History of geodesy

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computed the Earth's circumference in stadia as 48 × 5000 = 240,000. Some scholars see these results as luckily semi-accurate due to cancellation of errors. But since the Canopus observations are both mistaken by over a degree, the "experiment" may be not much more than a recycling of Eratosthenes's numbers, while altering 1/50 to the correct 1/48 of a circle. Later, either he or a follower appears to have altered the base distance to agree with Eratosthenes's Alexandria-to-Rhodes figure of 3750 stadia, since Posidonius' final circumference was 180,000 stadia, which equals 48 × 3750 stadia. The 180,000 stadia circumference of Posidonius is close to that which results from another method of measuring the Earth, by timing ocean sunsets from different heights, a method which is inaccurate due to horizontal

2512: 2826: 1988: 837: 2849: 3201:, if metrology had not created a common unit, adopted and respected by all civilized nations, and if in addition one had not compared, with great precision, to the same unit all the rulers for measuring geodesic bases, and all the pendulum rods that had hitherto been used or would be used in the future? Only when this series of metrological comparisons would be finished with a probable error of a thousandth of a millimeter would geodesy be able to link the works of the different nations one with another, and then proclaim the result of the measurement of the Globe. 1506: 3157:

the pendulum. Indeed, the determination of gravity by the pendulum is subject to two types of error. On the one hand the resistance of the air and on the other hand the movements that the oscillations of the pendulum impart to its plane of suspension. These movements were particularly important with the device designed by the Repsold brothers on Bessel's indications, because the pendulum had a large mass in order to counteract the effect of the viscosity of the air. While Emile Plantamour was carrying out a series of experiments with this device,

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longitudes obtained a much higher degree of accuracy. Of the greatest moment is the measurement near the parallel of 52° lat., which extended from Valentia in Ireland to Orsk in the southern Ural mountains over 69 degrees of longitude. F. G. W. Struve, who is to be regarded as the father of the Russo-Scandinavian latitude-degree measurements, was the originator of this investigation. Having made the requisite arrangements with the governments in 1857, he transferred them to his son Otto, who, in 1860, secured the co-operation of England.

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sun (reflected). When the brightness is first seen, the sun (-light passes almost) alongside, so the side only is illuminated and looks like a crescent. When the sun gradually gets further away, the light shines slanting, and the moon is full, round like a bullet. If half of a sphere is covered with (white) powder and looked at from the side, the covered part will look like a crescent; if looked at from the front, it will appear round. Thus we know that the celestial bodies are spherical.

914:) of known length and measuring the length of its shadow on the ground; it is then possible to calculate the angle of the Sun's rays, which he claims to be about 7°, or 1/50th the circumference of a circle. Taking the Earth as spherical, the Earth's circumference would be fifty times the distance between Alexandria and Syene, that is 250,000 stadia. Since 1 Egyptian stadium is equal to 157.5 metres, the result is 39,375 km, which is 1.4% less than the real number, 39,941 km. 2960: 2936: 3373:, used it to give a large sample justification for the method of least squares and the normal distribution. In 1822, Gauss was able to state that the least-squares approach to regression analysis is optimal in the sense that in a linear model where the errors have a mean of zero, are uncorrelated, and have equal variances, the best linear unbiased estimator of the coefficients is the least-squares estimator. This result is known as the 640: 2018:, that Earth was "round". The bishop's confusing exposition and choice of imprecise Latin terms have divided scholarly opinion on whether he meant a sphere or a disk or even whether he meant anything specific. Notable recent scholars claim that he taught a spherical Earth. Isidore did not admit the possibility of people dwelling at the antipodes, considering them as legendary and noting that there was no evidence for their existence. 2902: 923:

can be divided by all natural numbers from 1 to 10: some historians believe that Eratosthenes changed from the 250,000 value written by Cleomedes to this new value to simplify calculations; other historians of science, on the other side, believe that Eratosthenes introduced a new length unit based on the length of the meridian, as stated by Pliny, who writes about the stadion "according to Eratosthenes' ratio".

1029: 6329:"Mitteleuropäische Gradmessung, General-Bericht über die mitteleuropäische Gradmessung für das Jahr 1865. : Exposé de l'état des Travaux géodesiques poursuivis en Espagne, communiqué a la Commission permanente de la Conférence internationale, par le Colonel Ibáñez, membre de l'Académie Royale des sciences et délégué du Gouvernement espagnol. (Séance du 9 avril 1866), Berlin, Reimer, 1866, 70 p." 553:, 4.42) who claimed to have had the Sun on their right when circumnavigating in a clockwise direction. To modern historians, these details confirm the truth of the Phoenicians' report. The historian Dmitri Panchenko hypothesizes that it was the Phoenician circumnavigation of Africa that inspired the theory of a spherical Earth, the earliest mention of which was made by the philosopher 431: 3117: 2038:, that Earth was round. He explained the unequal length of daylight from "the roundness of the Earth, for not without reason is it called 'the orb of the world' on the pages of Holy Scripture and of ordinary literature. It is, in fact, set like a sphere in the middle of the whole universe." (De temporum ratione, 32). The large number of surviving manuscripts of 784:, Archimedes demonstrates that "The surface of any fluid at rest is the surface of a sphere whose centre is the same as that of the Earth." Subsequently, in propositions 8 and 9 of the same work, he assumes the result of proposition 2 that Earth is a sphere and that the surface of a fluid on it is a sphere centered on the center of Earth. 631:, his one work that was available throughout the Middle Ages in Latin, he wrote that the Creator "made the world in the form of a globe, round as from a lathe, having its extremes in every direction equidistant from the centre, the most perfect and the most like itself of all figures", though the word "world" here refers to the heavens. 2304:

star carrier model". Making skillful use of philology, these authors cleverly reinterpreted the greatest technical and literary works of Chinese antiquity. From this sprang a new science wholly dedicated to the demonstration of the Chinese origin of astronomy and more generally of all European science and technology.

580:(6th century BC) was among those said to have originated the idea, but this might reflect the ancient Greek practice of ascribing every discovery to one or another of their ancient wise men. Pythagoras was a mathematician, and he supposedly reasoned that the gods would create a perfect figure which to him was a 6253:"Nouvelle détermination de la longueur de l'arc de méridien compris entre Montjouy et Formentera, dévoilant l'inexactitude de celle dont il est fait mention dans la Base du système métrique décimal in Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels" 2291:(格致草) treatise of Xiong Mingyu (熊明遇) published in 1648 showed a printed picture of Earth as a spherical globe, with the text stating that "the round Earth certainly has no square corners". The text also pointed out that sailing ships could return to their port of origin after circumnavigating the waters of Earth. 3041:

to admit. As this survey was also part of the groundwork for the map of France, Antoine Yvon Villarceau checked, from 1861 to 1866, the geodesic opérations in eight points of the meridian arc. Some of the errors in the operations of Delambre and Méchain were corrected. In 1866, at the conference of the

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that Delambre and Méchain had made an error in the measurement of the French meridian arc. Some thought that the base of the metric system could be attacked by pointing out some errors that crept into the measurement of the two French scientists. Méchain had even noticed an inaccuracy he did not dare

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The influence of the map is distinctly Western, as traditional maps of Chinese cartography held the graduation of the sphere at 365.25 degrees, while the Western graduation was of 360 degrees. The adoption of European astronomy, facilitated by the failure of indigenous astronomy to make progress, was

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X 5, ERnest Brehaut wrote: "The explanation of the passage and of the figure which illustrates it seems to be that Isidore accepted the terminology of the spherical earth from Hyginus without taking the time to understand it—if indeed he had the ability to do so—and applied it without compunction to

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However, these results could only be considered provisional insofar as they did not take into account the movements that the oscillations of the pendulum impart to its suspension plane, which constitute an important factor of error in measuring both the duration of the oscillations and the length of

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D. Rawlins: "Methods for Measuring the Earth's Size by Determining the Curvature of the Sea" and "Racking the Stade for Eratosthenes", appendices to "The Eratosthenes–Strabo Nile Map. Is It the Earliest Surviving Instance of Spherical Cartography? Did It Supply the 5000 Stades Arc for Eratosthenes'

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applied to the calculation of a network of triangles and the reduction of the observations generally. The systematic manner in which all the observations were taken with the view of securing final results of extreme accuracy was admirable. Bessel was also the first scientist who realised the effect

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took part, the association decided in favor of the reversion pendulum, which was used in Switzerland, and it was resolved to redo in Berlin, in the station where Bessel made his famous measurements, the determination of gravity by means of apparatus of various kinds employed in different countries,

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A circumnavigation alone does not prove that Earth is spherical: it could be cylindric, irregularly globular, or one of many other shapes. Still, combined with trigonometric evidence of the form used by Eratosthenes 1,700 years prior, the Magellan expedition removed any reasonable doubt in educated

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Bede was lucid about Earth's sphericity, writing "We call the earth a globe, not as if the shape of a sphere were expressed in the diversity of plains and mountains, but because, if all things are included in the outline, the earth's circumference will represent the figure of a perfect globe... For

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was hidden from view in most parts of Greece but that it just grazed the horizon at Rhodes. Posidonius is supposed to have measured the angular elevation of Canopus at Alexandria and determined that the angle was 1/48 of a circle. He used a distance from Alexandria to Rhodes, 5000 stadia, and so he

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trips conducted by professional bematists, whose job was to precisely measure the extent of the territory of Egypt for agricultural and taxation-related purposes. Furthermore, the fact that Eratosthenes' measure corresponds precisely to 252,000 stadia might be intentional, since it is a number that

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If they were like balls they would surely obstruct each other when they met. I replied that these celestial bodies were certainly like balls. How do we know this? By the waxing and waning of the moon. The moon itself gives forth no light, but is like a ball of silver; the light is the light of the

1002:. His mid-career conversion resulted in the latter work's systematic exaggeration of degree longitudes in the Mediterranean by a factor close to the ratio of the two seriously differing sizes discussed here, which indicates that the conventional size of the Earth was what changed, not the stadion. 3152:

for the measurement of gravity in six stations of the Swiss geodetic network. Following the example set by this country and under the patronage of the International Geodetic Association, Austria, Bavaria, Prussia, Russia and Saxony undertook gravity determinations on their respective territories.

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invited the Governments of Belgium, France, Prussia and England to connect their triangulations in order to measure the length of an arc of parallel in latitude 52° and to test the accuracy of the figure and dimensions of the Earth, as derived from the measurements of arc of meridian. In order to

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Many measurements of degrees of longitudes along central parallels in Europe were projected and partly carried out as early as the first half of the 19th century; these, however, only became of importance after the introduction of the electric telegraph, through which calculations of astronomical

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European astronomy was so much judged worth consideration that numerous Chinese authors developed the idea that the Chinese of antiquity had anticipated most of the novelties presented by the missionaries as European discoveries, for example, the rotundity of the Earth and the "heavenly spherical

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studied Eratosthenes' findings before sailing west for the Indies. However, ultimately he rejected Eratosthenes in favour of other maps and arguments that interpreted Earth's circumference to be a third smaller than it really is. If, instead, Columbus had accepted Eratosthenes' findings, he might

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and established his school, Plato also taught his students that Earth was a sphere, though he offered no justifications. "My conviction is that the Earth is a round body in the centre of the heavens, and therefore has no need of air or of any similar force to be a support." If man could soar high

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top. This yielded more accurate measurements of Earth's circumference and made it possible for a single person to measure it from a single location. Biruni's method was intended to avoid "walking across hot, dusty deserts", and the idea came to him when he was on top of a tall mountain in India

6164:"XIII. Results of the comparisons of the standards of length of England, Austria, Spain, United States, Cape of Good Hope, and of a second Russian standard, made at the Ordnance Survey Office, Southampton. With a preface and notes on the Greek and Egyptian measures of length by Sir Henry James" 3147:

who used it in 1818 brought the improvements which would result from the precious indications of Bessel, and which converted the reversible pendulum into one of the most admirable instruments which the scientists of the nineteenth century could use. The reversible pendulum built by the Repsold

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combine the measurements, it was necessary to compare the geodetic standards of length used in the different countries. The British Government invited those of France, Belgium, Prussia, Russia, India, Australia, Austria, Spain, United States and Cape of Good Hope to send their standards to the

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from 1870 to his death in 1888. Jean-Antonin-Léon Bassot completed the task in 1896. According to the calculations made at the central bureau of the international association on the great meridian arc extending from the Shetland Islands, through Great Britain, France and Spain to El Aghuat in

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models, and the model's accuracy in predicting the Moon and Sun's motion for Vedic rituals, probably came from direct astronomical observations. The cosmographic theories and assumptions in ancient India likely developed independently and in parallel, but these were influenced by some unknown

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was selected to direct the U.S. Survey of the Coast, and sent on a mission to France and England to procure instruments and standards of measurement. The unit of length to which all distances measured by the Survey of the Coast — which became the United States Coast Survey in 1836 and the

817:. The length that Eratosthenes intended for a "stade" is not known, but his figure only has an error of around one to five percent. Assuming a value for the stadion between 155 and 160 metres, the error is between −2.4% and +0.8%. Eratosthenes described his technique in a book entitled 3228:

decided the creation of an international geodetic standard at the General Conference held in Paris in 1875. The Conference of the International Association of Geodesy also dealt with the best instrument to be used for the determination of gravity. After an in-depth discussion in which

6440:"Rapport sur un mémoire de M. Peirce concernant la constante de la pesanteur à Paris et les corrections exigées par les anciennes déterminations de Borda et de Biot. in Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels" 3196:

stated. If precision metrology had needed the help of geodesy, it could not continue to prosper without the help of metrology. Indeed, how to express all the measurements of terrestrial arcs as a function of a single unit, and all the determinations of the force of gravity with the

3353:. He had managed to complete Laplace's program of specifying a mathematical form of the probability density for the observations, depending on a finite number of unknown parameters, and define a method of estimation that minimises the error of estimation. Gauss showed that the 1075:

cited various phenomena observed at sea as suggesting that Earth was spherical. He observed that elevated lights or areas of land were visible to sailors at greater distances than those less elevated, and stated that the curvature of the sea was obviously responsible for this.

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and the method of estimation. He then turned the problem around by asking what form the density should have and what method of estimation should be used to get the arithmetic mean as estimate of the location parameter. In this attempt, he invented the normal distribution.

437: 2975:, was a degree measurement that consisted of a nearly 3000 km long network of geodetic survey points. The Struve Geodetic Arc was one of the most precise and largest projects of earth measurement at that time. In 1860 Friedrich Georg Wilhelm Struve published his 704:, and two cold inhospitable regions, "one near our upper or northern pole and the other near the southern pole", both impenetrable and girdled with ice. Although no humans could survive in the frigid zones, inhabitants in the southern temperate regions could exist. 2271:

However, Shen's ideas did not gain widespread acceptance or consideration, as the shape of Earth was not important to Confucian officials who were more concerned with human relations. In the 17th century, the idea of a spherical Earth, now considerably advanced by

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Just as a passenger in a boat moving downstream sees the stationary (trees on the river banks) as traversing upstream, so does an observer on earth see the fixed stars as moving towards the west at exactly the same speed (at which the earth moves from west to

5890:"Le système métrique des poids et mesures; son établissement et sa propagation graduelle, avec l'histoire des opérations qui ont servi à déterminer le mètre et le kilogramme : Bigourdan, Guillaume, 1851-1932 : Free Download, Borrow, and Streaming" 1816:

court in 1267. It was made of wood on which "seven parts of water are represented in green, three parts of land in white, with rivers, lakes". Ho Peng Yoke remarks that "it did not seem to have any general appeal to the Chinese in those days".

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Discurso de don Carlos Ibáñez e Ibáñez de Ibero en la recepción pública de don Joaquín Barraquer y Rovira en la Real Academia de Ciencias Exactas, Físicas y Naturales, Madrid, Imprenta de la Viuda e Hijo de D.E. Aguado, 1881, p. 70-71, 71-73,

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Jonction géodésique et astronomique de l'Algérie avec l'Espagne, exécutée en commun en 1879, par ordre des gouvernements d'Espagne et de France, sous la direction de M. le général Ibañez,... pour l'Espagne, M. le colonel Perrier,... pour la

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Clarke, Alexander Ross; James, Henry (1867-01-01). "X. Abstract of the results of the comparisons of the standards of length of England, France, Belgium, Prussia, Russia, India, Australia, made at the ordnance Survey Office, Southampton".

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would accede to the Association. Moreover, according to the calculations made at the central bureau of the international association on the West Europe-Africa Meridian-arc the meridian of Greenwich was nearer the mean than that of Paris.

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which are not seen in the northerly regions". Since this could only happen on a curved surface, he too believed Earth was a sphere "of no great size, for otherwise the effect of so slight a change of place would not be quickly apparent".

469:, with the heavens being a physical dome spanning over it. Early arguments for a spherical Earth pointed to various more subtle empirical observations, including how lunar eclipses were seen as circular shadows, as well as the fact that 2328:(c. 1192–1279) firmly argued that Earth was spherical, just like the shape of the heavens only smaller, since a square Earth would hinder the movement of the heavens and celestial bodies in his estimation. The 17th-century 2782:, observed that his clock, which had been regulated at Paris to beat seconds, lost about two minutes and a half daily at Cayenne, and that in order to bring it to measure mean solar time it was necessary to shorten the 625:

above the clouds, Earth would resemble "one of those balls which have leather coverings in twelve pieces, and is decked with various colours, of which the colours used by painters on Earth are in a manner samples." In

1121:, observers note these seem to rise from the sea, indicating that they were hidden by the curved surface of the sea. He also gives separate arguments that Earth is curved north–south and that it is curved east–west. 2050:

truly it is an orb placed in the centre of the universe; in its width it is like a circle, and not circular like a shield but rather like a ball, and it extends from its centre with perfect roundness on all sides."

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Arabic miles (111.8 km) per degree, which corresponds to a circumference of 40,248 km, very close to the currently modern values of 111.3 km per degree and 40,068 km circumference, respectively.

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where its profound influence became apparent in the early centuries AD. The Greek concept of an Earth surrounded by the spheres of the planets and that of the fixed stars, vehemently supported by astronomers like

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Base du système métrique décimal, ou Mesure de l'arc du méridien compris entre les parallèles de Dunkerque et Barcelone. T. 3 /, exécutée en 1792 et années suivantes, par MM. Méchain et Delambre, rédigée par M.

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Eratosthenes' method was actually more complicated, as stated by the same Cleomedes, whose purpose was to present a simplified version of the one described in Eratosthenes' book. The method was based on several

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published his method of calculating the orbits of celestial bodies. In that work he claimed to have been in possession of the method of least squares since 1795. This naturally led to a priority dispute with

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in the 5th century BC although some disagree. After the 5th century BC, just a few Greek writers of repute thought the world was anything but round. The Pythagorean idea was supported later by

3135:. The studies he conducted from 1825 to 1828 and his determination of the length of the pendulum beating the second in Berlin seven years later marked the beginning of a new era in geodesy. Indeed, the 1733:. To get the true dip angle the measured dip angle needs to be corrected by approximately 1/6, meaning that even with perfect measurement his estimate could only have been accurate to within about 20%. 6509:

Torge, Wolfgang (2016). Rizos, Chris; Willis, Pascal (eds.). "From a Regional Project to an International Organization: The "Baeyer-Helmert-Era" of the International Association of Geodesy 1862–1916".

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in the 5th century BC. However, nothing certain about their knowledge of geography and navigation has survived; therefore, later researchers have no evidence that they conceived of Earth as spherical.

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Ancient India as described by Megasthenês and Arrian; being a translation of the fragments of the Indika of Megasthenês collected by Dr. Schwanbeck, and of the first part of the Indika of Arrian

1117:, which remained the standard work of astronomy for 1,400 years, he advanced many arguments for the spherical nature of Earth. Among them was the observation that when a ship is sailing towards 4235:, Vol. 15 (1978), pp. 533–633 (554f.); Glick, Thomas F., Livesey, Steven John, Wallis, Faith (eds.): "Medieval Science, Technology, and Medicine: An Encyclopedia", Routledge, New York 2005, 434: 4806:(The Book of Curiosities of the Sciences and Marvels for the Eyes), 2.1 "On the mensuration of the Earth and its division into seven climes, as related by Ptolemy and others", (ff. 22b–23a) 3089:

office in Southampton. Notably the standards of France, Spain and United States were based on the metric system, whereas those of Prussia, Belgium and Russia where calibrated against the

1670:(Latinized as Alfraganus) was a Persian astronomer of the 9th century involved in measuring the diameter of Earth, and commissioned by Al-Ma'mun. His estimate given above for a degree (56 1659:

gave a concise proof of Earth's sphericity: at any given time, there is a point on the Earth where the Sun is directly overhead (which moves throughout the day and throughout the year).

1320:, presented Earth as flat as late as in the 6th century. This last remnant of the ancient model of the cosmos disappeared during the 7th century. From the 8th century and the beginning 2042:, copied to meet the Carolingian requirement that all priests should study the computus, indicates that many, if not most, priests were exposed to the idea of the sphericity of Earth. 6280:

Encyclopédie théologique: ou, Série de dictionnaires sur toutes les parties de la science religieuse ... t. 1-50, 1844-1862; nouv, sér. t. 1-52, 1851-1866; 3e sér. t. 1-66, 1854-1873

2429:(1979–1982) was the first expedition to make a circumpolar circumnavigation, travelling the world "vertically" traversing both of the poles of rotation using only surface transport. 6464: 1908:

Revising the figures attributed to Posidonius, another Greek philosopher determined 18,000 miles (29,000 km) as the Earth's circumference. This last figure was promulgated by

1422:(476–550 CE) was a pioneer of mathematical astronomy on the subcontinent. He describes the Earth as being spherical and says that it rotates on its axis, among other places in his 3161:

found a way to highlight the movements of the pendulum suspension plane by an ingenious optical amplification process. Isaac-Charles Élisée Cellérier, a Genevan mathematician and

1705:(973–1048), in contrast to his predecessors, who measured Earth's circumference by sighting the Sun simultaneously from two different locations, developed a new method of using 4514:

Klaus Anselm Vogel, "Sphaera terrae – das mittelalterliche Bild der Erde und die kosmographische Revolution", PhD dissertation Georg-August-Universität Göttingen, 1995, p. 19.

3410:, Volumes 1 & 2 (1880 & 1884, resp.). Helmert also derived the first global ellipsoid in 1906 with an accuracy of 100 meters (0.002 percent of the Earth's radii). The 547:

cast doubt on a report of the Sun observed shining from the north. He stated that the phenomenon was observed by Phoenician explorers during their circumnavigation of Africa (

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The issue could be settled by measuring, for a number of points on earth, the relationship between their distance (in north–south direction) and the angles between their

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uncritically used Alfraganus's figure as if it were in Roman miles instead of in Arabic miles, in order to prove a smaller size of Earth than that propounded by Ptolemy.

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shows that he could assume this knowledge among his congregation. The sermon was preached in the vernacular German, and thus was not intended for a learned audience.

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described the world as "being like an egg with a spherical yolk (the globe) surrounded by a layer of white (the atmosphere) and covered with a hard shell (the sky)".

1389:, c. 300 BC, has been interpreted as stating that the contemporary Brahmans believed in a spherical Earth as the center of the universe. With the spread of 910:

Under the previous assumptions, says Cleomedes, you can measure the Sun's angle of elevation at noon of the summer solstice in Alexandria, by using a vertical rod (a

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th of an in.). This fact was scarcely credited till it had been confirmed by the subsequent observations of Varin and Deshayes on the coasts of Africa and America.

4059:"The Eratosthenes-Strabo Nile Map. Is It the Earliest Surviving Instance of Spherical Cartography? Did It Supply the 5000 Stades Arc for Eratosthenes' Experiment?" 2608:, near the equator. Their measurements demonstrated an oblate Earth, with a flattening of 1:210. This approximation to the true shape of the Earth became the new 2046:

paraphrased Bede into Old English, saying, "Now the Earth's roundness and the Sun's orbit constitute the obstacle to the day's being equally long in every land."

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sources, there is no account of how the sphericity of Earth was discovered, or if it was initially simply a guess. A plausible explanation given by the historian

1460:(Gitika 3,6; Kalakriya 5; Gola 9,10). For example, he explained the apparent motion of heavenly bodies as only an illusion (Gola 9), with the following simile: 1885:

In medieval Europe, knowledge of the sphericity of Earth survived into the medieval corpus of knowledge by direct transmission of the texts of Greek antiquity (

3329:. In the same year he was appointed secretary of the mathematics class at the Berlin Academy of Sciences. Tralles maintained an important correspondence with 1025:

refer in their works to the rotundity of Earth as a matter of course. Pliny also considered the possibility of an imperfect sphere "shaped like a pinecone".

3349:. However, to Gauss's credit, he went beyond Legendre and succeeded in connecting the method of least squares with the principles of probability and to the 2095:, the astronomical knowledge in Christian Europe was extended beyond what was transmitted directly from ancient authors by transmission of learning from 6733:

The problem of the Earth's shape from Newton to Clairaut: the rise of mathematical science in eighteenth-century Paris and the fall of "normal" science.

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Glick, Thomas F., Livesey, Steven John, Wallis, Faith (eds.): "Medieval Science, Technology, and Medicine: An Encyclopedia", Routledge, New York 2005,

5544: 6144: 1667: 3250: 3246: 2451:, asserted that the tropical gap between our habitable region and the other habitable region to the south was smaller than Macrobius had believed. 2126:, based on Ptolemy, which primarily considers the sphere of the sky. However, it contains clear proofs of Earth's sphericity in the first chapter. 1725:

From the top of the mountain, he sighted the dip angle which, along with the mountain's height (which he calculated beforehand), he applied to the

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Bericht über die Verhandlungen der vom 30. September bis 7. October 1867 zu BERLIN abgehaltenen allgemeinen Conferenz der Europäischen Gradmessung

6370: 6314: 5932: 389: 726:, the structure of the universe was believed to be a series of perfect spheres. The Sun, Moon, planets and fixed stars were believed to move on 2207:, written in Italian in the early 14th century, portrays Earth as a sphere, discussing implications such as the different stars visible in the 592:

in the 5th century BC, and although the idea cannot reliably be ascribed to Pythagoras, it might nevertheless have been formulated in the

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It has been suggested that seafarers probably provided the first observational evidence that Earth was not flat, based on observations of the

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Soler, T. (1997-02-01). "A profile of General Carlos Ibáñez e Ibáñez de Ibero: first president of the International Geodetic Association".

3242: 3218: 2860:(Central European Arc Measurement) was established by several central European countries and a Central Bureau was set up at the expense of 2284:, who held high positions as astronomers at the imperial court, successfully challenged the Chinese belief that Earth was flat and square. 1487:; assuming a yojana to be 8 km (4.97097 miles) this gives a circumference of 39,736 kilometres (24,691 mi), close to the current 1010:

The idea of a spherical Earth slowly spread across the globe, and ultimately became the adopted view in all major astronomical traditions.

3302: 1335:(both 5th century AD) discussed the circumference of the sphere of the Earth, its central position in the universe, the difference of the 5409: 4255: 3290: 3275:

gained worldwide importance with the joining of United States, Mexico, Chile, Argentina and Japan. In 1883 the General Conference of the

211: 6846: 6028: 3399:, that several simultaneously observing persons determine slightly different values, especially recording the transition time of stars. 2809:

attraction of these huge piles of rock. As this vertical is everywhere perpendicular to the idealized surface of mean sea level, or the

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Muslim scholars who held to the spherical Earth theory used it to calculate the distance and direction from any given point on Earth to

1763:. He found the radius of Earth to be 6,339.6 kilometres (3,939.2 mi), a value not obtained in the West until the 16th century. His 4346:"Ein Versuch über die Archäologie der Globalisierung. Die Kugelgestalt der Erde und die globale Konzeption des Erdraums im Mittelalter" 3207:

and Henry James published the first results of the standards' comparisons in 1867. The same year Russia, Spain and Portugal joined the

3140: 379: 347: 2619:. Its purpose was to link the Greenwich and Paris' observatories. The survey is very significant as the forerunner of the work of the 3268: 3254: 3193: 3049: 1934:

Spread of this knowledge beyond the immediate sphere of Greco-Roman scholarship was necessarily gradual, associated with the pace of

1267:, which was one of the few examples of Greek scientific thought that was known in the Early Middle Ages in Western Europe, discussed 3069: 3053: 1316:, which tradition laid greater importance on a literalist interpretation of the Old Testament. Authors from that tradition, such as 880:

Cleomedes assumes that the distance between Syene and Alexandria was 5,000 stadia (a figure that was checked yearly by professional

3491: 1053:(c. 64 BC – 24 AD), who suggested that the spherical shape of Earth was probably known to seafarers around the 357: 6328: 4849: 5093: 2949: 1971:

It was not until the 16th century that his concept of the Earth's size was revised. During that period the Flemish cartographer,

669:

Aristotle reported the circumference of the Earth (which is actually slightly over 40,000 km or 24,000 miles) to be 400,000

2915: 931:

have never gone west, since he did not have the supplies or funding needed for the much longer eight-thousand-plus mile voyage.

4698:"The Ancient Geography of India: I. The Buddhist Period, Including the Campaigns of Alexander, and the Travels of Hwen-Thsang" 3165:

would independently develop a correction formula which would make it possible to use the observations made using this type of

2389:. The expedition was financed by the Spanish Crown. On August 10, 1519, the five ships under Magellan's command departed from 974:(c. 135 – 51 BC), using a similar method as Eratosthenes. Instead of observing the Sun, he noted that the star 6707: 6686: 6645: 6530: 5489: 5462: 4991: 4568: 4469: 4212: 4177: 4016: 2979:. The flattening of the earth was estimated at 1/294.26 and the earth's equatorial radius was estimated at 6378360.7 metres. 337: 6138: 3322: 3276: 3272: 3264: 3259: 3225: 3208: 3042: 2881: 2877: 2857: 2308:

Although mainstream Chinese science until the 17th century held the view that Earth was flat, square, and enveloped by the

5588:

Christopher Cullen, "A Chinese Eratosthenes of the Flat Earth: A Study of a Fragment of Cosmology in Huai Nan Tzu 淮南子",

4495:, Corpus Platonicum Medii Aevi, Plato Latinus, vol. 4, Leiden / London: Brill / Warburg Institute, pp. 141–144, 2320:(fl. 307–345), who suggested that Earth could be either square or round, in accordance with the shape of the heavens. The 4297:

Cullen, C. (1976). "A Chinese Eratosthenes of the Flat Earth: A Study of a Fragment of Cosmology in Huai Nan tzu 淮南子".

3687: 2813:, this means that the figure of the Earth is even more irregular than an ellipsoid of revolution. Thus the study of the " 2616: 2504:, another southward. When he computed the length of a degree from both chains, he found that the length of one degree of 1273: 5545:"Space and Time in Chinese Texts of Astronomy and of Mathematical Astronomy in the Seventeenth and Eighteenth Centuries" 4256:"Space and Time in Chinese Texts of Astronomy and of Mathematical Astronomy in the Seventeenth and Eighteenth Centuries" 4195:

Jamil, Jamil (2009). "Astronomy". In Fleet, Kate; Krämer, Gudrun; Matringe, Denis; Nawas, John; Rowson, Everett (eds.).

3093:, of which the oldest physical representative was the Toise of Peru. The Toise of Peru had been constructed in 1735 for 317: 6824: 2972: 1920:, using such maps, was led to believe that Asia was only 3,000 or 4,000 miles (4,800 or 6,400 km) west of Europe. 813: 118: 6084: 1964:

who were aware that Earth was spherical has been compiled by Reinhard Krüger, professor for Romance literature at the

6754: 6740: 6664: 5720: 5516: 5018: 4965: 4894: 4644: 4500: 4384: 4240: 3598: 2658: 1618:

used based on these measurements was 56 2/3 miles, giving an Earth circumference of 20,400 miles (32,830 km). 66

1611: 417: 6352:

Ibáñez e Ibáñez de Íbero, Carlos (1825-1891) Auteur du texte; Perrier, François (1833-1888) Auteur du texte (1886).

5172:

Barmore, Frank E. (April 1985), "Turkish Mosque Orientation and the Secular Variation of the Magnetic Declination",

3000:

Bases du système métrique décimal ou mesure de l'arc méridien compris entre les parallèles de Dunkerque et Barcelone

1729:

formula to calculate the curvature of the Earth. While this was an ingenious new method, Al-Biruni was not aware of

494:

is that it was "the experience of travellers that suggested such an explanation for the variation in the observable

6801: 5651:

Nowell, Charles E. ed. (1962). Magellan's Voyage around the World: Three Contemporary Accounts. Evanston: NU Press.

4911: 3139:

as it was used by geodesists at the end of the 19th century was largely due to the work of Bessel, because neither

2805:

of India, that the astronomical vertical tended to be pulled in the direction of large mountain ranges, due to the

1865: 2864:, within the Geodetic Institute at Berlin. One of its most important goals was the derivation of an international 1473:, Aryabhata also estimates the circumference of the Earth. He gives this as 4967 yojanas and its diameter as 1581 1410:, strengthened the astronomical principles. Some ideas were found possible to preserve, although in altered form. 584:, but there is no evidence for this claim. Some idea of the sphericity of Earth seems to have been known to both 6869: 3496:(digital animation). NASA/Goddard Space Flight Center. Goddard Multimedia Animation Number: 10910. Archived from 1608:) on flat desert land until they reached a place where the altitude of the North Pole had changed by one degree. 5211: 840:

Measure of Earth's circumference according to Cleomedes' simplified version, based on the wrong assumption that

821:, which has not been preserved. Eratosthenes could only measure the circumference of Earth by assuming that the 6278: 4178:

Materialien und Dokumente zur mittelalterlichen Erdkugeltheorie von der Spätantike bis zur Kolumbusfahrt (1492)

1357:, Macrobius described the Earth as a globe of insignificant size in comparison to the remainder of the cosmos. 548: 203: 5914:

Delambre, Jean-Baptiste (1749-1822) Auteur du texte; Méchain, Pierre (1744-1804) Auteur du texte (1806–1810).

4352:, Jahrbuch aus Lehre und Forschung der Universität Stuttgart, University of Stuttgart, 2007, pp. 28–52 (35–36) 2691: 2578: 3568: 3326: 3098: 3015: 2679: 1559:

in order to further mensuration and to calculate the distance and direction from any given point on Earth to

219: 2665:

on the international scientific committee meeting in Paris from 1798 to 1799 to determine the length of the

6759:

D. Rawlins: "Ancient Geodesy: Achievement and Corruption" 1984 (Greenwich Meridian Centenary, published in

6608:"Mathematiker des Monats Juni/Juli 2016 - Johann Georg Tralles | Berliner Mathematische Gesellschaft e. V." 4345: 3840: 2552: 2409:, continued the expedition and, on September 6, 1522, arrived at Seville, completing the circumnavigation. 1767:

contains a table giving the coordinates of six hundred places, almost all of which he had direct knowledge.

6114:"IUGG, the International Union of Geodesy and Geophysics | Union Geodesique et Geophysique Internationale" 4424: 4160: 2511: 2262:(1031-1095) used models of lunar eclipse and solar eclipse to conclude the roundness of celestial bodies. 5181: 3271:

was reelected as president. He remained in this position until his death in 1891. During this period the

2340:(78–139 AD) had used to describe the shape of the Sun and Moon (as in, that the former was as round as a 1517: 707: 5559: 3585:

Panchenko, Dmitri (2008). "Parmenides, the Nile and the Circumnavigation of Africa by the Phoenicians".

3334: 2143:

unanimously agreed that Earth is spherical or round. Grant observes that no author who had studied at a

653:(384–322 BC) was Plato's prize student and "the mind of the school". Aristotle observed "there are 5606:

Needham, Joseph (1986). Science and Civilization in China: Volume 3. Taipei: Caves Books, Ltd. pp. 499.

5043: 4711: 3282: 3052:

announced Spain's contribution to the remeasurement and extension of the French meridian arc. In 1870,

3037: 2825: 2802: 2755: 2675: 2585: 2548: 2096: 700:

he divided the world into five climatic zones: two temperate areas separated by a torrid zone near the

680:

Every portion of Earth tends toward the centre until by compression and convergence they form a sphere.

6774:

C. Taisbak: "Posidonius vindicated at all costs? Modern scholarship versus the stoic earth measurer".

4984:

The History of Cartography: Vol. 2.1, Cartography in the traditional Islamic and South Asian societies

3900: 1203:

Ptolemy also devised and provided instructions on how to make maps both of the whole inhabited world (

6060: 2944: 2642: 2481: 2313: 2236: 1805: 1134:

is a discussion of the data and of the methods he used. As with the model of the Solar System in the

711: 644: 498:

of the pole and the change in the area of circumpolar stars, a change that was quite drastic between

182: 6568: 6137: 6022: 3073:

Algeria, the Earth equatorial radius was 6377935 metres, the ellipticity being assumed as 1/299.15.

2982:

In the early 19th century, the Paris meridian's arc was recalculated with greater precision between

2686:, lasting from 1792 to 1799, which attempted to accurately measure the distance between a belfry in 1544:), both of whom worked from the premise that Earth was spherical and at the centre of the universe ( 6725: 5115: 5098: 5088: 4421:. Translated by Jones, Horace Leonard (Loeb Classical Library ed.). London: William Heinemann. 4400: 3990: 3431: 3403: 3374: 2405:, where Magellan was killed by Philippine natives in a battle. His second in command, the Spaniard 2155: 1987: 1297: 1154:, as it is today, but Ptolemy preferred to express it as the length of the longest day rather than 1014: 857: 719: 149: 96: 5814: 3633: 3056:

was in charge of resuming the triangulation between Dunkirk and Barcelona. This new survey of the

2734:

had to be equal to one ten-million of this distance, it was defined as 0,513074 toises or 443,296

2406: 676:

Aristotle provided physical and observational arguments supporting the idea of a spherical Earth:

576:

in shape. Some early Greek philosophers alluded to a spherical Earth, though with some ambiguity.

6484: 4971: 4923: 4362: 3106: 3102: 3081: 2920: 2814: 2597: 2589: 2508:

in the northern part of the chain was shorter than that in the southern part (see illustration).

2497: 2438: 1965: 1013:

In the West, the idea came to the Romans through the lengthy process of cross-fertilization with

970:

A parallel later ancient measurement of the size of the Earth was made by another Greek scholar,

715: 695: 617: 287: 247: 6607: 4584:

Ohashi, Yukio (1993). "Development of Astronomical Observations in Vedic and post-Vedic India".

2462:

with a margin of error of only 4%, when the current error at the time varied between 7 and 15%.

2190:, and several Italian dialects, explicitly refers to a spherical Earth. Likewise, the fact that 986:

The above-mentioned larger and smaller sizes of the Earth were those used by later Roman author

6563: 5697:

Universidade de São Paulo, Departamento de História, Sociedade de Estudos Históricos (Brazil),

4658: 4399:, Bk. 5 393: "As he rose on the swell he looked eagerly ahead, and could see land quite near." 3620: 3456: 3451: 3230: 3162: 2848: 2763: 2473: 2455: 2191: 2158:(c. 1120), an important manual for the instruction of lesser clergy, which was translated into 2117: 1834: 1730: 1614:

result is described in different sources as 66 2/3 miles, 56.5 miles, and 56 miles. The figure

1556: 980: 694:

The concepts of symmetry, equilibrium and cyclic repetition permeated Aristotle's work. In his

267: 5008: 4697: 4283: 2977:

Arc du méridien de 25° 20′ entre le Danube et la Mer Glaciale mesuré depuis 1816 jusqu’en 1855

2718:

of 1/334. The committee extrapolated from Delambre and Méchain's survey the distance from the

2593: 1804:

A terrestrial globe (Kura-i-ard) was among the presents sent by the Persian Muslim astronomer

1759:

were also made by Biruni. He introduced techniques to measure Earth and distances on it using

1375:

While the textual evidence has not survived, the precision of the constants used in pre-Greek

836: 5059: 3590: 3461: 3422:

and an accuracy of 200 m. It was adopted by the IUGG as "international ellipsoid 1924".

3415: 3370: 3346: 3217:

as a uniform length standard for the Arc Measurement and recommended the establishment of an

3204: 3132: 3061: 2710:

was defined as one ten-millionth of the shortest distance from the North Pole to the equator

2646: 2426: 2325: 2281: 2273: 2120:(c. 1195 – c. 1256 AD) wrote a famous work on Astronomy called 1521: 1394: 1317: 796: 733:

Though Aristotle's theory of physics survived in the Christian world for many centuries, the

569: 410: 327: 77: 6657:

Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth

3982: 3841:"NOAA National Ocean Service Education: Global Positioning Tutorial: The History of Geodesy" 2081:

prepares to shoot the world, a sphere with compartments representing earth, air, and water (

6555: 5988: 3937: 3466: 3441: 3366: 3341: 3318: 3105:, conducted in actual Ecuador from 1735 to 1744 in collaboration with the Spanish officers 2630: 2469: 2371: 2122: 2107: 1938:

of Europe. For example, the first evidence of knowledge of the spherical shape of Earth in

1917: 1861: 1691: 1456:"). The discovery that the Earth rotates on its own axis from west to east is described in 1428: 1167: 1143: 1126: 959: 939: 927: 864:

to popularise the discovery. Cleomedes invites his reader to consider two Egyptian cities,

459: 227: 177: 103: 6747:

Quest for the true figure of the Earth: ideas and expeditions in four centuries of geodesy

2043: 8: 6163: 5872:

American Philosophical Society.; Society, American Philosophical; Poupard, James (1825).

5713:

Full meridian of glory : perilous adventures in the competition to measure the Earth

5084: 4753: 3983: 3446: 3436: 3358: 3350: 3136: 2968: 2910: 2751: 2609: 2544: 2382: 2333: 2208: 2144: 1996: 1924: 1912:

through his world maps. The maps of Ptolemy strongly influenced the cartographers of the

1902: 1552: 1390: 1344: 1340: 1324:, "no cosmographer worthy of note has called into question the sphericity of the Earth". 1313: 998: 830: 822: 714:

go down (toward what Aristotle believed was the center of the Universe), and things like

139: 87: 6559: 5992: 3941: 3497: 2817:" became the next great undertaking in the science of studying the figure of the Earth. 1628:

miles results in a calculated planetary circumference of 24,000 miles (39,000 km).

1505: 1036:

by Earth's curvature. This was one of the first arguments favouring a round-Earth model.

906:

he assumes the simplified hypothesis that Syene and Alexandria are on the same meridian.

6836: 6674: 6635: 6589: 6405: 6364: 6308: 5926: 5392: 5384: 5193: 4678: 4322: 4314: 4275: 4078: 4058: 3953: 3727: 3719: 3471: 2998:. In 1821 they published their work as a fourth volume following the three volumes of " 2995: 2615:

In 1787 the first precise trigonometric survey to be undertaken within Britain was the

2532: 2528: 2410: 2398: 2386: 2183: 2167: 2008: 1890: 1830: 1524:. The Islamic theoretical framework largely relied on the fundamental contributions of 1370: 1309: 1252: 780: 734: 626: 491: 29: 6046:

Observations astronomiques et physiques faites en l'isle de Caïenne, par M. Richer,...

4818: 6820: 6797: 6789: 6750: 6736: 6703: 6682: 6660: 6641: 6593: 6581: 6526: 6409: 6227: 6203: 6185: 5788: 5767: 5726: 5716: 5522: 5512: 5485: 5458: 5434: 5396: 5197: 5014: 4987: 4961: 4912:"Applicable Problems in History of Mathematics: Practical Examples for the Classroom" 4890: 4682: 4640: 4564: 4496: 4488: 4465: 4404: 4380: 4326: 4236: 4208: 4082: 4012: 3731: 3594: 3513: 3395: 2779: 2662: 2536: 2100: 2063: 1976: 1972: 1857: 1838: 1793: 1756: 1702: 1589: 1585: 1332: 1321: 1301: 1097: 1054: 804: 746: 727: 503: 159: 144: 6699:

Encyclopedia of the History of Arabic Science: Technology, alchemy and life sciences

5979:

Levallois, J.-J. (1986). "L'Académie royale des Sciences et la figure de la Terre".

4204: 3957: 3019: 2991: 2683: 1484: 6864: 6573: 6518: 6397: 6175: 5959: 5847: 5822: 5757: 5509:

Science and Civilisation in China: An abridgement of Joseph Needham's original text

5376: 5362: 5185: 4927: 4670: 4306: 4267: 4200: 4070: 3945: 3814: 3711: 3381: 3330: 3238: 3198: 3149: 3124: 3110: 2987: 2634: 2353: 2309: 2187: 2092: 1935: 1545: 1453: 1366: 1312:

were clearly aware of the sphericity of Earth. "Flat Earthism" lingered longest in

1104: 987: 892: 845: 723: 522: 455: 403: 154: 6044: 5686:

Ordering the Heavens: Roman Astronomy and Cosmology in the Carolingian Renaissance

4733: 4009:

Adversaries and Authorities: Investigations into ancient Greek and Chinese science

3928:

Rorres, Chris (January 2016). "Archimedes' floating bodies on a spherical Earth".

6813: 6697: 6353: 5915: 5889: 5873: 4854: 4610: 4558: 4164: 3906: 3682: 3678: 3660: 3562: 3354: 3086: 3025: 2620: 2493: 2485: 2240: 2232: 2074: 1719: 1353: 1293: 1022: 6298: 2468:

performed the first modern meridian arc measurement in 1669–1670. He measured a

2332:

treatise also used the same terminology to describe the shape of Earth that the

1403: 683:

Travelers going south see southern constellations rise higher above the horizon.

6439: 6252: 5367: 5033: 4982:

Mercier, Raymond P. (1992). "Geodesy". In J. B. Harley; David Woodward (eds.).

4807: 4004: 3745: 3306: 3158: 3094: 3057: 3033: 2798: 2711: 2638: 2601: 2489: 2394: 2251: 2159: 2135: 1957: 1501:

Geography and cartography in medieval Islam: Mathematical geography and geodesy

1260: 1244: 1220: 1197: 1175: 1155: 670: 593: 499: 367: 134: 108: 6472:. Berlin: Central-Bureau der Europäischen Gradmessung. 1868. pp. 123–135. 5981:

Comptes rendus de l'Académie des sciences. Série générale, la Vie des sciences

5037: 4310: 4271: 3127:

was responsible for the nineteenth-century investigations of the shape of the

1084: 860:

has been lost; what has been preserved is the simplified version described by

6858: 6850:. Vol. 11 (11th ed.). Cambridge University Press. pp. 607–615. 6841: 6585: 6189: 6017: 5871: 5771: 5730: 4228: 3411: 3389: 3286: 3172: 3003: 2794: 2381:

The first direct demonstration of Earth's sphericity came in the form of the

2203: 2130: 2083: 1943: 1898: 1760: 1398: 955: 800: 742: 687: 530: 487: 6724:

An early version of this article was taken from the public domain source at

4931: 4299:

Bulletin of the School of Oriental and African Studies, University of London

3839:

US Department of Commerce, National Oceanic and Atmospheric Administration.

1979:

and all of Europe which had the effect of increasing the size of the earth.

1841:

used it to find the direction of Mecca from many cities and published it in

1300:, but this remained an eccentric current. Learned Christian authors such as 6401: 6180: 6092: 6021: 5964: 5947: 5762: 5745: 5526: 5511:. Ronan, Colin A. Cambridge: Cambridge University Press. pp. 415–416. 5477: 5450: 3357:

is indeed the best estimate of the location parameter by changing both the

2574: 2524: 2459: 2448: 2414: 2321: 2175: 1789: 1726: 1706: 1605: 1581: 1285: 1248: 1163: 1088:

A printed map from the 15th century depicting Ptolemy's description of the

983:. Posidonius furthermore expressed the distance of the Sun in Earth radii. 792: 738: 92: 6577: 5263:

Similarly, J. Fontaine refers to this passage as a "scientific absurdity".

3046: 6659:. Vol. 3 (reprint ed.). Cambridge: Cambridge University Press. 6522: 5279:

Wesley M. Stevens, "The Figure of the Earth in Isidore's 'De natura rerum

3978: 3388:

marked a new era in the science of geodesy. Here was found the method of

3144: 2959: 2852:

Negative lithography stone and positive print of a historic map of Munich

2830: 2806: 2747: 2641:. Soon after the Anglo-French Survey, in 1791 and 1797, he and his pupil 2624: 2465: 2378:(1492) provided more direct evidence of the size and shape of the world. 2296: 2171: 2014: 1991:

Spherical Earth with the four seasons. Illustration in 12th-century book

1961: 1948: 1939: 1913: 1809: 1407: 1386: 1243:

Knowledge of the spherical shape of Earth was received in scholarship of

1235:. Ptolemy was well aware that he knew about only a quarter of the globe. 1228: 1212: 947: 573: 49: 6032:. Vol. 08 (11th ed.). Cambridge University Press. p. 811. 5826: 4659:"Aryabhata and Axial Rotation of Earth - Khagola (The Celestial Sphere)" 4604: 4279: 3402:

Most of the relevant theories were then derived by the German geodesist

3325:. In 1810 he became the first holder of the chair of mathematics at the 3234:

in order to compare them and thus to have the equation of their scales.

2935: 2703: 2661:. This work earned Tralles to be appointed as the representative of the 1792:, specifically by correcting Ptolemy's estimate of the longitude of the 1604:, by using a rope to measure the distance travelled due north or south ( 745:

was shown to be a more correct explanation of the nature of matter than

4986:. Chicago & London: University of Chicago Press. pp. 182–184. 4674: 4170: 4074: 3166: 2719: 2715: 2571: 2560: 2477: 2337: 2277: 2228: 2163: 2078: 1781: 1777: 1650: 1615: 1289: 1281: 1268: 1139: 1108: 971: 896: 865: 849: 757: 589: 585: 577: 565: 554: 507: 466: 6485:"Bulletin de la Société des Sciences Naturelles de Neuchâtel. Vol. 10" 5388: 5112:"Islamic Educational, Scientific and Cultural Organization - ISESCO -" 4318: 3949: 3723: 3184:

with a 15000 times magnification of the surface's level of the Earth,

2519:

This result, if correct, meant that the earth was not a sphere, but a

2500:. Cassini divided the measured arc into two parts, one northward from 2099:. An early student of such learning was Gerbert d'Aurillac, the later 4886: 4527: 4484: 3011: 2865: 2699: 2695: 2555:

combined with the rotation of the Earth predicted the Earth to be an

2443: 2299:

reinterpretation that declared the imported ideas Chinese in origin:

2224: 2212: 2179: 2110:, 1098–1179), depicted the spherical Earth several times in her work 2059: 1886: 1741: 1525: 1510: 1419: 1328: 1256: 1193: 1171: 1159: 1033: 919: 891:

he assumes the simplified hypothesis that Syene was precisely on the

861: 650: 598: 544: 529:

is described as being undertaken by Phoenician explorers employed by

518: 128: 54: 5457:, Cambridge: Cambridge University Press, pp. 620–622, 737–738, 5150:

Li, Qi and Shu, An introduction to Science and Civilisation in China

4787: 4190: 4188: 4186: 2194:(mid-13th century) used the spherical Earth as an illustration in a 1138:, Ptolemy put all this information into a grand scheme. He assigned 639: 486:

Though the earliest written mention of a spherical Earth comes from

5815:"Die Basismessungen im Grossen Moos zwischen Walperswil und Sugiez" 5380: 5189: 4246: 4137: 3758: 3715: 3419: 3408:

Die mathematischen und physikalischen Theorien der höheren Geodäsie

3263:

from 1874 to 1886. In 1886 the association changed its name to the

3131:

by means of the pendulum's determination of gravity and the use of

2983: 2783: 2767: 2762:, in South America, for the purpose of investigating the amount of 2556: 2520: 2505: 2375: 2359: 2341: 2259: 2031: 1714: 1656: 1653: 1601: 1540: 1530: 1423: 1147: 1118: 1113: 992: 943: 900: 881: 826: 572:, an early Greek philosopher, believed strongly that the Earth was 536: 495: 307: 124: 113: 6085:"(IAG) International Association of Geodesy: Associations of IUGG" 2956:

of which Hassler had brought a copy in the United States in 1805.

811:'s circumference around 240 BC, computing a value of 252,000 560:

Speculation and theorizing ranged from the flat disc advocated by

5660:

Joseph Jacobs (2006), "The story of geographical discovery" p. 90

4630:, Vol. 15 (1978), pp. 533–633 (533, 554f.) "Chapter 6. Cosmology" 4183: 3185: 3065: 3007: 2869: 2861: 2834: 2759: 2723: 2687: 2654: 2605: 2390: 1909: 1785: 1752: 1737: 1593: 1535: 1488: 1377: 1305: 1151: 1090: 1063: 1046: 975: 701: 533: 470: 451: 187: 44: 21: 6726:

http://www.ngs.noaa.gov/PUBS_LIB/Geodesy4Layman/TR80003A.HTM#ZZ4

5365:(1968). "Science in Seventh-Century Armenia: Ananias of Sirak". 4176:

Continuation into Roman and medieval thought: Reinhard Krüger: "

2754:

from a spherical form. This astronomer, having been sent by the

2523:(taller than wide). However, this contradicted computations by 1513:(973–1048) to estimate the radius and circumference of the Earth 1219:

spanned 180 degrees of longitude from the Canary Islands in the

1162:

day increases from 12h to 24h as you go from the equator to the

6351: 5000: 4157: 4149: 3764: 3418:

derived a global ellipsoid in ~1910, based on intercontinental

3257:. He also was the president of the Permanent Commission of the 2873: 2842: 2750:

turned the attention of mathematicians to the deviation of the

2567: 2363: 2195: 1578: 1520:

was developed on the basis of a spherical Earth inherited from

1348: 1336: 1277:

to compute the relative diameters of the Sun, Earth, and Moon.

1232: 1185: 1072: 1050: 1018: 911: 873: 662: 621: 581: 526: 511: 297: 257: 195: 6835: 1551:

Early Islamic scholars recognized Earth's sphericity, leading

1146:

that spanned the globe (although most of this has been lost).

1028: 6113: 5039:

The Empire of Reason 2/6 (Science and Islam – Episode 2 of 3)

4622: 4620: 3214: 3177: 3128: 3090: 2810: 2775: 2735: 2731: 2727: 2667: 2501: 2317: 1953: 1923:

Ptolemy's view was not universal, however, and chapter 20 of

1869: 1846: 1826: 1813: 1710: 1597: 1565: 1560: 1224: 1189: 1068: 1058: 869: 841: 808: 737:

was eventually shown to be a more correct explanation of the

658: 613: 609: 561: 458:) began during antiquity and ultimately blossomed during the 82: 3564:

The Pacific Basin: A History of Its Geographical Exploration

1347:, and many other geographical details. In his commentary on 5878:. Vol. new ser.:v.2 (1825). Philadelphia p. 253. 5575:

Christopher Cullen, "Joseph Needham on Chinese Astronomy",

5538: 5536: 5326:, (Liverpool: Liverpool Univ. Pr., 2004), pp. lxxxv–lxxxix. 4785: 4464:, Cambridge: Cambridge University Press, pp. 119–120, 3213:

and the General Conference of the association proposed the

2771: 2588:

dispatched two expeditions. One expedition (1736–37) under

2402: 2367: 2027: 1894: 1130:

covering what was known about Earth. The first part of the

654: 517:

Another possible explanation can be traced back to earlier

384: 277: 6834:

Clarke, Alexander Ross; Helmert, Friedrich Robert (1911).

6228:"ETH-Bibliothek / Base du système métrique... [7]" 5455:

Planets, Stars, & Orbs: The Medieval Cosmos, 1200–1687

4626:

D. Pingree: "History of Mathematical Astronomy in India",

4617: 4423:, Vol.I Bk. I para. 20, pp .41, 43. An earlier edition is 3116: 1600:

in modern Syria. To determine the length of one degree of

1227:, and about 81 degrees of latitude from the Arctic to the 1192:) at the extreme right, beyond the island of "Taprobane" ( 775:) gave an upper bound for the circumference of the Earth. 6390:

Philosophical Transactions of the Royal Society of London

6168:

Philosophical Transactions of the Royal Society of London

5582: 5569: 5047: 2535:

was the first to derive the now standard formula for the

951: 950:, wrote that Earth is spherical (and actually orbits the 601:. Efforts commenced to determine the size of the sphere. 5533: 4544:

Martianus Capella, The Marriage of Philology and Mercury

4221: 3909:

Cambridge: Cambridge University Press. 1897. p. 254

2891: 1207:) and of the Roman provinces. In the second part of the 1142:

to all the places and geographic features he knew, in a

6300:

Histoire abrégée de l'astronomie / par Ernest Lebon,...

5715:. New York: Copernicus Books/Springer. pp. 39–75. 5602: 5600: 5598: 4493:

Timaeus a Calcidio translatus commentarioque instructus

2909:

It has been suggested that portions of this section be

2030:(c. 672–735) wrote in his influential treatise on 1747:

According to John J. O'Connor and Edmund F. Robertson,

1382:

quantitative Greek astronomy text in the medieval era.

1271:'s use of the geometrical circumstances of eclipses in 1111:, the centre of scholarship in the 2nd century. In the 5590:

Bulletin of the School of Oriental and African Studies

5484:, Cambridge: Cambridge University Press, p. 339, 4768: 4766: 4011:, Cambridge: Cambridge University Press, p. 60, 3838: 3006:

or measurement of the meridian arc comprised between

5946:

Martin, Jean-Pierre; McConnell, Anita (2008-12-20).

5913: 5744:

Martin, Jean-Pierre; McConnell, Anita (2008-12-20).

5595: 4734:"The Aryabhatiya: Foundations of Indian Mathematics" 3702:

Burch, George Bosworth (1954). "The Counter-Earth".

3490:

NASA/Goddard Space Flight Center (3 February 2012).

1897:. It became increasingly traceable with the rise of 1796:

from 62 degrees to the correct value of 42 degrees.

1071:

knew of this as early as the 7th or 8th century BC.

6735:Cambridge : Cambridge University Press, 1995 6162:Clarke, Alexander Ross; James, Henry (1873-01-01). 4656: 3080:In 1860, the Russian Government at the instance of 2515:

Cassini's ellipsoid; Huygens' theoretical ellipsoid

2211:, the altered position of the Sun, and the various 1509:Diagram illustrating a method proposed and used by 778:In proposition 2 of the First Book of his treatise 473:is seen lower in the sky as one travels southward. 6812: 6297:Lebon, Ernest (1846-1922) Auteur du texte (1899). 5948:"Joining the observatories of Paris and Greenwich" 5875:Transactions of the American Philosophical Society 5746:"Joining the observatories of Paris and Greenwich" 5264: 4763: 4340: 4338: 4336: 3541: 3539: 2011:(560–636) taught in his widely read encyclopedia, 1864:by the 15th century, when the Egyptian astronomer 1740:to formulate trigonometric equations and used the 1049:. This argument was put forward by the geographer 6517:. Cham: Springer International Publishing: 3–18. 6513:. International Association of Geodesy Symposia. 5082: 4602: 4462:Astronomies and Cultures in Early Medieval Europe 2385:, an expedition captained by Portuguese explorer 2344:bullet, and the latter was the shape of a ball). 6856: 6788: 4955: 4758:L'Islam et son impulsion scientifique originelle 4557:Ohashi, Yukio (1999). Andersen, Johannes (ed.). 4231:: "History of Mathematical Astronomy in India", 3665:Pythagoras and the Pythagoreans: a brief history 3251:International Committee for Weights and Measures 3247:International Committee for Weights and Measures 2575:distance corresponding to one degree of latitude 2347: 2069: 1975:, made successive reductions in the size of the 1680:Arabic miles) was much more accurate than the 60 1631:Another estimate given by his astronomers was 56 942:(c. 190 BC), who lived in the city of 5945: 5743: 4650: 4333: 4117:(6). National Science Teachers Association: 10. 3536: 3493:Looking Down a Well: A Brief History of Geodesy 1843:The Determination of the Co-ordinates of Cities 1288:inspired some early Christian scholars such as 564:to the spherical body reportedly postulated by 5592:, Vol. 39, No. 1 (1976), pp. 106–127 (107–109) 5542: 5265:Isidore of Seville (1960). J. Fontaine (ed.). 5256: 5013:. Harvard University Press. pp. 216–217. 3973: 3971: 3969: 3967: 1931:(c. 1357) supports Eratosthenes' calculation. 6833: 6696:Rashed, Roshdi; Morelon, Régis, eds. (1996). 6695: 5848:"Tralles, Johann Georg - Deutsche Biographie" 5579:, No. 87. (May 1980), pp. 39–53 (42 & 49) 5104: 4960:, Walch Publishing, pp. 60 & 112–3, 4909: 4836: 4714:. History.mcs.st-andrews.ac.uk. November 2000 4167:, volume 6, number 1, page 11, note 47, 1996. 3531:The History and Practice of Ancient Astronomy 2886:International Union of Geodesy and Geophysics 2884:(IAG) one of the constituent sections of the 2872:formula which should be optimal not only for 2441:, scholars discussed Macrobius's view of the 1868:(d. 1469/1471) measured it as 7 degrees from 1690:Roman miles (89.7 km) given by Ptolemy. 411: 6810: 5812: 5147: 4760:, Tiers-Monde, 1982, vol. 23, n° 92, p. 789. 4522: 4520: 3243:International Bureau of Weights and Measures 3219:International Bureau of Weights and Measures 3148:brothers was used in Switzerland in 1865 by 2766:and other astronomical objects, notably the 2413:, in recognition of his feat, gave Elcano a 6679:A History of Ancient Mathematical Astronomy 6482: 6386: 6369:: CS1 maint: numeric names: authors list ( 6313:: CS1 maint: numeric names: authors list ( 6161: 6145:Appletons' Cyclopædia of American Biography 5931:: CS1 maint: numeric names: authors list ( 5410:Hildegard of Bingen, Liber divinorum operum 5152:, New York, Dover Publications, p. 168 4870:Columbus and the Conquest of the Impossible 4109:"When Our Round Earth Was First Measured". 3964: 3580: 3578: 3120:Gravimeter with variant of Repsold pendulum 3060:, named West Europe-Africa Meridian-arc by 2839:Landesamt für Vermessung und Geoinformation 710:relied on a spherical Earth to explain why 6673: 6640:. Ithaca, N.Y.: Cornell University Press. 4951: 4949: 4947: 4819:"The Round Earth and Christopher Columbus" 4788:"Al-Biruni and the Mathematical Geography" 4695: 4449:. Harvard University Press. pp. 63–4. 3545: 3297: 3141:Johann Gottlieb Friedrich von Bohnenberger 2939:The beginning of the U. S. coastal survey. 2623:which was founded in 1791, one year after 2458:calculated the value of the degree of the 1709:calculations based on the angle between a 1491:value of 40,075 km (24,901 mi). 1196:, oversized) and the "Aurea Chersonesus" ( 990:at different times: 252,000 stadia in his 749:like earth, water, air, fire, and aether. 418: 404: 385:Spatial Reference System Identifier (SRID) 380:International Terrestrial Reference System 6567: 6179: 5978: 5963: 5939: 5761: 5420:Olaf Pedersen, "In Quest of Sacrobosco", 4916:Teaching Mathematics and Its Applications 4905: 4903: 4850:"How Islamic inventors changed the world" 4517: 4483: 4459: 4419:The Geography of Strabo, in Eight Volumes 4253: 3634:"Who first realized the Earth was round?" 3584: 3525: 3523: 3521: 3245:was created under the supervision of the 3176:Three-dimensional model of the so-called 2967:The Scandinavian-Russian meridian arc or 1263:commentary on and translation of Plato's 686:The shadow of Earth on the Moon during a 6250: 6148:. Vol. III. 1900. pp. 111–112. 6016: 5076: 4732:Gongol, William J. (December 14, 2003). 4252:Adoption by China via European science: 3656: 3654: 3612: 3610: 3575: 3301: 3171: 3115: 3024: 2958: 2934: 2847: 2824: 2510: 2472:using wooden rods, a telescope (for his 2432: 2421:(in Latin, "You went around me first"). 2397:, passed through what is now called the 2073: 1986: 1982: 1504: 1418:The Indian astronomer and mathematician 1083: 1027: 835: 638: 612:(427–347 BC) travelled to southern 429: 6815:How Did We Find Out the Earth is Round? 6654: 5639: 5627: 5615: 5506: 5342: 5250:Referring to Isidore's five circles in 5212:"CHRISTOPHER COLUMBUS AND FAKE HISTORY" 5171: 5135: 5094:MacTutor History of Mathematics Archive 5027: 4981: 4944: 4379:, (New York: Springer-Verlag), p. 118. 4056: 3556: 3554: 2950:United States Coast and Geodetic Survey 2543:. The formula played a central role in 1852: 934: 481: 6857: 6796:. New York, US: Elsevier. p. 45. 6423: 6421: 6419: 6382: 6380: 6292: 6290: 6157: 6155: 6042: 6012: 6010: 6008: 6006: 6004: 6002: 5952:Notes and Records of the Royal Society 5845: 5783: 5781: 5750:Notes and Records of the Royal Society 5439:. Translated by Thorndike, Lynn. 1949. 5361: 5352:. New York: Praeger Publishers. p. 87. 5209: 4958:Geometry Activities from Many Cultures 4900: 4731: 4583: 4556: 4416: 4369: 4296: 3927: 3631: 3518: 3101:as their standard of reference in the 2952:in 1878 — were referred is the French 2778:and Cayenne in order to determine the 2678:had commissioned an expedition led by 2596:(near the Earth's northern pole). The 2577:will grow toward the poles, as can be 2454:In 1505 the cosmographer and explorer 2401:, crossed the Pacific, and arrived in 2218: 1215:lists, and captions for the maps. His 1174:at the most western land he knew, the 856:Eratosthenes' method to calculate the 6769:Archive for History of Exact Sciences 6655:Needham, Joseph; Wang, Ling (1995) . 6633: 6545: 6508: 6296: 6276: 5710: 5502: 5500: 5476: 5449: 4776:, (Aldershot (U.K.): Variorum), 1993. 4563:. Springer Science. pp. 719–21. 4541: 4526: 4444: 4194: 4063:Archive for History of Exact Sciences 4003: 3977: 3701: 3651: 3616: 3607: 3560: 3365:In 1810, after reading Gauss's work, 3333:and supported his appointment to the 2913:out into another article titled 2892:Prime meridian and standard of length 2021: 2002: 1592:to measure the distance from Tadmur ( 6437: 5543:Martzloff, Jean-Claude (1993–1994). 5422:Journal for the History of Astronomy 5006: 4786:Sparavigna, Amelia Carolina (2014), 4586:Indian Journal of History of Science 3551: 3241:was signed in 1875 in Paris and the 3043:International Association of Geodesy 2971:, named after the German astronomer 2916:Meridian arc of Delambre and Méchain 2895: 2882:International Association of Geodesy 2741: 2053: 465:Many early conceptions of the Earth 6416: 6377: 6287: 6152: 5999: 5778: 5688:, (Leiden: Brill, 2007), pp. 62–63. 5669: 4804:Gharā'ib al-funūn wa-mulah al-`uyūn 4560:Highlights of Astronomy, Volume 11B 4436: 3688:Stanford Encyclopedia of Philosophy 3676: 3285:as prime meridian in the hope that 1485:varies considerably between sources 1327:Such widely read encyclopedists as 1079: 1032:When a ship is at the horizon, its 708:Aristotle's theory of natural place 390:Universal Transverse Mercator (UTM) 352:European Terrestrial Ref. Sys. 1989 13: 6782: 6637:Early Greek Astronomy to Aristotle 6204:"e-expo: Ferdinand Rudolf Hassler" 6139:"Hassler, Ferdinand Rudolph" 6061:"A Note on the History of the IAG" 5497: 4696:Cunningham, Sir Alexander (1871). 4657:Amartya Kumar Dutta (March 2006). 4628:Dictionary of Scientific Biography 4233:Dictionary of Scientific Biography 4045:De nuptiis Philologiae et Mercurii 3533:, page 47, Oxford University Press 3273:International Geodetic Association 3265:International Geodetic Association 3064:, was undertaken in France and in 2973:Friedrich Georg Wilhelm von Struve 2888:(IUGG) which was founded in 1919. 2876:but also for the whole world. The 2738:of the Toise of Peru (see below). 2547:and became known as the second of 2312:, this idea was criticized by the 1880: 1875: 1280:Theological doubt informed by the 673:(45,000 miles or 74,000 km). 262:Ordnance Survey Great Britain 1936 228:Discrete Global Grid and Geocoding 119:Horizontal position representation 14: 6881: 6749:. Burlington, VT: Ashgate, 2004 5482:God and Reason in the Middle Ages 4774:Astronomy in the Service of Islam 4447:A Source Book in Medieval Science 4136:Strabo 2.2.2, 2.5.24; D.Rawlins, 3794: 3779: 3762: 3036:declared in 1836 in front of the 2746:A discovery made in 1672-1673 by 2383:first circumnavigation in history 1849:, or Muslim direction of prayer. 1569:, or Muslim direction of prayer. 1238: 506:, particularly those between the 476: 6600: 6539: 6502: 6476: 6457: 6431: 6345: 6321: 6270: 6244: 6220: 6196: 6130: 6106: 6077: 6053: 6036: 5972: 5907: 5882: 5865: 5839: 5806: 5737: 5704: 5691: 5678: 5663: 5654: 5645: 5633: 4872:, pp. 20–1, Phoenix Press, 1974. 3811:Mathematics: A Practical Odyssey 3809:David Johnson and Thomas Mowry, 2900: 2880:was an early predecessor of the 1952:. A list of more than a hundred 1784:corrects geographical data from 1494: 1483:yojanas. The length of a yojana 1360: 996:and 180,000 stadia in his later 926:1,700 years after Eratosthenes, 178:Global Nav. Sat. Systems (GNSSs) 28: 5621: 5609: 5470: 5443: 5427: 5414: 5403: 5355: 5329: 5316: 5303: 5290: 5273: 5259:Encyclopedist of the Flat Earth 5244: 5231: 5218: 5203: 5174:Journal of Near Eastern Studies 5165: 5156: 5141: 5129: 5060:"This Month in Physics History" 5052: 5010:The Lost Art of Finding Our Way 4975: 4875: 4862: 4842: 4825: 4811: 4797: 4779: 4747: 4725: 4704: 4689: 4633: 4596: 4577: 4550: 4508: 4477: 4453: 4430: 4410: 4390: 4355: 4254:Martzloff, Jean-Claude (1993). 4205:10.1163/1573-3912_ei3_COM_22652 4142: 4130: 4121: 4102: 4089: 4050: 4037: 4024: 3997: 3921: 3893: 3881: 3869: 3857: 3832: 3820: 3803: 3788: 3773: 3751: 3738: 3695: 3269:Carlos Ibáñez e Ibáñez de Ibero 3255:Carlos Ibáñez e Ibáñez de Ibero 3194:Carlos Ibáñez e Ibáñez de Ibero 3050:Carlos Ibáñez e Ibáñez de Ibero 3029:West Europe-Africa Meridian Arc 2820: 2604:was sent to what is modern-day 1820: 1799: 1436:is divided into four sections: 1247:as a matter of course, in both 1005: 787: 741:than the geocentric model, and 342:N. American Vertical Datum 1988 6626: 4460:McCluskey, Stephen C. (1998), 3670: 3625: 3483: 2488:later continued Picard's arc ( 2447:. One of them, the Irish monk 1860:and geographers were aware of 1662: 903:the Sun was directly overhead; 372:Internet link to a point 2010 302:Geodetic Reference System 1980 220:Quasi-Zenith Sat. Sys. (QZSS) 1: 6718: 6483:Hirsch, Adolphe (1873–1876). 5813:Rickenbacher, Martin (2006). 5210:Korson, Gerald (2017-09-01). 3757:written as from the mouth of 3569:American Geographical Society 3472:Paris meridian § History 3327:Humboldt University of Berlin 3249:. The first president of the 2878:Mitteleuropäische Gradmessung 2858:Mitteleuropäische Gradmessung 2856:In the late 19th century the 2680:Jean Baptiste Joseph Delambre 2348:Circumnavigation of the globe 2246: 2147:thought that Earth was flat. 2070:High and late medieval Europe 1771: 1017:. Many Roman authors such as 965: 825:is so great that the rays of 761: 752: 643:Round Earth umbra during the 362:Chinese obfuscated datum 2002 6438:Faye, Hervé (January 1880). 6332:publications.iass-potsdam.de 6277:Migne, Jacques-Paul (1853). 6023:"Earth, Figure of the" 4592:(3): 185–88, 206–19, 240–45. 4546:. Columbia University Press. 3989:. Berlin: Springer. p. 3561:Friis, Herman Ralph (1967). 2786:by more than a line (about ⁄ 2756:Academy of Sciences of Paris 2133:commentators on Aristotle's 1956:and vernacular writers from 1572: 1413: 1211:, he provided the necessary 1184:indicated the countries of " 1124:He compiled an eight-volume 1067:as indicating that the poet 848:and on the same meridian as 634: 539:c. 610–595 BC. In 312:Geographic point coord. 1983 7: 5324:Bede: The Reckoning of Time 5182:University of Chicago Press 3930:American Journal of Physics 3425: 3380:The publication in 1838 of 3281:had proposed to select the 2579:demonstrated mathematically 1889:), and via authors such as 1751:Important contributions to 1645: 1612:Al-Ma'mun's arc measurement 1057:since at least the time of 819:On the Measure of the Earth 730:around a stationary Earth. 543:, written 431–425 BC, 272:Systema Koordinat 1942 goda 10: 6886: 6792:; Krakiwsky, E.J. (1986). 5852:www.deutsche-biographie.de 5348:Russell, Jeffrey B. 1991. 5337:On the Seasons of the Year 5007:Huth, John Edward (2013). 4881:Lenn Evan Goodman (1992), 4868:Felipe Fernández-Armesto, 4603:E. At. Schwanbeck (1877). 4227:Direct adoption by India: 3323:Berlin Academy of Sciences 3253:was the Spanish geodesist 3038:French Academy of Sciences 2990:by the French astronomers 2803:Great Trigonometric Survey 2676:French Academy of Sciences 2586:French Academy of Sciences 2570:. On an oblate Earth, the 2559:(wider than tall), with a 2351: 2097:Medieval Islamic astronomy 1498: 1448:("reckoning of time") and 1364: 1107:(90–168 AD) lived in 444:A brief history of geodesy 332:World Geodetic System 1984 6283:(in French). p. 419. 5701:(1965), ed. 61-64, p. 350 5674:. Ratna Sagar. p. 7. 5507:Needham, Joseph (1995) . 5226:Altnordische Kosmographie 4956:Beatrice Lumpkin (1997), 4837:Rashed & Morelon 1996 4311:10.1017/S0041977X00052137 4272:10.1163/26669323-01101005 3386:Gradmessung in Ostpreußen 3321:was made a member of the 3002:" (Basis for the decimal 2945:Ferdinand Rudolph Hassler 2645:measured the base of the 2643:Ferdinand Rudolph Hassler 1697: 1198:Southeast Asian peninsula 1061:, citing a line from the 1040: 645:August 2008 lunar eclipse 322:North American Datum 1983 292:South American Datum 1969 6251:Puissant, Louis (1836). 5436:The Sphere of Sacrobosco 5350:Inventing the Flat Earth 5099:University of St Andrews 4057:Rawlins, Dennis (1983). 3985:The Forgotten Revolution 3477: 3432:Bedford Level experiment 3404:Friedrich Robert Helmert 3382:Friedrich Wilhelm Bessel 3335:University of Königsberg 3331:Friedrich Wilhelm Bessel 2797:Bouguer noticed, as did 2156:Honorius Augustodunensis 1736:Biruni also made use of 1584:commissioned a group of 1298:Athanasius of Alexandria 1015:Hellenistic civilization 604: 183:Global Pos. System (GPS) 150:Spatial reference system 6847:Encyclopædia Britannica 6029:Encyclopædia Britannica 5789:"Tralles, Johann Georg" 5618:, pp. 220, 498–499 5257:Ernest Brehaut (1912). 5228:, Berlin, 1990, p. 102. 4924:Oxford University Press 4712:"Aryabhata I biography" 3902:The works of Archimedes 3587:Libyae lustrare extrema 3298:Geodesy and mathematics 3278:Europäische Gradmessung 3260:Europäische Gradmessung 3226:Europäische Gradmessung 3210:Europäische Gradmessung 3178:"Potsdamer Kartoffel" ( 3103:French Geodesic Mission 3082:Otto Wilhelm von Sturve 3068:under the direction of 2815:undulation of the geoid 2764:astronomical refraction 2590:Pierre Louis Maupertuis 2549:Newton's laws of motion 2425:circles in Europe. The 2419:Primus circumdedisti me 2276:, ultimately spread to 2231:and the development of 1966:University of Stuttgart 1866:'Abd al-'Aziz al-Wafa'i 1837:; in the 11th century, 618:Pythagorean mathematics 6870:History of measurement 6763:, v.28, 255–268, 1985) 6402:10.1098/rstl.1867.0010 6181:10.1098/rstl.1873.0014 5965:10.1098/rsnr.2008.0029 5846:Biographie, Deutsche. 5763:10.1098/rsnr.2008.0029 5711:Paul., Murdin (2009). 5322:Faith Wallis, trans., 5162:See Lyons, 2009, p. 85 4910:Behnaz Savizi (2007). 4833:Mathematical Geography 4445:Grant, Edward (1974). 4197:Encyclopaedia of Islam 4152:Geographical Directory 4150:Investigations of the 3632:Hannam, James (2023). 3457:History of hydrography 3452:History of cartography 3314: 3231:Charles Sanders Peirce 3189: 3163:Charles Sanders Peirce 3121: 3030: 2964: 2940: 2853: 2845: 2714:, assuming an Earth's 2516: 2456:Duarte Pacheco Pereira 2306: 2269: 2192:Bertold von Regensburg 2141:Treatise on the Sphere 2118:Johannes de Sacrobosco 2112:Liber Divinorum Operum 2088: 1999: 1993:Liber Divinorum Operum 1916:. It is probable that 1845:. This determined the 1835:spherical trigonometry 1769: 1731:atmospheric refraction 1563:. This determined the 1557:spherical trigonometry 1514: 1397:filtered eastwards to 1274:On Sizes and Distances 1150:was measured from the 1101: 1037: 1034:lower part is obscured 981:atmospheric refraction 853: 797:Hellenistic astronomer 647: 620:. When he returned to 447: 6811:Isaac Asimov (1972). 6794:Geodesy: the Concepts 6771:, v.26, 211–219, 1982 6578:10.1007/s001900050086 6043:Richer, Jean (1679). 5148:Ho Peng Yoke (1985), 4932:10.1093/teamat/hrl009 4542:Stahl, W. H. (1952). 3845:oceanservice.noaa.gov 3591:University of Seville 3529:James Evans, (1998), 3462:History of navigation 3371:central limit theorem 3347:Adrien-Marie Legendre 3305: 3205:Alexander Ross Clarke 3175: 3119: 3062:Alexander Ross Clarke 3028: 2962: 2938: 2851: 2828: 2712:passing through Paris 2553:theory of gravitation 2514: 2496:and southward to the 2482:Gian Domenico Cassini 2433:European calculations 2427:Transglobe Expedition 2407:Juan Sebastián Elcano 2352:Further information: 2301: 2264: 2223:The invention of the 2077: 2040:The Reckoning of Time 2036:The Reckoning of Time 1990: 1983:Early Medieval Europe 1831:Muslim mathematicians 1749: 1553:Muslim mathematicians 1522:Hellenistic astronomy 1508: 1395:Hellenistic astronomy 1365:Further information: 1318:Cosmas Indicopleustes 1284:model implied in the 1087: 1031: 858:Earth's circumference 839: 795:(276–194 BC), a 642: 502:" around the eastern 442: 78:Geographical distance 6634:Dicks, D.R. (1970). 6523:10.1007/1345_2015_42 6446:. pp. 1463–1466 5558:: 69. Archived from 5339:, Peter Baker, trans 5287:, 71(1980): 268–277. 5085:Robertson, Edmund F. 3593:. pp. 189–194. 3467:History of surveying 3442:History of the metre 3406:in his famous books 3375:Gauss–Markov theorem 3369:, after proving the 3367:Pierre-Simon Laplace 3342:Carl Friedrich Gauss 3319:Johann Georg Tralles 3143:, its inventor, nor 2963:Struve Geodetic Arc. 2801:in the 19th century 2726:which was 5 130 740 2631:Johann Georg Tralles 2474:angular measurements 2123:Tractatus de Sphaera 2108:Hildegard von Bingen 1918:Christopher Columbus 1862:magnetic declination 1853:Magnetic declination 1692:Christopher Columbus 1345:southern hemispheres 960:Aristarchus of Samos 954:, influenced by the 940:Seleucus of Seleucia 935:Seleucus of Seleucia 928:Christopher Columbus 482:Initial developments 460:Age of Enlightenment 252:Sea Level Datum 1929 104:Geodetic coordinates 6778:v.18, 253–269, 1974 6761:Vistas in Astronomy 6675:Neugebauer, Otto E. 6560:1997JGeod..71..176S 5993:1986CRASG...3..261L 5827:10.5169/seals-16152 5699:Revista de História 5684:Bruce S. Eastwood, 5642:, pp. 227, 499 5424:, 16(1985): 175–221 5335:Ælfric of Eynsham, 5267:Traité de la Nature 5083:O'Connor, John J.; 4831:Edward S. Kennedy, 4754:Muhammad Hamidullah 4148:D.Rawlins (2007). " 4111:The Science Teacher 4043:Martianus Capella, 3942:2016AmJPh..84...61R 3503:on 21 February 2014 3447:History of cadastre 3437:Figure of the Earth 3359:probability density 3351:normal distribution 3137:reversible pendulum 2969:Struve Geodetic Arc 2833:plates for maps of 2617:Anglo-French Survey 2610:reference ellipsoid 2545:classical mechanics 2480:(for computation). 2393:. They crossed the 2282:Jesuit missionaries 2219:Early modern period 2209:southern hemisphere 2145:medieval university 1997:Hildegard of Bingen 1925:Sir John Mandeville 1744:to measure angles. 1391:Hellenistic culture 1385:Greek ethnographer 1314:Syriac Christianity 1158:(the length of the 956:heliocentric theory 823:distance to the Sun 521:sailors. The first 282:European Datum 1950 240:Standards (history) 140:Reference ellipsoid 88:Figure of the Earth 6548:Journal of Geodesy 6491:. pp. 255–256 6489:www.e-periodica.ch 6259:. pp. 428–433 6208:www.f-r-hassler.ch 5896:. pp. 148–154 5819:www.e-periodica.ch 4839:, pp. 185–201 4675:10.1007/BF02835968 4532:Commentary on the 4489:Klibansky, Raymond 4344:Krüger, Reinhard: 4163:2008-03-06 at the 4097:Naturalis Historia 4075:10.1007/BF00348500 3667:, page 53. Hackett 3315: 3311:Traité de géodésie 3283:Greenwich meridian 3190: 3133:Clairaut's theorem 3122: 3058:Paris meridian arc 3031: 2996:Jean-Baptiste Biot 2965: 2941: 2854: 2846: 2780:Earth-Sun distance 2637:, then the entire 2533:Christiaan Huygens 2529:Christiaan Huygens 2517: 2492:arc) northward to 2411:Charles I of Spain 2399:Strait of Magellan 2387:Ferdinand Magellan 2168:Middle High German 2089: 2022:Bede the Venerable 2009:Isidore of Seville 2003:Isidore of Seville 2000: 1942:is a 12th-century 1891:Isidore of Seville 1858:Muslim astronomers 1586:Muslim astronomers 1515: 1371:Indian mathematics 1310:Augustine of Hippo 1259:'s fourth-century 1253:Early Christianity 1102: 1038: 854: 781:On Floating Bodies 747:classical elements 735:heliocentric model 648: 594:Pythagorean school 492:Otto E. Neugebauer 467:held it to be flat 448: 160:Vertical positions 6731:J. L. Greenberg: 6709:978-0-415-12412-6 6688:978-3-540-06995-9 6647:978-0-8014-0561-7 6532:978-3-319-30895-1 6303:pp. 168–171. 5921:pp. 415–433. 5672:ICSE Geography IX 5491:978-0-521-00337-7 5464:978-0-521-56509-7 5363:Hewsen, Robert H. 5255:the flat earth." 4993:978-0-226-31635-2 4858:. March 11, 2006. 4570:978-0-7923-5556-4 4538:. pp. 18–24. 4471:978-0-521-77852-7 4214:978-90-04-17852-6 4018:978-0-521-55695-8 3950:10.1119/1.4934660 3396:personal equation 3180:Potato of Potsdam 2933: 2932: 2928: 2742:Asia and Americas 2663:Helvetic Republic 2537:centrifugal force 2374:'s voyage to the 2295:accompanied by a 2274:Western astronomy 2256:Chinese Cosmology 2139:and Sacrobosco's 2106:Saint Hildegard ( 2101:Pope Sylvester II 2064:Anania Shirakatsi 2054:Anania Shirakatsi 2044:Ælfric of Eynsham 1977:Mediterranean Sea 1903:medieval learning 1794:Mediterranean Sea 1703:Abu Rayhan Biruni 1518:Islamic astronomy 1444:("mathematics"), 1333:Martianus Capella 1302:Basil of Caesarea 1098:Nicolaus Germanus 1055:Mediterranean Sea 895:, saying that at 805:Alexandria, Egypt 799:from what is now 728:celestial spheres 504:Mediterranean Sea 500:Greek settlements 440: 428: 427: 376: 375: 155:Spatial relations 145:Satellite geodesy 100: 6877: 6851: 6839: 6830: 6818: 6807: 6713: 6692: 6670: 6651: 6621: 6620: 6618: 6617: 6604: 6598: 6597: 6571: 6543: 6537: 6536: 6506: 6500: 6499: 6497: 6496: 6480: 6474: 6473: 6471: 6461: 6455: 6454: 6452: 6451: 6435: 6429: 6425: 6414: 6413: 6384: 6375: 6374: 6368: 6360: 6349: 6343: 6342: 6340: 6339: 6334:. pp. 56–58 6325: 6319: 6318: 6312: 6304: 6294: 6285: 6284: 6274: 6268: 6267: 6265: 6264: 6248: 6242: 6241: 6239: 6238: 6224: 6218: 6217: 6215: 6214: 6200: 6194: 6193: 6183: 6159: 6150: 6149: 6141: 6134: 6128: 6127: 6125: 6124: 6110: 6104: 6103: 6101: 6100: 6091:. Archived from 6081: 6075: 6074: 6072: 6071: 6057: 6051: 6050: 6040: 6034: 6033: 6025: 6014: 5997: 5996: 5976: 5970: 5969: 5967: 5943: 5937: 5936: 5930: 5922: 5911: 5905: 5904: 5902: 5901: 5894:Internet Archive 5886: 5880: 5879: 5869: 5863: 5862: 5860: 5859: 5843: 5837: 5836: 5834: 5833: 5810: 5804: 5803: 5801: 5800: 5785: 5776: 5775: 5765: 5741: 5735: 5734: 5708: 5702: 5695: 5689: 5682: 5676: 5675: 5667: 5661: 5658: 5652: 5649: 5643: 5637: 5631: 5625: 5619: 5613: 5607: 5604: 5593: 5586: 5580: 5577:Past and Present 5573: 5567: 5566: 5564: 5549: 5540: 5531: 5530: 5504: 5495: 5494: 5474: 5468: 5467: 5447: 5441: 5440: 5431: 5425: 5418: 5412: 5407: 5401: 5400: 5359: 5353: 5346: 5340: 5333: 5327: 5320: 5314: 5307: 5301: 5294: 5288: 5282: 5277: 5271: 5270: 5262: 5248: 5242: 5235: 5229: 5222: 5216: 5215: 5207: 5201: 5200: 5169: 5163: 5160: 5154: 5153: 5145: 5139: 5133: 5127: 5126: 5124: 5123: 5114:. Archived from 5108: 5102: 5101: 5080: 5074: 5073: 5071: 5070: 5056: 5050: 5040: 5031: 5025: 5024: 5004: 4998: 4997: 4979: 4973: 4970: 4953: 4942: 4941: 4939: 4938: 4907: 4898: 4879: 4873: 4866: 4860: 4859: 4846: 4840: 4829: 4823: 4822: 4815: 4809: 4801: 4795: 4794: 4783: 4777: 4770: 4761: 4751: 4745: 4744: 4742: 4741: 4729: 4723: 4722: 4720: 4719: 4708: 4702: 4701: 4693: 4687: 4686: 4654: 4648: 4637: 4631: 4624: 4615: 4614: 4600: 4594: 4593: 4581: 4575: 4574: 4554: 4548: 4547: 4540:, translated in 4539: 4524: 4515: 4512: 4506: 4505: 4481: 4475: 4474: 4457: 4451: 4450: 4442: 4434: 4428: 4425:available online 4422: 4417:Strabo (1960) . 4414: 4408: 4405:available online 4394: 4388: 4373: 4367: 4359: 4353: 4350:Wechselwirkungen 4342: 4331: 4330: 4294: 4292: 4291: 4282:. Archived from 4250: 4244: 4225: 4219: 4218: 4192: 4181: 4174: 4168: 4146: 4140: 4134: 4128: 4125: 4119: 4118: 4106: 4100: 4093: 4087: 4086: 4054: 4048: 4041: 4035: 4028: 4022: 4021: 4001: 3995: 3994: 3988: 3975: 3962: 3961: 3925: 3919: 3918: 3916: 3914: 3905:. Translated by 3897: 3891: 3885: 3879: 3873: 3867: 3861: 3855: 3854: 3852: 3851: 3836: 3830: 3824: 3818: 3815:Cengage Learning 3807: 3801: 3800: 3792: 3786: 3785: 3777: 3771: 3770: 3755: 3749: 3742: 3736: 3735: 3699: 3693: 3692: 3683:Zalta, Edward N. 3674: 3668: 3658: 3649: 3648: 3646: 3644: 3638:Antigone Journal 3629: 3623: 3614: 3605: 3604: 3582: 3573: 3572: 3558: 3549: 3548:, pp. 575–6 3543: 3534: 3527: 3516: 3512: 3510: 3508: 3502: 3487: 3239:Metre Convention 3150:Émile Plantamour 3125:Friedrich Bessel 3111:Antonio de Ulloa 3070:François Perrier 3054:François Perrier 2988:Balearic Islands 2924: 2904: 2903: 2896: 2635:Bernese Oberland 2600:(1735–44) under 2541:De vi centrifuga 2521:prolate spheroid 2354:Age of Discovery 2310:celestial sphere 2241:arc measurements 2233:logarithm tables 2093:High Middle Ages 2058:The 7th-century 1936:Christianisation 1689: 1688: 1684: 1679: 1678: 1674: 1640: 1639: 1635: 1627: 1626: 1622: 1546:geocentric model 1482: 1481: 1477: 1454:celestial sphere 1367:Indian astronomy 1105:Claudius Ptolemy 1080:Claudius Ptolemy 988:Claudius Ptolemy 893:Tropic of Cancer 846:Tropic of Cancer 829:are practically 774: 772: 766: 763: 724:geocentric model 523:circumnavigation 441: 420: 413: 406: 244: 243: 223: 215: 207: 199: 191: 131: 90: 32: 18: 17: 6885: 6884: 6880: 6879: 6878: 6876: 6875: 6874: 6855: 6854: 6837:"Geodesy" 6827: 6804: 6785: 6783:Further reading 6721: 6716: 6710: 6689: 6667: 6648: 6629: 6624: 6615: 6613: 6611:www.math.berlin 6606: 6605: 6601: 6569:10.1.1.492.3967 6544: 6540: 6533: 6507: 6503: 6494: 6492: 6481: 6477: 6469: 6463: 6462: 6458: 6449: 6447: 6436: 6432: 6426: 6417: 6385: 6378: 6362: 6361: 6350: 6346: 6337: 6335: 6327: 6326: 6322: 6306: 6305: 6295: 6288: 6275: 6271: 6262: 6260: 6249: 6245: 6236: 6234: 6226: 6225: 6221: 6212: 6210: 6202: 6201: 6197: 6160: 6153: 6136: 6135: 6131: 6122: 6120: 6112: 6111: 6107: 6098: 6096: 6083: 6082: 6078: 6069: 6067: 6059: 6058: 6054: 6049:pp. 3, 66. 6041: 6037: 6015: 6000: 5977: 5973: 5944: 5940: 5924: 5923: 5912: 5908: 5899: 5897: 5888: 5887: 5883: 5870: 5866: 5857: 5855: 5844: 5840: 5831: 5829: 5811: 5807: 5798: 5796: 5787: 5786: 5779: 5742: 5738: 5723: 5709: 5705: 5696: 5692: 5683: 5679: 5668: 5664: 5659: 5655: 5650: 5646: 5638: 5634: 5626: 5622: 5614: 5610: 5605: 5596: 5587: 5583: 5574: 5570: 5562: 5552:Chinese Science 5547: 5541: 5534: 5519: 5505: 5498: 5492: 5475: 5471: 5465: 5448: 5444: 5433: 5432: 5428: 5419: 5415: 5408: 5404: 5360: 5356: 5347: 5343: 5334: 5330: 5321: 5317: 5308: 5304: 5295: 5291: 5280: 5278: 5274: 5252:De Natura Rerum 5249: 5245: 5236: 5232: 5223: 5219: 5208: 5204: 5170: 5166: 5161: 5157: 5146: 5142: 5134: 5130: 5121: 5119: 5110: 5109: 5105: 5081: 5077: 5068: 5066: 5058: 5057: 5053: 5038: 5032: 5028: 5021: 5005: 5001: 4994: 4980: 4976: 4968: 4954: 4945: 4936: 4934: 4908: 4901: 4880: 4876: 4867: 4863: 4855:The Independent 4848: 4847: 4843: 4835:, pp=187–8, in 4830: 4826: 4817: 4816: 4812: 4802: 4798: 4784: 4780: 4772:David A. King, 4771: 4764: 4752: 4748: 4739: 4737: 4730: 4726: 4717: 4715: 4710: 4709: 4705: 4694: 4690: 4655: 4651: 4638: 4634: 4625: 4618: 4601: 4597: 4582: 4578: 4571: 4555: 4551: 4534:Dream of Scipio 4525: 4518: 4513: 4509: 4503: 4482: 4478: 4472: 4458: 4454: 4441:. pp. I.4. 4435: 4431: 4415: 4411: 4403:translation is 4401:Samuel Butler's 4395: 4391: 4377:Early Astronomy 4375:Hugh Thurston, 4374: 4370: 4363:Natural History 4360: 4356: 4343: 4334: 4289: 4287: 4260:Chinese Science 4251: 4247: 4226: 4222: 4215: 4193: 4184: 4175: 4171: 4165:Wayback Machine 4147: 4143: 4135: 4131: 4126: 4122: 4108: 4107: 4103: 4094: 4090: 4055: 4051: 4042: 4038: 4029: 4025: 4019: 4005:Lloyd, G. E. R. 4002: 3998: 3976: 3965: 3926: 3922: 3912: 3910: 3899: 3898: 3894: 3886: 3882: 3878:, 297b31–298a10 3874: 3870: 3862: 3858: 3849: 3847: 3837: 3833: 3825: 3821: 3808: 3804: 3793: 3789: 3784:. p. 110b. 3778: 3774: 3756: 3752: 3748:, Book II 298 B 3743: 3739: 3700: 3696: 3677:Huffman, Carl. 3675: 3671: 3661:Charles H. Kahn 3659: 3652: 3642: 3640: 3630: 3626: 3615: 3608: 3601: 3583: 3576: 3559: 3552: 3546:Neugebauer 1975 3544: 3537: 3528: 3519: 3506: 3504: 3500: 3489: 3488: 3484: 3480: 3428: 3355:arithmetic mean 3300: 3099:De La Condamine 3087:Ordnance Survey 2929: 2905: 2901: 2894: 2823: 2789: 2744: 2692:Montjuïc castle 2621:Ordnance Survey 2557:oblate spheroid 2486:Jacques Cassini 2439:Carolingian era 2435: 2417:with the motto 2362:exploration of 2356: 2350: 2249: 2221: 2072: 2056: 2024: 2005: 1985: 1946:translation of 1883: 1881:Greek influence 1878: 1876:Medieval Europe 1855: 1823: 1802: 1774: 1720:Pind Dadan Khan 1700: 1686: 1682: 1681: 1676: 1672: 1671: 1665: 1648: 1637: 1633: 1632: 1624: 1620: 1619: 1577:Around 830 CE, 1575: 1503: 1497: 1479: 1475: 1474: 1416: 1373: 1363: 1354:Dream of Scipio 1322:medieval period 1294:John Chrysostom 1241: 1188:" and "Sinae" ( 1095: 1082: 1043: 1008: 968: 937: 790: 770: 768: 764: 755: 722:go up. In this 637: 607: 484: 479: 450:The history of 430: 424: 395: 394: 241: 233: 232: 221: 213: 205: 197: 189: 173: 165: 164: 123: 73: 65: 64: 40: 12: 11: 5: 6883: 6873: 6872: 6867: 6853: 6852: 6842:Chisholm, Hugh 6831: 6826:978-0802761217 6825: 6808: 6802: 6784: 6781: 6780: 6779: 6772: 6767:Experiment?", 6764: 6757: 6743: 6729: 6720: 6717: 6715: 6714: 6708: 6693: 6687: 6681:. Birkhäuser. 6671: 6665: 6652: 6646: 6630: 6628: 6625: 6623: 6622: 6599: 6554:(3): 176–188. 6538: 6531: 6501: 6475: 6456: 6430: 6415: 6376: 6344: 6320: 6286: 6269: 6243: 6219: 6195: 6151: 6129: 6105: 6076: 6052: 6035: 6020:, ed. (1911). 6018:Chisholm, Hugh 5998: 5971: 5958:(4): 355–372. 5938: 5906: 5881: 5864: 5838: 5805: 5793:hls-dhs-dss.ch 5777: 5756:(4): 355–372. 5736: 5721: 5703: 5690: 5677: 5662: 5653: 5644: 5632: 5620: 5608: 5594: 5581: 5568: 5565:on 2009-03-05. 5532: 5517: 5496: 5490: 5469: 5463: 5442: 5426: 5413: 5402: 5381:10.1086/350333 5354: 5341: 5328: 5315: 5302: 5289: 5272: 5243: 5230: 5224:Rudolf Simek, 5217: 5202: 5190:10.1086/373112 5164: 5155: 5140: 5128: 5103: 5075: 5051: 5034:Jim Al-Khalili 5026: 5019: 4999: 4992: 4974: 4966: 4943: 4899: 4874: 4861: 4841: 4824: 4810: 4796: 4778: 4762: 4746: 4724: 4703: 4688: 4649: 4632: 4616: 4595: 4576: 4569: 4549: 4536:, V.9–VI.7, XX 4516: 4507: 4501: 4476: 4470: 4452: 4429: 4409: 4389: 4368: 4354: 4332: 4305:(1): 106–127. 4245: 4220: 4213: 4182: 4169: 4141: 4129: 4127:Cleomedes 1.10 4120: 4101: 4088: 4069:(3): 211–219. 4049: 4036: 4023: 4017: 3996: 3963: 3920: 3892: 3880: 3868: 3856: 3831: 3819: 3802: 3787: 3772: 3769:. p. 108. 3750: 3746:On the Heavens 3737: 3716:10.1086/368583 3694: 3669: 3650: 3624: 3606: 3599: 3574: 3550: 3535: 3517: 3481: 3479: 3476: 3475: 3474: 3469: 3464: 3459: 3454: 3449: 3444: 3439: 3434: 3427: 3424: 3307:Louis Puissant 3299: 3296: 3159:Adolphe Hirsch 3034:Louis Puissant 2992:François Arago 2931: 2930: 2908: 2906: 2899: 2893: 2890: 2822: 2819: 2799:George Everest 2787: 2743: 2740: 2704:Paris Panthéon 2684:Pierre Méchain 2639:Canton of Bern 2602:Pierre Bouguer 2598:second mission 2498:Spanish border 2490:Paris meridian 2434: 2431: 2395:Atlantic Ocean 2349: 2346: 2324:mathematician 2252:Joseph Needham 2248: 2245: 2235:allowed exact 2220: 2217: 2160:Middle English 2136:On the Heavens 2087:, around 1400) 2071: 2068: 2055: 2052: 2023: 2020: 2004: 2001: 1984: 1981: 1958:Late Antiquity 1895:Venerable Bede 1882: 1879: 1877: 1874: 1854: 1851: 1822: 1819: 1801: 1798: 1773: 1770: 1699: 1696: 1664: 1661: 1647: 1644: 1574: 1571: 1499:Main article: 1496: 1493: 1467: 1466: 1415: 1412: 1362: 1359: 1245:Late Antiquity 1240: 1239:Late Antiquity 1237: 1231:and deep into 1221:Atlantic Ocean 1176:Canary Islands 1166:). He put the 1156:degrees of arc 1081: 1078: 1042: 1039: 1007: 1004: 967: 964: 936: 933: 908: 907: 904: 899:on the summer 889: 886:mensores regii 789: 786: 754: 751: 692: 691: 684: 681: 636: 633: 606: 603: 483: 480: 478: 477:Hellenic world 475: 426: 425: 423: 422: 415: 408: 400: 397: 396: 393: 392: 387: 382: 374: 373: 370: 364: 363: 360: 354: 353: 350: 344: 343: 340: 334: 333: 330: 324: 323: 320: 314: 313: 310: 304: 303: 300: 294: 293: 290: 284: 283: 280: 274: 273: 270: 264: 263: 260: 254: 253: 250: 242: 239: 238: 235: 234: 231: 230: 225: 217: 209: 201: 193: 185: 180: 174: 171: 170: 167: 166: 163: 162: 157: 152: 147: 142: 137: 135:Map projection 132: 121: 116: 111: 109:Geodetic datum 106: 101: 85: 80: 74: 71: 70: 67: 66: 63: 62: 57: 52: 47: 41: 38: 37: 34: 33: 25: 24: 9: 6: 4: 3: 2: 6882: 6871: 6868: 6866: 6863: 6862: 6860: 6849: 6848: 6843: 6838: 6832: 6828: 6822: 6817: 6816: 6809: 6805: 6799: 6795: 6791: 6787: 6786: 6777: 6773: 6770: 6765: 6762: 6758: 6756: 6755:0-7546-5020-0 6752: 6748: 6745:M .R. Hoare: 6744: 6742: 6741:0-521-38541-5 6738: 6734: 6730: 6727: 6723: 6722: 6711: 6705: 6702:. CRC Press. 6701: 6700: 6694: 6690: 6684: 6680: 6676: 6672: 6668: 6666:0-521-05801-5 6662: 6658: 6653: 6649: 6643: 6639: 6638: 6632: 6631: 6612: 6609: 6603: 6595: 6591: 6587: 6583: 6579: 6575: 6570: 6565: 6561: 6557: 6553: 6549: 6542: 6534: 6528: 6524: 6520: 6516: 6512: 6511:IAG 150 Years 6505: 6490: 6486: 6479: 6468: 6467: 6460: 6445: 6441: 6434: 6424: 6422: 6420: 6411: 6407: 6403: 6399: 6395: 6391: 6383: 6381: 6372: 6366: 6358: 6357: 6348: 6333: 6330: 6324: 6316: 6310: 6302: 6301: 6293: 6291: 6282: 6281: 6273: 6258: 6254: 6247: 6233: 6232:www.e-rara.ch 6229: 6223: 6209: 6205: 6199: 6191: 6187: 6182: 6177: 6173: 6169: 6165: 6158: 6156: 6147: 6146: 6140: 6133: 6119: 6115: 6109: 6095:on 2016-01-23 6094: 6090: 6086: 6080: 6066: 6062: 6056: 6048: 6047: 6039: 6031: 6030: 6024: 6019: 6013: 6011: 6009: 6007: 6005: 6003: 5994: 5990: 5986: 5982: 5975: 5966: 5961: 5957: 5953: 5949: 5942: 5934: 5928: 5920: 5919: 5910: 5895: 5891: 5885: 5877: 5876: 5868: 5853: 5849: 5842: 5828: 5824: 5820: 5816: 5809: 5794: 5790: 5784: 5782: 5773: 5769: 5764: 5759: 5755: 5751: 5747: 5740: 5732: 5728: 5724: 5722:9780387755342 5718: 5714: 5707: 5700: 5694: 5687: 5681: 5673: 5666: 5657: 5648: 5641: 5636: 5630:, p. 498 5629: 5624: 5617: 5612: 5603: 5601: 5599: 5591: 5585: 5578: 5572: 5561: 5557: 5553: 5546: 5539: 5537: 5528: 5524: 5520: 5518:0-521-21821-7 5514: 5510: 5503: 5501: 5493: 5487: 5483: 5479: 5478:Grant, Edward 5473: 5466: 5460: 5456: 5452: 5451:Grant, Edward 5446: 5438: 5437: 5430: 5423: 5417: 5411: 5406: 5398: 5394: 5390: 5386: 5382: 5378: 5374: 5370: 5369: 5364: 5358: 5351: 5345: 5338: 5332: 5325: 5319: 5313:, IX.ii.133 . 5312: 5306: 5299: 5293: 5286: 5276: 5269:. p. 16. 5268: 5261:. p. 30. 5260: 5253: 5247: 5240: 5234: 5227: 5221: 5213: 5206: 5199: 5195: 5191: 5187: 5183: 5179: 5175: 5168: 5159: 5151: 5144: 5138:, p. 374 5137: 5132: 5118:on 2012-03-31 5117: 5113: 5107: 5100: 5096: 5095: 5090: 5086: 5079: 5065: 5061: 5055: 5049: 5045: 5041: 5035: 5030: 5022: 5020:9780674072824 5016: 5012: 5011: 5003: 4995: 4989: 4985: 4978: 4972: 4969: 4967:0-8251-3285-1 4963: 4959: 4952: 4950: 4948: 4933: 4929: 4925: 4921: 4917: 4913: 4906: 4904: 4896: 4895:0-415-01929-X 4892: 4888: 4884: 4878: 4871: 4865: 4857: 4856: 4851: 4845: 4838: 4834: 4828: 4820: 4814: 4808: 4805: 4800: 4793: 4789: 4782: 4775: 4769: 4767: 4759: 4755: 4750: 4735: 4728: 4713: 4707: 4699: 4692: 4684: 4680: 4676: 4672: 4668: 4664: 4660: 4653: 4646: 4645:0-415-96930-1 4642: 4636: 4629: 4623: 4621: 4612: 4608: 4607: 4599: 4591: 4587: 4580: 4572: 4566: 4562: 4561: 4553: 4545: 4537: 4533: 4529: 4523: 4521: 4511: 4504: 4502:9780854810529 4498: 4494: 4490: 4486: 4480: 4473: 4467: 4463: 4456: 4448: 4443:as quoted in 4440: 4433: 4426: 4420: 4413: 4406: 4402: 4398: 4393: 4386: 4385:0-387-94107-X 4382: 4378: 4372: 4365: 4364: 4358: 4351: 4347: 4341: 4339: 4337: 4328: 4324: 4320: 4316: 4312: 4308: 4304: 4300: 4286:on 2021-10-26 4285: 4281: 4277: 4273: 4269: 4266:(11): 66–92. 4265: 4261: 4257: 4249: 4242: 4241:0-415-96930-1 4238: 4234: 4230: 4224: 4216: 4210: 4206: 4202: 4198: 4191: 4189: 4187: 4179: 4173: 4166: 4162: 4159: 4155: 4153: 4145: 4139: 4138:Contributions 4133: 4124: 4116: 4112: 4105: 4098: 4092: 4084: 4080: 4076: 4072: 4068: 4064: 4060: 4053: 4046: 4040: 4033: 4027: 4020: 4014: 4010: 4006: 4000: 3992: 3987: 3986: 3980: 3974: 3972: 3970: 3968: 3959: 3955: 3951: 3947: 3943: 3939: 3935: 3931: 3924: 3908: 3904: 3903: 3896: 3889: 3888:Meteorologica 3884: 3877: 3872: 3865: 3860: 3846: 3842: 3835: 3828: 3823: 3816: 3812: 3806: 3799:. p. 33. 3798: 3791: 3783: 3776: 3768: 3767: 3760: 3754: 3747: 3741: 3733: 3729: 3725: 3721: 3717: 3713: 3709: 3705: 3698: 3690: 3689: 3684: 3680: 3673: 3666: 3662: 3657: 3655: 3639: 3635: 3628: 3622: 3618: 3613: 3611: 3602: 3600:9788447211562 3596: 3592: 3588: 3581: 3579: 3571:. p. 19. 3570: 3566: 3565: 3557: 3555: 3547: 3542: 3540: 3532: 3526: 3524: 3522: 3515: 3499: 3495: 3494: 3486: 3482: 3473: 3470: 3468: 3465: 3463: 3460: 3458: 3455: 3453: 3450: 3448: 3445: 3443: 3440: 3438: 3435: 3433: 3430: 3429: 3423: 3421: 3417: 3413: 3409: 3405: 3400: 3398: 3397: 3393:later called 3391: 3390:least squares 3387: 3383: 3378: 3376: 3372: 3368: 3363: 3360: 3356: 3352: 3348: 3343: 3338: 3336: 3332: 3328: 3324: 3320: 3312: 3308: 3304: 3295: 3292: 3291:Great Britain 3288: 3287:United States 3284: 3280: 3279: 3274: 3270: 3266: 3262: 3261: 3256: 3252: 3248: 3244: 3240: 3235: 3232: 3227: 3222: 3220: 3216: 3212: 3211: 3206: 3202: 3200: 3195: 3187: 3183: 3181: 3174: 3170: 3168: 3164: 3160: 3154: 3151: 3146: 3142: 3138: 3134: 3130: 3126: 3118: 3114: 3112: 3108: 3104: 3100: 3096: 3092: 3088: 3083: 3078: 3074: 3071: 3067: 3063: 3059: 3055: 3051: 3048: 3044: 3039: 3035: 3027: 3023: 3021: 3017: 3013: 3009: 3005: 3004:metric system 3001: 2997: 2993: 2989: 2985: 2980: 2978: 2974: 2970: 2961: 2957: 2955: 2951: 2946: 2937: 2927: 2926:(August 2020) 2922: 2918: 2917: 2912: 2907: 2898: 2897: 2889: 2887: 2883: 2879: 2875: 2871: 2867: 2863: 2859: 2850: 2844: 2840: 2836: 2832: 2829:Archive with 2827: 2818: 2816: 2812: 2808: 2807:gravitational 2804: 2800: 2796: 2795:South America 2791: 2785: 2781: 2777: 2773: 2769: 2765: 2761: 2757: 2753: 2752:Earth's shape 2749: 2739: 2737: 2733: 2729: 2725: 2721: 2717: 2713: 2709: 2705: 2701: 2697: 2693: 2689: 2685: 2681: 2677: 2672: 2670: 2669: 2664: 2660: 2656: 2652: 2648: 2644: 2640: 2636: 2633:surveyed the 2632: 2628: 2626: 2622: 2618: 2613: 2611: 2607: 2603: 2599: 2595: 2591: 2587: 2582: 2580: 2576: 2573: 2569: 2564: 2562: 2558: 2554: 2550: 2546: 2542: 2538: 2534: 2530: 2526: 2522: 2513: 2509: 2507: 2503: 2499: 2495: 2491: 2487: 2484:then his son 2483: 2479: 2475: 2471: 2467: 2463: 2461: 2457: 2452: 2450: 2446: 2445: 2440: 2430: 2428: 2422: 2420: 2416: 2412: 2408: 2404: 2400: 2396: 2392: 2388: 2384: 2379: 2377: 2373: 2369: 2365: 2361: 2355: 2345: 2343: 2339: 2335: 2331: 2327: 2323: 2319: 2315: 2311: 2305: 2300: 2298: 2292: 2290: 2285: 2283: 2279: 2275: 2268: 2263: 2261: 2258:reports that 2257: 2253: 2244: 2242: 2238: 2237:triangulation 2234: 2230: 2226: 2216: 2214: 2210: 2206: 2205: 2204:Divine Comedy 2199: 2197: 2193: 2189: 2185: 2181: 2177: 2173: 2169: 2165: 2161: 2157: 2153: 2148: 2146: 2142: 2138: 2137: 2132: 2127: 2125: 2124: 2119: 2115: 2113: 2109: 2104: 2102: 2098: 2094: 2086: 2085: 2084:Vox Clamantis 2080: 2076: 2067: 2065: 2061: 2051: 2047: 2045: 2041: 2037: 2033: 2029: 2019: 2017: 2016: 2010: 1998: 1994: 1989: 1980: 1978: 1974: 1969: 1967: 1963: 1959: 1955: 1951: 1950: 1945: 1944:Old Icelandic 1941: 1937: 1932: 1930: 1926: 1921: 1919: 1915: 1911: 1906: 1904: 1900: 1899:scholasticism 1896: 1892: 1888: 1873: 1871: 1867: 1863: 1859: 1850: 1848: 1844: 1840: 1836: 1832: 1828: 1818: 1815: 1811: 1807: 1797: 1795: 1791: 1787: 1783: 1779: 1768: 1766: 1765:Masudic canon 1762: 1761:triangulation 1758: 1754: 1748: 1745: 1743: 1739: 1734: 1732: 1728: 1723: 1722:, Pakistan). 1721: 1718:(present day 1716: 1712: 1708: 1707:trigonometric 1704: 1695: 1693: 1669: 1660: 1658: 1655: 1652: 1643: 1629: 1617: 1613: 1609: 1607: 1603: 1599: 1595: 1591: 1587: 1583: 1580: 1570: 1568: 1567: 1562: 1558: 1554: 1549: 1547: 1543: 1542: 1537: 1533: 1532: 1527: 1523: 1519: 1512: 1507: 1502: 1495:Islamic world 1492: 1490: 1486: 1472: 1463: 1462: 1461: 1459: 1455: 1451: 1447: 1443: 1439: 1435: 1431: 1430: 1426:magnum opus, 1425: 1421: 1411: 1409: 1405: 1400: 1399:ancient India 1396: 1393:in the east, 1392: 1388: 1383: 1380: 1379: 1372: 1368: 1361:Ancient India 1358: 1356: 1355: 1350: 1346: 1342: 1338: 1334: 1330: 1325: 1323: 1319: 1315: 1311: 1307: 1303: 1299: 1295: 1291: 1287: 1283: 1278: 1276: 1275: 1270: 1266: 1262: 1258: 1254: 1250: 1246: 1236: 1234: 1230: 1226: 1222: 1218: 1214: 1210: 1206: 1201: 1199: 1195: 1191: 1187: 1183: 1179: 1177: 1173: 1169: 1165: 1161: 1157: 1153: 1149: 1145: 1141: 1137: 1133: 1129: 1128: 1122: 1120: 1116: 1115: 1110: 1106: 1099: 1093: 1092: 1086: 1077: 1074: 1070: 1066: 1065: 1060: 1056: 1052: 1048: 1035: 1030: 1026: 1024: 1020: 1016: 1011: 1003: 1001: 1000: 995: 994: 989: 984: 982: 977: 973: 963: 961: 957: 953: 949: 945: 941: 932: 929: 924: 921: 915: 913: 905: 902: 898: 894: 890: 887: 883: 879: 878: 877: 875: 871: 867: 863: 859: 851: 847: 843: 838: 834: 832: 828: 824: 820: 816: 815: 810: 806: 802: 801:Cyrene, Libya 798: 794: 785: 783: 782: 776: 759: 750: 748: 744: 743:atomic theory 740: 736: 731: 729: 725: 721: 717: 713: 709: 705: 703: 699: 698: 689: 688:lunar eclipse 685: 682: 679: 678: 677: 674: 672: 667: 664: 660: 656: 652: 646: 641: 632: 630: 629: 623: 619: 615: 611: 602: 600: 595: 591: 587: 583: 579: 575: 571: 567: 563: 558: 556: 552: 551: 550:The Histories 546: 542: 541:The Histories 538: 535: 532: 528: 524: 520: 515: 513: 509: 505: 501: 497: 493: 489: 488:ancient Greek 474: 472: 468: 463: 461: 457: 453: 445: 421: 416: 414: 409: 407: 402: 401: 399: 398: 391: 388: 386: 383: 381: 378: 377: 371: 369: 366: 365: 361: 359: 356: 355: 351: 349: 346: 345: 341: 339: 336: 335: 331: 329: 326: 325: 321: 319: 316: 315: 311: 309: 306: 305: 301: 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Retrieved 5792: 5753: 5749: 5739: 5712: 5706: 5698: 5693: 5685: 5680: 5671: 5665: 5656: 5647: 5640:Needham 1959 5635: 5628:Needham 1959 5623: 5616:Needham 1959 5611: 5589: 5584: 5576: 5571: 5560:the original 5555: 5551: 5508: 5481: 5472: 5454: 5445: 5435: 5429: 5421: 5416: 5405: 5372: 5366: 5357: 5349: 5344: 5336: 5331: 5323: 5318: 5310: 5305: 5300:, XIV.v.17 . 5297: 5292: 5284: 5275: 5266: 5258: 5251: 5246: 5241:, XIV.ii.1 . 5238: 5233: 5225: 5220: 5205: 5177: 5173: 5167: 5158: 5149: 5143: 5136:Needham 1959 5131: 5120:. Retrieved 5116:the original 5106: 5092: 5078: 5067:. Retrieved 5063: 5054: 5029: 5009: 5002: 4983: 4977: 4957: 4935:. Retrieved 4919: 4915: 4882: 4877: 4869: 4864: 4853: 4844: 4832: 4827: 4813: 4803: 4799: 4791: 4781: 4773: 4757: 4749: 4738:. Retrieved 4736:. GONGOL.com 4727: 4716:. Retrieved 4706: 4691: 4669:(3): 51–68. 4666: 4662: 4652: 4635: 4627: 4605: 4598: 4589: 4585: 4579: 4559: 4552: 4543: 4535: 4531: 4510: 4492: 4479: 4461: 4455: 4446: 4438: 4432: 4418: 4412: 4396: 4392: 4376: 4371: 4361: 4357: 4349: 4302: 4298: 4288:. Retrieved 4284:the original 4263: 4259: 4248: 4232: 4223: 4196: 4172: 4151: 4144: 4132: 4123: 4114: 4110: 4104: 4096: 4091: 4066: 4062: 4052: 4044: 4039: 4034:, i.7.49-52. 4031: 4026: 4008: 3999: 3984: 3979:Russo, Lucio 3936:(1): 61–70. 3933: 3929: 3923: 3911:. Retrieved 3907:Heath, T. L. 3901: 3895: 3887: 3883: 3875: 3871: 3863: 3859: 3848:. Retrieved 3844: 3834: 3826: 3822: 3817:, 2011, p. 7 3810: 3805: 3796: 3790: 3781: 3775: 3765: 3753: 3740: 3707: 3703: 3697: 3686: 3679:"Pythagoras" 3672: 3664: 3641:. Retrieved 3637: 3627: 3586: 3563: 3530: 3505:. Retrieved 3498:the original 3492: 3485: 3407: 3401: 3394: 3385: 3379: 3364: 3339: 3316: 3310: 3277: 3258: 3236: 3223: 3209: 3203: 3191: 3179: 3155: 3123: 3079: 3075: 3032: 2999: 2981: 2976: 2966: 2953: 2942: 2925: 2914: 2855: 2838: 2821:19th century 2792: 2745: 2707: 2673: 2666: 2651:Grosses Moos 2650: 2647:Grand Marais 2629: 2614: 2594:Torne Valley 2592:was sent to 2583: 2565: 2540: 2539:in his work 2525:Isaac Newton 2518: 2464: 2460:meridian arc 2453: 2442: 2436: 2423: 2418: 2415:coat of arms 2380: 2357: 2329: 2322:Yuan-dynasty 2307: 2302: 2293: 2288: 2286: 2270: 2265: 2255: 2250: 2222: 2202: 2200: 2176:Middle Dutch 2151: 2149: 2140: 2134: 2128: 2121: 2116: 2111: 2105: 2090: 2082: 2057: 2048: 2039: 2035: 2025: 2012: 2006: 1992: 1970: 1947: 1933: 1928: 1922: 1907: 1884: 1856: 1842: 1824: 1821:Applications 1806:Jamal-al-Din 1803: 1800:Jamal-al-Din 1790:Al-Khwarizmi 1775: 1764: 1750: 1746: 1735: 1727:law of sines 1724: 1701: 1666: 1649: 1630: 1610: 1606:meridian arc 1576: 1564: 1550: 1539: 1529: 1516: 1470: 1468: 1457: 1449: 1445: 1441: 1437: 1433: 1427: 1417: 1404:Varāhamihira 1384: 1376: 1374: 1352: 1326: 1286:Hebrew Bible 1279: 1272: 1264: 1249:Neoplatonism 1242: 1216: 1208: 1204: 1202: 1181: 1180: 1164:polar circle 1135: 1131: 1125: 1123: 1112: 1103: 1089: 1062: 1044: 1012: 1009: 1006:Roman Empire 997: 991: 985: 969: 938: 925: 916: 909: 885: 855: 818: 812: 807:, estimated 793:Eratosthenes 791: 788:Eratosthenes 779: 777: 756: 739:Solar System 732: 712:heavy things 706: 696: 693: 675: 668: 649: 627: 608: 559: 549: 540: 516: 485: 464: 456:/dʒiːˈɒdɪsi/ 449: 443: 172:Technologies 127: / 59: 39:Fundamentals 15: 6790:Vaníček, P. 6627:Works cited 6396:: 161–180. 6174:: 445–469. 5854:(in German) 5795:(in German) 5311:Etymologiae 5298:Etymologiae 5239:Etymologiae 5089:"Al-Biruni" 4099:, XII $ 53. 4030:Cleomedes, 3913:13 November 3890:, 362a31–35 3829:, 298a2–10) 3710:: 267–294. 3643:28 February 3145:Henry Kater 2831:lithography 2748:Jean Richer 2625:William Roy 2551:. Newton's 2531:. In 1659, 2466:Jean Picard 2334:Eastern-Han 2314:Jin-dynasty 2297:sinocentric 2172:Old Russian 2152:Elucidarium 2091:During the 2015:Etymologies 1962:Middle Ages 1949:Elucidarius 1940:Scandinavia 1914:Middle Ages 1810:Kublai Khan 1780:astronomer 1668:Al-Farghānī 1663:Al-Farghānī 1590:geographers 1555:to develop 1471:Aryabhatiya 1458:Aryabhatiya 1434:Aryabhatiya 1429:Āryabhaṭīya 1408:Brahmagupta 1387:Megasthenes 1229:East Indies 1213:topographic 1140:coordinates 948:Mesopotamia 803:working in 697:Meteorology 574:rectangular 50:Geodynamics 6859:Categories 6819:. Walker. 6719:References 6616:2020-08-30 6495:2020-08-29 6450:2020-08-25 6338:2020-08-24 6263:2020-08-24 6237:2018-05-29 6213:2018-05-29 6123:2017-11-06 6099:2017-11-06 6070:2017-11-06 5900:2020-08-24 5858:2020-08-24 5832:2020-08-24 5799:2020-08-24 5184:: 81–98 , 5122:2011-10-08 5069:2020-10-16 4937:2010-02-21 4740:2008-11-16 4718:2008-11-16 4609:. p. 4290:2022-02-19 4229:D. Pingree 3866:, 297a9–21 3850:2022-08-21 3744:Aristotle 3663:, (2001), 3619:, p. 3617:Dicks 1970 3507:6 February 3414:geodesist 3167:gravimeter 3107:Jorge Juan 2720:North Pole 2716:flattening 2627:'s death. 2572:meridional 2563:of 1:230. 2561:flattening 2478:logarithms 2360:Portuguese 2338:Zhang Heng 2330:Ge zhi cao 2289:Ge zhi cao 2278:Ming China 2247:Ming China 2229:theodolite 2215:of Earth. 2213:time zones 2164:Old French 2131:scholastic 2079:John Gower 1833:developed 1782:Al-Zarqali 1772:Al-Zarqali 1651:Andalusian 1616:Alfraganus 1489:equatorial 1290:Lactantius 1282:flat Earth 1269:Hipparchus 1209:Geographia 1182:Geographia 1132:Geographia 1127:Geographia 1109:Alexandria 1096:(1482, by 999:Geographia 972:Posidonius 966:Posidonius 897:local noon 866:Alexandria 850:Alexandria 844:is on the 769: 212 767: – c. 765: 287 758:Archimedes 753:Archimedes 590:Empedocles 586:Parmenides 578:Pythagoras 570:Anaximenes 566:Pythagoras 555:Parmenides 519:Phoenician 508:Nile Delta 446:from NASA. 6776:Centaurus 6594:119447198 6586:1432-1394 6564:CiteSeerX 6410:109333769 6365:cite book 6309:cite book 6190:0261-0523 5927:cite book 5772:0035-9149 5731:314175913 5670:RK Jain. 5397:145014073 5375:(1): 36. 5309:Isidore, 5296:Isidore, 5237:Isidore, 5198:161732080 4926:: 45–50. 4887:Routledge 4885:, p. 31, 4683:126334632 4663:Resonance 4528:Macrobius 4485:Calcidius 4437:Ptolemy. 4327:171017315 4154:1979–2007 4083:118004246 4047:, VI.598. 4032:Caelestia 3732:144330867 3047:Neuchâtel 3012:Barcelona 2866:ellipsoid 2730:. 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