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). Hipparchus was a Greek astronomer and mathematician. In the second method he hypothesized that the distance from the centre of Earth to the Sun is 490 times Earths radiusperhaps chosen because that is the shortest distance consistent with a parallax that is too small for detection by the unaided eye. This was the basis for the astrolabe. Ptolemy established a ratio of 60: 5+14. Unlike Ptolemy, Hipparchus did not use ecliptic coordinates to describe stellar positions. 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. He did this by using the supplementary angle theorem, half angle formulas, and linear interpolation. Hipparchus, the mathematician and astronomer, was born around the year 190 BCE in Nicaea, in what is present-day Turkey. 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". Set the local time to around 7:25 am. This is the first of three articles on the History of Trigonometry. [15] Right ascensions, for instance, could have been observed with a clock, while angular separations could have been measured with another device. Diller A. [51], He was the first to use the grade grid, to determine geographic latitude from star observations, and not only from the Sun's altitude, a method known long before him, and to suggest that geographic longitude could be determined by means of simultaneous observations of lunar eclipses in distant places. In, This page was last edited on 24 February 2023, at 05:19. 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. The Greeks were mostly concerned with the sky and the heavens. : 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. 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. 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 was able to solve the geometry . [17] But the only such tablet explicitly dated, is post-Hipparchus so the direction of transmission is not settled by the tablets. Hipparchus is sometimes called the "father of astronomy",[7][8] a title first conferred on him by Jean Baptiste Joseph Delambre.[9]. Hipparchus insists that a geographic map must be based only on astronomical measurements of latitudes and longitudes and triangulation for finding unknown distances. 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. 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. THE EARTH-MOON DISTANCE How did Hipparchus discover trigonometry? This was the basis for the astrolabe. 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). "Hipparchus and the Stoic Theory of Motion". Because the eclipse occurred in the morning, the Moon was not in the meridian, and it has been proposed that as a consequence the distance found by Hipparchus was a lower limit. [4][5] He was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. With these values and simple geometry, Hipparchus could determine the mean distance; because it was computed for a minimum distance of the Sun, it is the maximum mean distance possible for the Moon. In the practical part of his work, the so-called "table of climata", Hipparchus listed latitudes for several tens of localities. [2] Hipparchus was born in Nicaea, Bithynia, and probably died on the island of Rhodes, Greece. Since the work no longer exists, most everything about it is speculation. 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. Similarly, Cleomedes quotes Hipparchus for the sizes of the Sun and Earth as 1050:1; this leads to a mean lunar distance of 61 radii. He also introduced the division of a circle into 360 degrees into Greece. Hipparchus knew of two possible explanations for the Suns apparent motion, the eccenter and the epicyclic models (see Ptolemaic system). Hipparchus compiled a table of the chords of angles and made them available to other scholars. One method used an observation of a solar eclipse that had been total near the Hellespont (now called the Dardanelles) but only partial at Alexandria. Chapront J., Touze M. Chapront, Francou G. (2002): Duke D.W. (2002). Alternate titles: Hipparchos, Hipparchus of Bithynia, Professor of Classics, University of Toronto. Late in his career (possibly about 135BC) Hipparchus compiled his star catalog. Parallax lowers the altitude of the luminaries; refraction raises them, and from a high point of view the horizon is lowered. "The Introduction of Dated Observations and Precise Measurement in Greek Astronomy" Archive for History of Exact Sciences Hipparchus of Nicaea was an Ancient Greek astronomer and mathematician. Bianchetti S. (2001). "Associations between the ancient star catalogs". Let the time run and verify that a total solar eclipse did occur on this day and could be viewed from the Hellespont. 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. Thus, by all the reworking within scientific progress in 265 years, not all of Hipparchus's stars made it into the Almagest version of the star catalogue. [18] The obvious main objection is that the early eclipse is unattested, although that is not surprising in itself, and there is no consensus on whether Babylonian observations were recorded this remotely. In this case, the shadow of the Earth is a cone rather than a cylinder as under the first assumption. ), Greek astronomer and mathematician who made fundamental contributions to the advancement of astronomy as a mathematical science and to the foundations of trigonometry. However, all this was theory and had not been put to practice. 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. This is a highly critical commentary in the form of two books on a popular poem by Aratus based on the work by Eudoxus. And the same individual attempted, what might seem presumptuous even in a deity, viz. Greek astronomer Hipparchus . 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. Before Hipparchus, astronomers knew that the lengths of the seasons are not equal. [56] Actually, it has been even shown that the Farnese globe shows constellations in the Aratean tradition and deviates from the constellations in mathematical astronomy that is used by Hipparchus. Emma Willard, Astronography, Or, Astronomical Geography, with the Use of Globes: Arranged Either for Simultaneous Reading and Study in Classes, Or for Study in the Common Method, pp 246, Denison Olmsted, Outlines of a Course of Lectures on Meteorology and Astronomy, pp 22, University of Toronto Quarterly, Volumes 1-3, pp 50, Histoire de l'astronomie ancienne, Jean Baptiste Joseph Delambre, Volume 1, p lxi; "Hipparque, le vrai pre de l'Astronomie"/"Hipparchus, the true father of Astronomy", Bowen A.C., Goldstein B.R. To do so, he drew on the observations and maybe mathematical tools amassed by the Babylonian Chaldeans over generations. They write new content and verify and edit content received from contributors. 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. (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. Hipparchus's use of Babylonian sources has always been known in a general way, because of Ptolemy's statements, but the only text by Hipparchus that survives does not provide sufficient information to decide whether Hipparchus's knowledge (such as his usage of the units cubit and finger, degrees and minutes, or the concept of hour stars) was based on Babylonian practice. Hipparchus assumed that the difference could be attributed entirely to the Moons observable parallax against the stars, which amounts to supposing that the Sun, like the stars, is indefinitely far away. He did this by using the supplementary angle theorem, half angle formulas, and linear interpolation. Hipparchus observed (at lunar eclipses) that at the mean distance of the Moon, the diameter of the shadow cone is 2+12 lunar diameters. [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. On this Wikipedia the language links are at the top of the page across from the article title. Although these tables have not survived, it is claimed that twelve books of tables of chords were written by Hipparchus. Hipparchus produced a table of chords, an early example of a trigonometric table. He also compared the lengths of the tropical year (the time it takes the Sun to return to an equinox) and the sidereal year (the time it takes the Sun to return to a fixed star), and found a slight discrepancy. Ch. There are stars cited in the Almagest from Hipparchus that are missing in the Almagest star catalogue. Hipparchus also tried to measure as precisely as possible the length of the tropical yearthe period for the Sun to complete one passage through the ecliptic. Posted at 20:22h in chesapeake bay crater size by code radio police gta city rp. The origins of trigonometry occurred in Ancient Egypt and Babylon, where . G J Toomer's chapter "Ptolemy and his Greek Predecessors" in "Astronomy before the Telescope", British Museum Press, 1996, p.81. Did Hipparchus invent trigonometry? Hipparchus discovered the table of values of the trigonometric ratios. Hipparchus produced a table of chords, an early example of a trigonometric table. Updates? Besides geometry, Hipparchus also used arithmetic techniques developed by the Chaldeans. Galileo was the greatest astronomer of his time. Hipparchus calculated the length of the year to within 6.5 minutes and discovered the precession of the . He is known to have been a working astronomer between 162 and 127BC. The earlier study's M found that Hipparchus did not adopt 26 June solstices until 146 BC, when he founded the orbit of the Sun which Ptolemy later adopted. View three larger pictures Biography Little is known of Hipparchus's life, but he is known to have been born in Nicaea in Bithynia. (1967). 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. From the size of this parallax, the distance of the Moon as measured in Earth radii can be determined. Pliny the Elder writes in book II, 2426 of his Natural History:[40]. Apparently Hipparchus later refined his computations, and derived accurate single values that he could use for predictions of solar eclipses. [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. 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). Steele J.M., Stephenson F.R., Morrison L.V. Hipparchus was born in Nicaea (Greek ), in Bithynia. Hipparchus produced a table of chords, an early example of a trigonometric table. For more information see Discovery of precession. Vol. Hipparchus was recognized as the first mathematician known to have possessed a trigonometric table, which he needed when computing the eccentricity of the orbits of the Moon and Sun. 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. Aratus wrote a poem called Phaenomena or Arateia based on Eudoxus's work. He was then in a position to calculate equinox and solstice dates for any year. Hipparchus also adopted the Babylonian astronomical cubit unit (Akkadian ammatu, Greek pchys) that was equivalent to 2 or 2.5 ('large cubit'). Let us know if you have suggestions to improve this article (requires login). Apparently it was well-known at the time. In the second and third centuries, coins were made in his honour in Bithynia that bear his name and show him with a globe. 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. With an astrolabe Hipparchus was the first to be able to measure the geographical latitude and time by observing fixed stars. 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 on the distance of the sun. 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. 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. 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. ?, Aristarkhos ho Samios; c. 310 c. . Aubrey Diller has shown that the clima calculations that Strabo preserved from Hipparchus could have been performed by spherical trigonometry using the only accurate obliquity known to have been used by ancient astronomers, 2340. The angle is related to the circumference of a circle, which is divided into 360 parts or degrees.. Calendars were often based on the phases of the moon (the origin of the word month) and the seasons. Mott Greene, "The birth of modern science?" The random noise is two arc minutes or more nearly one arcminute if rounding is taken into account which approximately agrees with the sharpness of the eye. Today we usually indicate the unknown quantity in algebraic equations with the letter x. Hipparchus was born in Nicaea, Bithynia (now Iznik, Turkey) and most likely died on the island of Rhodes. D. Rawlins noted that this implies a tropical year of 365.24579 days = 365days;14,44,51 (sexagesimal; = 365days + 14/60 + 44/602 + 51/603) and that this exact year length has been found on one of the few Babylonian clay tablets which explicitly specifies the System B month. 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. It remained, however, for Ptolemy (127145 ce) to finish fashioning a fully predictive lunar model. His approach would give accurate results if it were correctly carried out but the limitations of timekeeping accuracy in his era made this method impractical. Another value for the year that is attributed to Hipparchus (by the astrologer Vettius Valens in the first century) is 365 + 1/4 + 1/288 days (= 365.25347 days = 365days 6hours 5min), but this may be a corruption of another value attributed to a Babylonian source: 365 + 1/4 + 1/144 days (= 365.25694 days = 365days 6hours 10min). He is known for discovering the change in the orientation of the Earth's axis and the axis of other planets with respect to the center of the Sun. At the end of his career, Hipparchus wrote a book entitled Peri eniausou megthous ("On the Length of the Year") regarding his results. In any case the work started by Hipparchus has had a lasting heritage, and was much later updated by al-Sufi (964) and Copernicus (1543). The term "trigonometry" was derived from Greek trignon, "triangle" and metron, "measure".. 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 "The astronomy of Hipparchus and his time: A study based on pre-ptolemaic sources". Hipparchus's equinox observations gave varying results, but he points out (quoted in Almagest III.1(H195)) that the observation errors by him and his predecessors may have been as large as 14 day. 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. 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. After Hipparchus the next Greek mathematician known to have made a contribution to trigonometry was Menelaus. 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. 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. He is also famous for his incidental discovery of the. Hipparchus's catalogue is reported in Roman times to have enlisted about 850 stars but Ptolemy's catalogue has 1025 stars. Chords are closely related to sines. Hipparchus's ideas found their reflection in the Geography of Ptolemy. Such weather calendars (parapgmata), which synchronized the onset of winds, rains, and storms with the astronomical seasons and the risings and settings of the constellations, were produced by many Greek astronomers from at least as early as the 4th century bce. He knew the . (The true value is about 60 times. All thirteen clima figures agree with Diller's proposal. His theory influence is present on an advanced mechanical device with code name "pin & slot". Born sometime around the year 190 B.C., he was able to accurately describe the. Hipparchus could have constructed his chord table using the Pythagorean theorem and a theorem known to Archimedes. The branch called "Trigonometry" basically deals with the study of the relationship between the sides and angles of the right-angle triangle. 2 - Why did Ptolemy have to introduce multiple circles. Expressed as 29days + 12hours + .mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num,.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0 0.1em}.mw-parser-output .sfrac .den{border-top:1px solid}.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}793/1080hours this value has been used later in the Hebrew calendar. Hipparchus was born in Nicaea, Bithynia, and probably died on the island of Rhodes, Greece. Ch. 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. 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. His birth date (c.190BC) was calculated by Delambre based on clues in his work. Hipparchus: The birth of trigonometry occurred in the chord tables of Hipparchus (c 190 - 120 BCE) who was born shortly after Eratosthenes died. 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. Once again you must zoom in using the Page Up key. ", Toomer G.J. Apparently his commentary Against the Geography of Eratosthenes was similarly unforgiving of loose and inconsistent reasoning. In On Sizes and Distances (now lost), Hipparchus reportedly measured the Moons orbit in relation to the size of Earth. Hipparchus is the first astronomer known to attempt to determine the relative proportions and actual sizes of these orbits. He had immense in geography and was one of the most famous astronomers in ancient times. Hipparchus used the multiple of this period by a factor of 17, because that interval is also an eclipse period, and is also close to an integer number of years (4,267 moons: 4,573 anomalistic periods: 4,630.53 nodal periods: 4,611.98 lunar orbits: 344.996 years: 344.982 solar orbits: 126,007.003 days: 126,351.985 rotations). The most ancient device found in all early civilisations, is a "shadow stick". Hipparchus discovered the wobble of Earth's axis by comparing previous star charts to the charts he created during his study of the stars. 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. 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. The three most important mathematicians involved in devising Greek trigonometry are Hipparchus, Menelaus, and Ptolemy. (Previous to the finding of the proofs of Menelaus a century ago, Ptolemy was credited with the invention of spherical trigonometry.) Hipparchus calculated the length of the year to within 6.5 minutes and discovered the precession of the equinoxes. 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. The 345-year periodicity is why[25] the ancients could conceive of a mean month and quantify it so accurately that it is correct, even today, to a fraction of a second of time. He also introduced the division of a circle into 360 degrees into Greece. See [Toomer 1974] for a more detailed discussion. 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]. (1997). 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. One evening, Hipparchus noticed the appearance of a star where he was certain there had been none before. Pappus of Alexandria described it (in his commentary on the Almagest of that chapter), as did Proclus (Hypotyposis IV). 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. 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 . 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. (1980). Hipparchus, also spelled Hipparchos, (born, Nicaea, Bithynia [now Iznik, Turkey]died after 127 bce, Rhodes? of trigonometry. 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 could draw a triangle formed by the two places and the Moon, and from simple geometry was able to establish a distance of the Moon, expressed in Earth radii. ", Toomer G.J. He is considered the founder of trigonometry,[1] but is most famous for his incidental discovery of the precession of the equinoxes. He was also the inventor of trigonometry. ), Greek astronomer and mathematician who made fundamental contributions to the advancement of astronomy as a mathematical science and to the foundations of trigonometry. This model described the apparent motion of the Sun fairly well. common errors in the reconstructed Hipparchian star catalogue and the Almagest suggest a direct transfer without re-observation within 265 years. Pliny also remarks that "he also discovered for what exact reason, although the shadow causing the eclipse must from sunrise onward be below the earth, it happened once in the past that the Moon was eclipsed in the west while both luminaries were visible above the earth" (translation H. Rackham (1938), Loeb Classical Library 330 p.207). Please refer to the appropriate style manual or other sources if you have any questions. "Hipparchus and the Ancient Metrical Methods on the Sphere". Besides geometry, Hipparchus also used arithmetic techniques developed by the Chaldeans. 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. Delambre, in 1817, cast doubt on Ptolemy's work. Hipparchus produced a table of chords, an early example of a trigonometric table. ), Italian philosopher, astronomer and mathematician. 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. The papyrus also confirmed that Hipparchus had used Callippic solar motion in 158 BC, a new finding in 1991 but not attested directly until P. Fouad 267 A. An Investigation of the Ancient Star Catalog. [15], Nevertheless, this system certainly precedes Ptolemy, who used it extensively about AD 150. Most of Hipparchuss adult life, however, seems to have been spent carrying out a program of astronomical observation and research on the island of Rhodes. [59], A line in Plutarch's Table Talk states that Hipparchus counted 103,049 compound propositions that can be formed from ten simple propositions. It is unknown what instrument he used. Hipparchus calculated the length of the year to within 6.5 minutes and discovered the precession of the equinoxes. "The Size of the Lunar Epicycle According to Hipparchus. (1974). This same Hipparchus, who can never be sufficiently commended, discovered a new star that was produced in his own age, and, by observing its motions on the day in which it shone, he was led to doubt whether it does not often happen, that those stars have motion which we suppose to be fixed.
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