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. This was the basis for the astrolabe. 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. He made observations of consecutive equinoxes and solstices, but the results were inconclusive: he could not distinguish between possible observational errors and variations in the tropical year. [37][38], Hipparchus also constructed a celestial globe depicting the constellations, based on his observations. The somewhat weird numbers are due to the cumbersome unit he used in his chord table according to one group of historians, who explain their reconstruction's inability to agree with these four numbers as partly due to some sloppy rounding and calculation errors by Hipparchus, for which Ptolemy criticised him while also making rounding errors. 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. Like most of his predecessorsAristarchus of Samos was an exceptionHipparchus assumed a spherical, stationary Earth at the centre of the universe (the geocentric cosmology). 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. 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. Chords are closely related to sines. Hipparchus compiled a table of the chords of angles and made them available to other scholars. 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. ???? [48], Conclusion: Hipparchus's star catalogue is one of the sources of the Almagest star catalogue but not the only source.[47]. 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. G J Toomer's chapter "Ptolemy and his Greek Predecessors" in "Astronomy before the Telescope", British Museum Press, 1996, p.81. In, Wolff M. (1989). In the first book, Hipparchus assumes that the parallax of the Sun is 0, as if it is at infinite distance. The exact dates of his life are not known, but Ptolemy attributes astronomical observations to him in the period from 147 to 127BC, and some of these are stated as made in Rhodes; earlier observations since 162BC might also have been made by him. He is also famous for his incidental discovery of the. was a Greek astronomer, geographer, and mathematician of the Hellenistic period. Hipparchus is considered the greatest observational astronomer from classical antiquity until Brahe. 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. 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. Comparing both charts, Hipparchus calculated that the stars had shifted their apparent position by around two degrees. Apparently Hipparchus later refined his computations, and derived accurate single values that he could use for predictions of solar eclipses. "Hipparchus and the Ancient Metrical Methods on the Sphere". With his solar and lunar theories and his trigonometry, he may have been the first to develop a reliable method to predict solar eclipses. Corrections? 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. I. 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]). Trigonometry was a significant innovation, because it allowed Greek astronomers to solve any triangle, and made it possible to make quantitative astronomical models and predictions using their preferred geometric techniques.[20]. Hipparchus (190 120 BCE) Hipparchus lived in Nicaea. 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. THE EARTH-MOON DISTANCE Hipparchus of Nicaea was an Ancient Greek astronomer and mathematician. In the practical part of his work, the so-called "table of climata", Hipparchus listed latitudes for several tens of localities. Another table on the papyrus is perhaps for sidereal motion and a third table is for Metonic tropical motion, using a previously unknown year of 365+141309 days. [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]. [50] Hipparchus's celestial globe was an instrument similar to modern electronic computers. Some scholars do not believe ryabhaa's sine table has anything to do with Hipparchus's chord table. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. Ptolemy's catalog in the Almagest, which is derived from Hipparchus's catalog, is given in ecliptic coordinates. 2 He is called . It is unknown who invented this method. He is best known for his discovery of the precession of the equinoxes and contributed significantly to the field of astronomy on every level. 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. Hipparchus is the first astronomer known to attempt to determine the relative proportions and actual sizes of these orbits. He was also the inventor of trigonometry. This would be the second eclipse of the 345-year interval that Hipparchus used to verify the traditional Babylonian periods: this puts a late date to the development of Hipparchus's lunar theory. Isaac Newton and Euler contributed developments to bring trigonometry into the modern age. 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. He . The origins of trigonometry occurred in Ancient Egypt and Babylon, where . Our editors will review what youve submitted and determine whether to revise the article. (1934). [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. In, This page was last edited on 24 February 2023, at 05:19. It is a combination of geometry, and astronomy and has many practical applications over history. He did this by using the supplementary angle theorem, half angle formulas, and linear interpolation. Dividing by 52 produces 5,458 synodic months = 5,923 precisely. It was also observed in Alexandria, where the Sun was reported to be obscured 4/5ths by the Moon. Diller A. Hipparchus produced a table of chords, an early example of a trigonometric table. 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. "Hipparchus' Empirical Basis for his Lunar Mean Motions,", Toomer G.J. Hipparchus of Nicea (l. c. 190 - c. 120 BCE) was a Greek astronomer, geographer, and mathematician regarded as the greatest astronomer of antiquity and one of the greatest of all time. For more information see Discovery of precession. 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). 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). ), Italian philosopher, astronomer and mathematician. (See animation.). He had immense in geography and was one of the most famous astronomers in ancient times. How did Hipparchus discover trigonometry? ", Toomer G.J. The history of trigonometry and of trigonometric functions sticks to the general lines of the history of math. 3550jl1016a Vs 3550jl1017a . The shadow cast from a shadow stick was used to . [26] Modern scholars agree that Hipparchus rounded the eclipse period to the nearest hour, and used it to confirm the validity of the traditional values, rather than to try to derive an improved value from his own observations. Ch. Scholars have been searching for it for centuries. With Hipparchuss mathematical model one could calculate not only the Suns orbital location on any date, but also its position as seen from Earth. 2 - How did Hipparchus discover the wobble of Earth's. Ch. The eccentric model he fitted to these eclipses from his Babylonian eclipse list: 22/23 December 383BC, 18/19 June 382BC, and 12/13 December 382BC. Toomer, "The Chord Table of Hipparchus" (1973). [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). Ptolemy cites more than 20 observations made there by Hipparchus on specific dates from 147 to 127, as well as three earlier observations from 162 to 158 that may be attributed to him. According to Synesius of Ptolemais (4th century) he made the first astrolabion: this may have been an armillary sphere (which Ptolemy however says he constructed, in Almagest V.1); or the predecessor of the planar instrument called astrolabe (also mentioned by Theon of Alexandria).
