes? "Hipparchus' Empirical Basis for his Lunar Mean Motions,", Toomer G.J. 104". It seems he did not introduce many improvements in methods, but he did propose a means to determine the geographical longitudes of different cities at lunar eclipses (Strabo Geographia 1 January 2012). In any case, according to Pappus, Hipparchus found that the least distance is 71 (from this eclipse), and the greatest 81 Earth radii. The three most important mathematicians involved in devising Greek trigonometry are Hipparchus, Menelaus, and Ptolemy. ), Italian philosopher, astronomer and mathematician. 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]. https://www.britannica.com/biography/Hipparchus-Greek-astronomer, Ancient History Encyclopedia - Biography of Hipparchus of Nicea, Hipparchus - Student Encyclopedia (Ages 11 and up). Comparing both charts, Hipparchus calculated that the stars had shifted their apparent position by around two degrees. Hipparchus opposed the view generally accepted in the Hellenistic period that the Atlantic and Indian Oceans and the Caspian Sea are parts of a single ocean. Encyclopaedia Britannica's editors oversee subject areas in which they have extensive knowledge, whether from years of experience gained by working on that content or via study for an advanced degree. Many credit him as the founder of trigonometry. He also helped to lay the foundations of trigonometry.Although he is commonly ranked among the greatest scientists of antiquity, very little is known about his life, and only one of his many writings is still in existence. He was then in a position to calculate equinox and solstice dates for any year. 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. Even if he did not invent it, Hipparchus is the first person whose systematic use of trigonometry we have documentary evidence. This has led to speculation that Hipparchus knew about enumerative combinatorics, a field of mathematics that developed independently in modern mathematics. With this method, as the parallax of the Sun decreases (i.e., its distance increases), the minimum limit for the mean distance is 59 Earth radiiexactly the mean distance that Ptolemy later derived. In particular, he improved Eratosthenes' values for the latitudes of Athens, Sicily, and southern extremity of India. For his astronomical work Hipparchus needed a table of trigonometric ratios. (1934). Alexander Jones "Ptolemy in Perspective: Use and Criticism of his Work from Antiquity to the Nineteenth Century, Springer, 2010, p.36. From this perspective, the Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn (all of the solar system bodies visible to the naked eye), as well as the stars (whose realm was known as the celestial sphere), revolved around Earth each day. The armillary sphere was probably invented only latermaybe by Ptolemy only 265 years after Hipparchus. Hipparchus seems to have used a mix of ecliptic coordinates and equatorial coordinates: in his commentary on Eudoxus he provides stars' polar distance (equivalent to the declination in the equatorial system), right ascension (equatorial), longitude (ecliptic), polar longitude (hybrid), but not celestial latitude. This is inconsistent with a premise of the Sun moving around the Earth in a circle at uniform speed. Hipparchus "Even if he did not invent it, Hipparchus is the first person of whose systematic use of trigonometry we have documentary evidence." (Heath 257) Some historians go as far as to say that he invented trigonometry. This is the first of three articles on the History of Trigonometry. Mott Greene, "The birth of modern science?" Comparing both charts, Hipparchus calculated that the stars had shifted their apparent position by around two degrees. Hipparchus thus calculated that the mean distance of the Moon from Earth is 77 times Earths radius. 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. Hipparchus discovered the precessions of equinoxes by comparing his notes with earlier observers; his realization that the points of solstice and equinox moved slowly from east to west against the . In the second and third centuries, coins were made in his honour in Bithynia that bear his name and show him with a globe. were probably familiar to Greek astronomers well before Hipparchus. This was presumably found[30] by dividing the 274 years from 432 to 158 BC, into the corresponding interval of 100,077 days and 14+34 hours between Meton's sunrise and Hipparchus's sunset solstices. There are stars cited in the Almagest from Hipparchus that are missing in the Almagest star catalogue. 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. Dividing by 52 produces 5,458 synodic months = 5,923 precisely. Hipparchus is the first astronomer known to attempt to determine the relative proportions and actual sizes of these orbits. This opinion was confirmed by the careful investigation of Hoffmann[40] who independently studied the material, potential sources, techniques and results of Hipparchus and reconstructed his celestial globe and its making. This was the basis for the astrolabe. It is known to us from Strabo of Amaseia, who in his turn criticised Hipparchus in his own Geographia. In combination with a grid that divided the celestial equator into 24 hour lines (longitudes equalling our right ascension hours) the instrument allowed him to determine the hours. How did Hipparchus discover trigonometry? Pliny the Elder writes in book II, 2426 of his Natural History:[40]. [note 1] What was so exceptional and useful about the cycle was that all 345-year-interval eclipse pairs occur slightly more than 126,007 days apart within a tight range of only approximately 12 hour, guaranteeing (after division by 4,267) an estimate of the synodic month correct to one part in order of magnitude 10 million. Hipparchus was a Greek mathematician who compiled an early example of trigonometric tables and gave methods for solving spherical triangles. Hipparchus knew of two possible explanations for the Suns apparent motion, the eccenter and the epicyclic models (see Ptolemaic system). 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 He had immense in geography and was one of the most famous astronomers in ancient times. The traditional value (from Babylonian System B) for the mean synodic month is 29days; 31,50,8,20 (sexagesimal) = 29.5305941 days. In this only work by his hand that has survived until today, he does not use the magnitude scale but estimates brightnesses unsystematically. Before Hipparchus, Meton, Euctemon, and their pupils at Athens had made a solstice observation (i.e., timed the moment of the summer solstice) on 27 June 432BC (proleptic Julian calendar). Hipparchus also studied the motion of the Moon and confirmed the accurate values for two periods of its motion that Chaldean astronomers are widely presumed to have possessed before him,[24] whatever their ultimate origin. His contribution was to discover a method of using the observed dates of two equinoxes and a solstice to calculate the size and direction of the displacement of the Suns orbit. Hipparchus also undertook to find the distances and sizes of the Sun and the Moon. Hipparchus produced a table of chords, an early example of a trigonometric table. Others do not agree that Hipparchus even constructed a chord table. The first known table of chords was produced by the Greek mathematician Hipparchus in about 140 BC. 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. Hipparchus's treatise Against the Geography of Eratosthenes in three books is not preserved. : 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. Pliny (Naturalis Historia II.X) tells us that Hipparchus demonstrated that lunar eclipses can occur five months apart, and solar eclipses seven months (instead of the usual six months); and the Sun can be hidden twice in thirty days, but as seen by different nations. Ptolemy mentions (Almagest V.14) that he used a similar instrument as Hipparchus, called dioptra, to measure the apparent diameter of the Sun and Moon. Hipparchus measured the apparent diameters of the Sun and Moon with his diopter. Although these tables have not survived, it is claimed that twelve books of tables of chords were written by Hipparchus. [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.). Corrections? How did Hipparchus discover a Nova? Hipparchus produced a table of chords, an early example of a trigonometric table. Prediction of a solar eclipse, i.e., exactly when and where it will be visible, requires a solid lunar theory and proper treatment of the lunar parallax. Ancient Instruments and Measuring the Stars. We do not know what "exact reason" Hipparchus found for seeing the Moon eclipsed while apparently it was not in exact opposition to the Sun. That means, no further statement is allowed on these hundreds of stars. 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. He was equipped with a trigonometry table. Greek astronomer Hipparchus . Besides geometry, Hipparchus also used arithmetic techniques developed by the Chaldeans. Did Hipparchus invent trigonometry? This makes Hipparchus the founder of trigonometry. In essence, Ptolemy's work is an extended attempt to realize Hipparchus's vision of what geography ought to be. Hipparchus (/hprks/; Greek: , Hipparkhos; c.190 c.120BC) was a Greek astronomer, geographer, and mathematician. Hipparchus must have been the first to be able to do this. ?rk?s/; Greek: ????? 1:28 Solving an Ancient Tablet's Mathematical Mystery But the papyrus makes the date 26 June, over a day earlier than the 1991 paper's conclusion for 28 June. In modern terms, the chord subtended by a central angle in a circle of given radius equals the radius times twice the sine of half of the angle, i.e. He considered every triangle as being inscribed in a circle, so that each side became a chord. 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. [60][61], He may be depicted opposite Ptolemy in Raphael's 15091511 painting The School of Athens, although this figure is usually identified as Zoroaster.[62]. "Hipparchus recorded astronomical observations from 147 to 127 BC, all apparently from the island of Rhodes. This model described the apparent motion of the Sun fairly well. Diller A. Not only did he make extensive observations of star positions, Hipparchus also computed lunar and solar eclipses, primarily by using trigonometry. Hipparchus produced a table of chords, an early example of a trigonometric table. Although he is commonly ranked among the greatest scientists of antiquity, very little is known about his life, and only one of his many writings is still in existence. Hipparchus was an ancient Greek polymath whose wide-ranging interests include geography, astronomy, and mathematics. Ch. [3], Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity. Hipparchus of Nicaea (c. 190 - c. 120 B.C.) Apparently Hipparchus later refined his computations, and derived accurate single values that he could use for predictions of solar eclipses. The purpose of this table of chords was to give a method for solving triangles which avoided solving each triangle from first principles. Theon of Smyrna wrote that according to Hipparchus, the Sun is 1,880 times the size of the Earth, and the Earth twenty-seven times the size of the Moon; apparently this refers to volumes, not diameters. The branch called "Trigonometry" basically deals with the study of the relationship between the sides and angles of the right-angle triangle. 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. As with most of his work, Hipparchus's star catalog was adopted and perhaps expanded by Ptolemy. He is best known for his discovery of the precession of the equinoxes and contributed significantly to the field of astronomy on every level. Aratus wrote a poem called Phaenomena or Arateia based on Eudoxus's work. [15], Nevertheless, this system certainly precedes Ptolemy, who used it extensively about AD 150. According to Ptolemy, Hipparchus measured the longitude of Spica and Regulus and other bright stars. View three larger pictures Biography Little is known of Hipparchus's life, but he is known to have been born in Nicaea in Bithynia. For other uses, see, Geometry, trigonometry and other mathematical techniques, Distance, parallax, size of the Moon and the Sun, Arguments for and against Hipparchus's star catalog in the Almagest. And the same individual attempted, what might seem presumptuous even in a deity, viz. He tabulated values for the chord function, which for a central angle in a circle gives the length of the straight line segment between the points where the angle intersects the circle. Besides geometry, Hipparchus also used arithmetic techniques developed by the Chaldeans. (1980). Alexandria is at about 31 North, and the region of the Hellespont about 40 North. 2 He is called . A lunar eclipse is visible simultaneously on half of the Earth, and the difference in longitude between places can be computed from the difference in local time when the eclipse is observed. [41] This hypothesis is based on the vague statement by Pliny the Elder but cannot be proven by the data in Hipparchus's commentary on Aratus's poem. Steele J.M., Stephenson F.R., Morrison L.V. It is believed that he was born at Nicaea in Bithynia. This was the basis for the astrolabe. Hipparchus Previously, Eudoxus of Cnidus in the fourth centuryBC had described the stars and constellations in two books called Phaenomena and Entropon. (It has been contended that authors like Strabo and Ptolemy had fairly decent values for these geographical positions, so Hipparchus must have known them too. 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. However, by comparing his own observations of solstices with observations made in the 5th and 3rd centuries bce, Hipparchus succeeded in obtaining an estimate of the tropical year that was only six minutes too long. (See animation.). 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). Hipparchus discovered the wobble of Earth's axis by comparing previous star charts to the charts he created during his study of the stars. [10], Relatively little of Hipparchus's direct work survives into modern times. In the first book, Hipparchus assumes that the parallax of the Sun is 0, as if it is at infinite distance. Delambre in his Histoire de l'Astronomie Ancienne (1817) concluded that Hipparchus knew and used the equatorial coordinate system, a conclusion challenged by Otto Neugebauer in his A History of Ancient Mathematical Astronomy (1975). 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. In Raphael's painting The School of Athens, Hipparchus is depicted holding his celestial globe, as the representative figure for astronomy.[39]. [36] In 2022, it was announced that a part of it was discovered in a medieval parchment manuscript, Codex Climaci Rescriptus, from Saint Catherine's Monastery in the Sinai Peninsula, Egypt as hidden text (palimpsest). Ptolemy discovered the table of arcs. On this Wikipedia the language links are at the top of the page across from the article title. "The Size of the Lunar Epicycle According to Hipparchus. 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. . Hipparchus was born in Nicaea (Greek ), in Bithynia. From the geometry of book 2 it follows that the Sun is at 2,550 Earth radii, and the mean distance of the Moon is 60+12 radii. 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]. Aristarchus of Samos (/?r??st? He knew that this is because in the then-current models the Moon circles the center of the Earth, but the observer is at the surfacethe Moon, Earth and observer form a triangle with a sharp angle that changes all the time. G J Toomer's chapter "Ptolemy and his Greek Predecessors" in "Astronomy before the Telescope", British Museum Press, 1996, p.81. Hipparchus's long draconitic lunar period (5,458 months = 5,923 lunar nodal periods) also appears a few times in Babylonian records. He knew the . This is an indication that Hipparchus's work was known to Chaldeans.[32]. [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]. Unlike Ptolemy, Hipparchus did not use ecliptic coordinates to describe stellar positions. Input the numbers into the arc-length formula, Enter 0.00977 radians for the radian measure and 2,160 for the arc length: 2,160 = 0.00977 x r. Divide each side by 0.00977. He developed trigonometry and constructed trigonometric tables, and he solved several problems of spherical trigonometry. Hipparchus had good reasons for believing that the Suns path, known as the ecliptic, is a great circle, i.e., that the plane of the ecliptic passes through Earths centre. Since the work no longer exists, most everything about it is speculation. 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. He had two methods of doing this. Even if he did not invent it, Hipparchus is the first person whose systematic use of trigonometry we have documentary evidence. Born sometime around the year 190 B.C., he was able to accurately describe the. In the practical part of his work, the so-called "table of climata", Hipparchus listed latitudes for several tens of localities. The epicycle model he fitted to lunar eclipse observations made in Alexandria at 22 September 201BC, 19 March 200BC, and 11 September 200BC. Hipparchus calculated the length of the year to within 6.5 minutes and discovered the precession of the equinoxes. It is believed that he computed the first table of chords for this purpose. Rawlins D. (1982). [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. [40] He used it to determine risings, settings and culminations (cf. ", Toomer G.J. This would correspond to a parallax of 7, which is apparently the greatest parallax that Hipparchus thought would not be noticed (for comparison: the typical resolution of the human eye is about 2; Tycho Brahe made naked eye observation with an accuracy down to 1). The two points at which the ecliptic and the equatorial plane intersect, known as the vernal and autumnal equinoxes, and the two points of the ecliptic farthest north and south from the equatorial plane, known as the summer and winter solstices, divide the ecliptic into four equal parts. He is known to have been a working astronomer between 162 and 127BC. In geographic theory and methods Hipparchus introduced three main innovations. Hipparchus produced a table of chords, an early example of a trigonometric table. Trigonometry Trigonometry simplifies the mathematics of triangles, making astronomy calculations easier. Once again you must zoom in using the Page Up key. All thirteen clima figures agree with Diller's proposal. He is considered the founder of trigonometry,[1] but is most famous for his incidental discovery of the precession of the equinoxes. Hipparchus obtained information from Alexandria as well as Babylon, but it is not known when or if he visited these places. As a young man in Bithynia, Hipparchus compiled records of local weather patterns throughout the year. (1997). . 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. 2 - Why did Ptolemy have to introduce multiple circles. Roughly five centuries after Euclid's era, he solved hundreds of algebraic equations in his great work Arithmetica, and was the first person to use algebraic notation and symbolism. 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. 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. also Almagest, book VIII, chapter 3). He computed this for a circle with a circumference of 21,600 units and a radius (rounded) of 3,438 units; this circle has a unit length of 1 arcminute along its perimeter. ", Toomer G.J. Bo C. Klintberg states, "With mathematical reconstructions and philosophical arguments I show that Toomer's 1973 paper never contained any conclusive evidence for his claims that Hipparchus had a 3438'-based chord table, and that the Indians used that table to compute their sine tables. To do so, he drew on the observations and maybe mathematical tools amassed by the Babylonian Chaldeans over generations. However, all this was theory and had not been put to practice. Bianchetti S. (2001). At the end of the third century BC, Apollonius of Perga had proposed two models for lunar and planetary motion: Apollonius demonstrated that these two models were in fact mathematically equivalent. The history of trigonometry and of trigonometric functions sticks to the general lines of the history of math. ?, Aristarkhos ho Samios; c. 310 c. . 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. 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). It is unknown what instrument he used. He found that at the mean distance of the Moon, the Sun and Moon had the same apparent diameter; at that distance, the Moon's diameter fits 650 times into the circle, i.e., the mean apparent diameters are 360650 = 03314. Ulugh Beg reobserved all the Hipparchus stars he could see from Samarkand in 1437 to about the same accuracy as Hipparchus's. Articles from Britannica Encyclopedias for elementary and high school students. Although Hipparchus strictly distinguishes between "signs" (30 section of the zodiac) and "constellations" in the zodiac, it is highly questionable whether or not he had an instrument to directly observe / measure units on the ecliptic. That apparent diameter is, as he had observed, 360650 degrees.