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149-516: Flat Earth is an archaic and scientifically disproven conception of the Earth's shape as a plane or disk . Many ancient cultures subscribed to a flat-Earth cosmography , notably including ancient near eastern cosmology . The model has undergone a recent resurgence as a conspiracy theory . The idea of a spherical Earth appeared in ancient Greek philosophy with Pythagoras (6th century BC). However, most pre-Socratics (6th–5th century BC) retained

298-655: A celestial sphere . This invention undoubtedly made him the first to realize the obliquity of the Zodiac as the Roman philosopher Pliny the Elder reports in Natural History (II, 8). It is a little early to use the term ecliptic , but his knowledge and work on astronomy confirm that he must have observed the inclination of the celestial sphere in relation to the plane of the Earth to explain

447-402: A graticule is drawn on the surface, but varying curvature in any other direction. For an oblate ellipsoid, the polar radius of curvature r p {\displaystyle r_{p}} is larger than the equatorial because the pole is flattened: the flatter the surface, the larger the sphere must be to approximate it. Conversely, the ellipsoid's north–south radius of curvature at

596-405: A sphere to model the Earth as a close approximation. However, a more accurate figure is needed for measuring distances and areas on the scale beyond the purely local. Better approximations can be made by modeling the entire surface as an oblate spheroid , using spherical harmonics to approximate the geoid , or modeling a region with a best-fit reference ellipsoid . For surveys of small areas,

745-410: A body distinct from the elements). the infinite, and not air or water, in order that the other things may not be destroyed by their infinity. They are in opposition one to another. air is cold, water moist, and fire hot. and therefore, if any one of them were infinite, the rest would have ceased to be by this time. Accordingly they say that what is infinite is something other than the elements, and from it

894-460: A boundless stock from which the waste of existence is continually made good, "elements.". That is only the natural development of the thought we have ascribed to Thales, and there can be no doubt that Anaximander at least formulated it distinctly. Indeed, we can still follow to some extent the reasoning which led him to do so. Thales had regarded water as the most likely thing to be that of which all others are forms; Anaximander appears to have asked how

1043-428: A circle and therefore that the ellipsoid is triaxial has been a matter of scientific inquiry for many years. Modern technological developments have furnished new and rapid methods for data collection and, since the launch of Sputnik 1 , orbital data have been used to investigate the theory of ellipticity. More recent results indicate a 70 m difference between the two equatorial major and minor axes of inertia, with

1192-522: A concave model. According to Macdonell: "the conception of the Earth being a disc surrounded by an ocean does not appear in the Samhitas . But it was naturally regarded as circular, being compared with a wheel (10.89) and expressly called circular (parimandala) in the Shatapatha Brahmana ." By about the 5th century AD, the siddhanta astronomy texts of South Asia, particularly of Aryabhata , assume

1341-446: A degree of arc along the Paris meridian . Improved maps and better measurement of distances and areas of national territories motivated these early attempts. Surveying instrumentation and techniques improved over the ensuing centuries. Models for the figure of the Earth improved in step. In the mid- to late 20th century, research across the geosciences contributed to drastic improvements in

1490-440: A few doxographers provide us with the little information that remains. However, we know from Aristotle that Thales, also from Miletus, precedes Anaximander. It is debatable whether Thales actually was the teacher of Anaximander, but there is no doubt that Anaximander was influenced by Thales' theory that everything is derived from water. One thing that is not debatable is that even the ancient Greeks considered Anaximander to be from

1639-517: A flat-Earth cosmography with the Earth surrounded by an ocean, with the axis mundi , a world tree ( Yggdrasil ), or pillar ( Irminsul ) in the centre. In the world-encircling ocean sat a snake called Jormungandr . The Norse creation account preserved in Gylfaginning (VIII) states that during the creation of the Earth, an impassable sea was placed around it: And Jafnhárr said: "Of the blood, which ran and welled forth freely out of his wounds, they made

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1788-570: A flattening at the South Pole and a bulge of the same degree at the North Pole , with the sea level increased about 9 m (30 ft) at the latter. This theory implies the northern middle latitudes to be slightly flattened and the southern middle latitudes correspondingly bulged. Potential factors involved in this aberration include tides and subcrustal motion (e.g. plate tectonics ). John A. O'Keefe and co-authors are credited with

1937-403: A hen's egg and as round as a crossbow bullet; the Earth is like the yolk of the egg, and lies in the centre. This analogy with a curved egg led some modern historians, notably Joseph Needham , to conjecture that Chinese astronomers were, after all, aware of the Earth's sphericity. The egg reference, however, was rather meant to clarify the relative position of the flat Earth to the heavens: In

2086-472: A horizontal plane. The position of its shadow on the plane indicated the time of day. As it moves through its apparent course, the Sun draws a curve with the tip of the projected shadow, which is shortest at noon, when pointing due south. The variation in the tip's position at noon indicates the solar time and the seasons; the shadow is longest on the winter solstice and shortest on the summer solstice. The invention of

2235-508: A leading figure in the School of Antioch and mentor of John Chrysostom , may have argued for a flat Earth; however, Diodorus' opinion on the matter is known only from a later criticism. Chrysostom, one of the four Great Church Fathers of the Eastern Church and Archbishop of Constantinople , explicitly espoused the idea, based on scripture, that the Earth floats miraculously on the water beneath

2384-405: A less active fire to break free. Thunderbolts are the result of a thicker and more violent air flow. He saw the sea as a remnant of the mass of humidity that once surrounded Earth. A part of that mass evaporated under the Sun's action, thus causing the winds and even the rotation of the celestial bodies, which he believed were attracted to places where water is more abundant. He explained rain as

2533-414: A less learned character) the actual form of words used suggests strongly a circle rather than a sphere", though she notes that even in these works the language is ambiguous. Portuguese navigation down and around the coast of Africa in the latter half of the 1400s gave wide-scale observational evidence for Earth's sphericity. In these explorations, the Sun's position moved more northward the further south

2682-476: A log. It has been argued, however, that Thales actually believed in a spherical Earth. Anaximander (c. 550 BC) believed that the Earth was a short cylinder with a flat, circular top that remained stable because it was the same distance from all things. Anaximenes of Miletus believed that "the Earth is flat and rides on air; in the same way the Sun and the Moon and the other heavenly bodies, which are all fiery, ride

2831-633: A passage of Zhang Heng's cosmogony not translated by Needham, Zhang himself says: "Heaven takes its body from the Yang, so it is round and in motion. Earth takes its body from the Yin, so it is flat and quiescent". The point of the egg analogy is simply to stress that the Earth is completely enclosed by Heaven, rather than merely covered from above as the Kai Tian describes. Chinese astronomers, many of them brilliant men by any standards, continued to think in flat-Earth terms until

2980-435: A planar (flat) model of Earth's surface suffices because the local topography overwhelms the curvature. Plane-table surveys are made for relatively small areas without considering the size and shape of the entire Earth. A survey of a city, for example, might be conducted this way. By the late 1600s, serious effort was devoted to modeling the Earth as an ellipsoid, beginning with French astronomer Jean Picard 's measurement of

3129-465: A portrait of the man. Anaximander was an early proponent of science and tried to observe and explain different aspects of the universe, with a particular interest in its origins , claiming that nature is ruled by laws, just like human societies, and anything that disturbs the balance of nature does not last long. Like many thinkers of his time, Anaximander's philosophy included contributions to many disciplines. In astronomy , he attempted to describe

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3278-455: A pre-Socratic effort to demystify physical processes. His major contribution to history was writing the oldest prose document about the Universe and the origins of life; for this he is often called the "Father of Cosmology " and founder of astronomy. However, pseudo-Plutarch states that he still viewed celestial bodies as deities. He placed the celestial bodies in the wrong order. He thought that

3427-460: A product of the humidity pumped up from Earth by the sun. For him, the Earth was slowly drying up and water only remained in the deepest regions, which someday would go dry as well. According to Aristotle's Meteorology (II, 3), Democritus also shared this opinion. Anaximander speculated about the beginnings and origin of animal life, and that humans came from other animals in waters. According to his evolutionary theory , animals sprang out of

3576-417: A representation of the entire "world" or cosmos . A recent study of medieval concepts of the sphericity of the Earth noted that "since the eighth century, no cosmographer worthy of note has called into question the sphericity of the Earth". However, the work of these intellectuals may not have had significant influence on public opinion, and it is difficult to tell what the wider population may have thought of

3725-462: A slightly rounded metal surface. The centre or “navel” of the world ( ὀμφαλός γῆς omphalós gẽs ) could have been Delphi , but is more likely in Anaximander's time to have been located near Miletus. The Aegean Sea was near the map's centre and enclosed by three continents, themselves located in the middle of the ocean and isolated like islands by sea and rivers. Europe was bordered on the south by

3874-504: A solid dome with the Sun, Moon, planets, and stars embedded in it. Both Homer and Hesiod described a disc cosmography on the Shield of Achilles . This poetic tradition of an Earth-encircling ( gaiaokhos ) sea ( Oceanus ) and a disc also appears in Stasinus of Cyprus, Mimnermus , Aeschylus , and Apollonius Rhodius . Homer's description of the disc cosmography on the shield of Achilles with

4023-490: A sort of primal chaos . According to him, the Universe originates in the separation of opposites in the primordial matter. It embraces the opposites of hot and cold, wet and dry, and directs the movement of things; an entire host of shapes and differences then grow that are found in "all the worlds" (for he believed there were many). "Anaximander taught, then, that there was an eternal. The indestructible something out of which everything arises, and into which everything returns;

4172-590: A spherical Earth as they develop mathematical methods for quantitative astronomy for calendar and time keeping. The medieval Indian texts called the Puranas describe the Earth as a flat-bottomed, circular disk with concentric oceans and continents. This general scheme is present not only in the Hindu cosmologies, but also in Buddhist and Jain cosmologies of South Asia. However, some Puranas include other models. The fifth canto of

4321-413: A system of hollow concentric wheels, filled with fire, with the rims pierced by holes like those of a flute. Consequently, the Sun was the fire that one could see through a hole the same size as the Earth on the farthest wheel, and an eclipse corresponded with the occlusion of that hole. The diameter of the solar wheel was twenty-seven times that of the Earth (or twenty-eight, depending on the sources) and

4470-472: A tolerably elastic system. Some scholars see a gap between the existing mythical and the new rational way of thought which is the main characteristic of the archaic period (8th to 6th century BC) in the Greek city-states . This has given rise to the phrase "Greek miracle". But there may not have been such an abrupt break as initially appears. The basic elements of nature ( water , air , fire , earth ) which

4619-415: A western Christian writer and advisor to the first Christian Roman Emperor, Constantine , writing sometime between 304 and 313 AD, ridiculed the notion of antipodes and the philosophers who fancied that "the universe is round like a ball. They also thought that heaven revolves in accordance with the motion of the heavenly bodies. ... For that reason, they constructed brass globes, as though after

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4768-596: A world map comes from the late Babylonian Map of the World later than 9th century BC but is based probably on a much older map. These maps indicated directions, roads, towns, borders, and geological features. Anaximander's innovation was to represent the entire inhabited land known to the ancient Greeks. Such an accomplishment is more significant than it at first appears. Anaximander most likely drew this map for three reasons. First, it could be used to improve navigation and trade between Miletus 's colonies and other colonies around

4917-407: Is a characteristic of perfect spheres, the Earth deviates from spherical by only a third of a percent, sufficiently close to treat it as a sphere in many contexts and justifying the term "the radius of the Earth". The concept of a spherical Earth dates back to around the 6th century BC , but remained a matter of philosophical speculation until the 3rd century BC . The first scientific estimation of

5066-474: Is a historical myth that medieval Europeans generally thought the Earth was flat. This myth was created in the 17th century by Protestants to argue against Catholic teachings. In early Egyptian and Mesopotamian thought , the world was portrayed as a disk floating in the ocean. A similar model is found in the Homeric account from the 8th century BC in which "Okeanos, the personified body of water surrounding

5215-506: Is derived in the last resort from Theophrastos, who certainly knew his book. He seems once at least to have quoted Anaximander's own words, and he criticised his style. Here are the remains of what he said of him in the First Book: "Anaximander of Miletos, son of Praxiades, a fellow-citizen and associate of Thales, said that the material cause and first element of things was the Infinite, he being

5364-414: Is generally the concern of topographers, hydrographers , and geophysicists . While it is the surface on which Earth measurements are made, mathematically modeling it while taking the irregularities into account would be extremely complicated. The Pythagorean concept of a spherical Earth offers a simple surface that is easy to deal with mathematically. Many astronomical and navigational computations use

5513-480: Is impossible, since no document provides chronological references. Themistius , a 4th-century Byzantine rhetorician , mentions that he was the "first of the known Greeks to publish a written document on nature." Therefore, his texts would be amongst the earliest written in prose , at least in the Western world. By the time of Plato , his philosophy was almost forgotten, and Aristotle , his successor Theophrastus , and

5662-426: Is intended to model the entire Earth or only some portion of it. A sphere has a single radius of curvature , which is simply the radius of the sphere. More complex surfaces have radii of curvature that vary over the surface. The radius of curvature describes the radius of the sphere that best approximates the surface at that point. Oblate ellipsoids have a constant radius of curvature east to west along parallels , if

5811-691: Is not an independent authority, and the only question is what Theophrastos wrote." For him, it became no longer a mere point in time, but a source that could perpetually give birth to whatever will be. The indefiniteness is spatial in early usages as in Homer (indefinite sea) and as in Xenophanes (6th century BC) who said that the Earth went down indefinitely (to apeiron ) i.e. beyond the imagination or concept of men. Burnet (1930) in Early Greek Philosophy says: "Nearly all we know of Anaximander's system

5960-531: Is peopled. For Scripture, which proves the truth of its historical statements by the accomplishment of its prophecies, gives no false information; and it is too absurd to say, that some men might have taken ship and traversed the whole wide ocean, and crossed from this side of the world to the other, and that thus even the inhabitants of that distant region are descended from that one first man. Some historians do not view Augustine's scriptural commentaries as endorsing any particular cosmological model, endorsing instead

6109-406: Is satisfactory for geography , astronomy and many other purposes. Several models with greater accuracy (including ellipsoid ) have been developed so that coordinate systems can serve the precise needs of navigation , surveying , cadastre , land use , and various other concerns. Earth's topographic surface is apparent with its variety of land forms and water areas. This topographic surface

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6258-408: Is small, only about one part in 300. Historically, flattening was computed from grade measurements . Nowadays, geodetic networks and satellite geodesy are used. In practice, many reference ellipsoids have been developed over the centuries from different surveys. The flattening value varies slightly from one reference ellipsoid to another, reflecting local conditions and whether the reference ellipsoid

6407-477: Is the net effect of gravitation (due to mass attraction) and centrifugal force (due to rotation). It can be measured very accurately at the surface and remotely by satellites. True vertical generally does not correspond to theoretical vertical ( deflection ranges up to 50") because topography and all geological masses disturb the gravitational field. Therefore, the gross structure of the Earth's crust and mantle can be determined by geodetic-geophysical models of

6556-570: Is very likely that leaders of Miletus sent him there as a legislator to create a constitution or simply to maintain the colony's allegiance. Anaximander lived the final few years of his life as a subject of the Persian Achaemenid Empire . Anaximander's theories were influenced by the Greek mythical tradition, and by some ideas of Thales  – the father of Western philosophy  – as well as by observations made by older civilizations in

6705-548: The Bhagavata Purana , for example, includes sections that describe the Earth both as flat and spherical. During the early period of the Christian Church, the spherical view continued to be widely held, with some notable exceptions. Athenagoras , an eastern Christian writing around the year 175 AD, said that the Earth was spherical. Methodius (c. 290 AD), an eastern Christian writing against "the theory of

6854-814: The Mediterranean Sea and was separated from Asia by the Black Sea, the Lake Maeotis , and, further east, either by the Phasis River (now called the Rioni in Georgia ) or the Tanais . The Nile flowed south into the ocean, separating Libya (which was the name for the part of the then-known African continent) from Asia. The Suda relates that Anaximander explained some basic notions of geometry. It also mentions his interest in

7003-578: The Middle Ages with great difficulties that affected the continent's intellectual production. Most scientific treatises of classical antiquity (in Greek ) were unavailable, leaving only simplified summaries and compilations. In contrast, the Eastern Roman Empire did not fall, and it preserved the learning. Still, many textbooks of the Early Middle Ages supported the sphericity of the Earth in

7152-624: The Monist school which began in Miletus, with Thales followed by Anaximander and which ended with Anaximenes . 3rd-century Roman rhetorician Aelian depicts Anaximander as leader of the Milesian colony to Apollonia on the Black Sea coast, and hence some have inferred that he was a prominent citizen. Indeed, Various History (III, 17) explains that philosophers sometimes also dealt with political matters. It

7301-537: The firmament . Christian Topography (547) by the Alexandrian monk Cosmas Indicopleustes , who had traveled as far as Sri Lanka and the source of the Blue Nile , is now widely considered the most valuable geographical document of the early medieval age, although it received relatively little attention from contemporaries. In it, the author repeatedly expounds the doctrine that the universe consists of only two places,

7450-406: The medieval universities commonly advanced evidence in favor of the idea that the Earth was a sphere. Jill Tattersall shows that in many vernacular works in 12th- and 13th-century French texts the Earth was considered "round like a table" rather than "round like an apple". She writes, "[I]n virtually all the examples quoted ... from epics and from non-'historical' romances (that is, works of

7599-404: The politics of Miletus and was sent as a leader to one of its colonies. Anaximander, son of Praxiades, was born in the third year of the 42nd Olympiad (610 BC). According to Apollodorus of Athens , Greek grammarian of the 2nd century BC, he was sixty-four years old during the second year of the 58th Olympiad (547–546 BC) and died shortly afterwards. Establishing a timeline of his work

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7748-415: The " intermediate " with the something " distinct from " the elements ." "It is certain that he [Anaximander] cannot have said anything about elements, which no one thought of before Empedokles, and no one could think of before Parmenides. The question has only been mentioned because it has given rise to a lengthy controversy, and because it throws light on the historical value of Aristotle's statements. From

7897-583: The "Infinite" with a "material cause", Theophrastos is following the Aristotelian tradition of "nearly always discussing the facts from the point of view of his own system". Aristotle writes ( Metaphysics , I.III 3–4) that the Pre-Socratics were searching for the element that constitutes all things. While each pre-Socratic philosopher gave a different answer as to the identity of this element ( water for Thales and air for Anaximenes), Anaximander understood

8046-421: The "immense ocean from which everything is born and upon which the Earth floats." Anaximander was then able to envisage the Earth at the centre of an infinite space, in which case it required no support as there was nowhere "down" to fall. In Rovelli's view, the shape – a cylinder or a sphere – is unimportant compared to the appreciation of a "finite body that floats free in space." Anaximander's realization that

8195-464: The 11th century from Arabic translations. Lucretius (1st century BC) opposed the concept of a spherical Earth, because he considered that an infinite universe had no center towards which heavy bodies would tend. Thus, he thought the idea of animals walking around topsy-turvy under the Earth was absurd. By the 1st century AD, Pliny the Elder was in a position to say that everyone agreed on the spherical shape of Earth, though disputes continued regarding

8344-433: The 13th-century scholar Li Ye , who argued that the movements of the round heaven would be hindered by a square Earth, did not advocate a spherical Earth, but rather that its edge should be rounded off so as to be circular. However, Needham disagrees, affirming that Li Ye believed the Earth to be spherical, similar in shape to the heavens but much smaller. This was preconceived by the 4th-century scholar Yu Xi , who argued for

8493-446: The 2010s at latest, believers in a flat earth have increased, both as membership in modern flat Earth societies , and as unaffiliated individuals using social media . In a 2018 study reported on by Scientific American , only 82% of 18 to 24 year old American respondents agreed with the statement "I have always believed the world is round". However, a firm belief in a flat Earth is rare, with less than 2% acceptance in all age groups. It

8642-649: The Boundless " intermediate between the elements " than to say that it is " distinct from the elements." Indeed, if once we introduce the elements at all, the former description is the more adequate of the two. At any rate, if we refuse to understand these passages as referring to Anaximander, we shall have to say that Aristotle paid a great deal of attention to some one whose very name has been lost, and who not only agreed with some of Anaximander's views, but also used some of his most characteristic expressions. We may add that in one or two places Aristotle certainly seems to identify

8791-509: The Chaldeans and the Egyptians" said: "Let us first lay bare ... the theory of the Chaldeans and the Egyptians. They say that the circumference of the universe is likened to the turnings of a well-rounded globe, the Earth being a central point. They say that since its outline is spherical, ... the Earth should be the center of the universe, around which the heaven is whirling." Lactantius ,

8940-512: The Earth (the Kai Tian theory), or like a sphere surrounding it (the Hun Tian theory), or as being without substance while the heavenly bodies float freely (the Hsüan yeh theory), the Earth was at all times flat, although perhaps bulging up slightly. The model of an egg was often used by Chinese astronomers such as Zhang Heng (78–139 AD) to describe the heavens as spherical: The heavens are like

9089-444: The Earth as a sphere each yield a mean radius of 6,371 km (3,959 mi). Regardless of the model, any radius falls between the polar minimum of about 6,357 km (3,950 mi) and the equatorial maximum of about 6,378 km (3,963 mi). The difference 21 km (13 mi) correspond to the polar radius being approximately 0.3% shorter than the equatorial radius. As theorized by Isaac Newton and Christiaan Huygens ,

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9238-430: The Earth as flat, and this perception remained unchanged until their encounters with Jesuit missionaries in the 17th century. Traditionalist Muslim scholars have maintained that the earth is flat, though, since the 9th century, Muslim scholars tended to believe in a spherical Earth. Despite the scientific facts and obvious effects of Earth's sphericity , pseudoscientific flat-Earth conspiracy theories persist, and from

9387-407: The Earth below the firmament and heaven above it. Carefully drawing on arguments from scripture, he describes the Earth as a rectangle, 400 days' journey long by 200 wide, surrounded by four oceans and enclosed by four massive walls which support the firmament. The spherical Earth theory is contemptuously dismissed as "pagan". Severian , Bishop of Gabala ( d. 408), wrote that the Earth is flat and

9536-407: The Earth floats free without falling and does not need to be resting on something has been indicated by many as the first cosmological revolution and the starting point of scientific thinking. Karl Popper calls this idea "one of the boldest, most revolutionary, and most portentous ideas in the whole history of human thinking." Such a model allowed the concept that celestial bodies could pass under

9685-402: The Earth is flattened at the poles and bulged at the equator . Thus, geodesy represents the figure of the Earth as an oblate spheroid . The oblate spheroid, or oblate ellipsoid , is an ellipsoid of revolution obtained by rotating an ellipse about its shorter axis. It is the regular geometric shape that most nearly approximates the shape of the Earth. A spheroid describing the figure of

9834-419: The Earth or other celestial body is called a reference ellipsoid . The reference ellipsoid for Earth is called an Earth ellipsoid . An ellipsoid of revolution is uniquely defined by two quantities. Several conventions for expressing the two quantities are used in geodesy, but they are all equivalent to and convertible with each other: Eccentricity and flattening are different ways of expressing how squashed

9983-406: The Earth's mass attraction ( gravitation ) and the centrifugal force of the Earth's rotation . As a result of the uneven distribution of the Earth's mass, the geoidal surface is irregular and, since the ellipsoid is a regular surface, the separations between the two, referred to as geoid undulations , geoid heights, or geoid separations, will be irregular as well. The geoid is a surface along which

10132-497: The Earth, opening the way to Greek astronomy. Rovelli suggests that seeing the stars circling the Pole star , and both vanishing below the horizon on one side and reappearing above it on the other, would suggest to the astronomer that there was a void both above and below the Earth. Anaximander's bold use of non- mythological explanatory hypotheses considerably distinguishes him from previous cosmology writers such as Hesiod . It indicates

10281-483: The Earth, or in (another) sun and moon there, thou art to hold a council, deprive him of his sacerdotal rank, and expel him from the Church. Some authorities have suggested that the sphericity of the Earth was among the aspects of Vergilius's teachings that Boniface and Zachary considered objectionable. Others have considered this unlikely, and take the wording of Zachary's response to indicate at most an objection to belief in

10430-473: The Earth-circle is round like a ball and not equally near the sun at every point. But where the curved surface lies nearest the sun's path, there will the greatest heat be; and some of the lands that lie continuously under the unbroken rays cannot be inhabited. In ancient China , the prevailing belief was that the Earth was flat and square, while the heavens were round, an assumption virtually unquestioned until

10579-587: The Mediterranean Sea and Black Sea. Second, Thales would probably have found it easier to convince the Ionian city-states to join in a federation in order to push the Median threat away if he possessed such a tool. Finally, the philosophical idea of a global representation of the world simply for the sake of knowledge was reason enough to design one. Surely aware of the sea's convexity, he may have designed his map on

10728-494: The Near East, especially Babylon. All these were developed rationally. In his desire to find some universal principle, he assumed, like traditional religion, the existence of a cosmic order; and his ideas on this used the old language of myths which ascribed divine control to various spheres of reality. This was a common practice for the Greek philosophers in a society which saw gods everywhere, and therefore could fit their ideas into

10877-665: The South Pole. The polar asymmetry is about a thousand times smaller than the Earth's flattening and even smaller than its geoidal undulation in some regions. Modern geodesy tends to retain the ellipsoid of revolution as a reference ellipsoid and treat triaxiality and pear shape as a part of the geoid figure: they are represented by the spherical harmonic coefficients C 22 , S 22 {\displaystyle C_{22},S_{22}} and C 30 {\displaystyle C_{30}} , respectively, corresponding to degree and order numbers 2.2 for

11026-509: The Sun does not pass under it in the night, but "travels through the northern parts as if hidden by a wall". Basil of Caesarea (329–379) argued that the matter was theologically irrelevant. Early medieval Christian writers felt little urge to assume flatness of the Earth, though they had fuzzy impressions of the writings of Ptolemy and Aristotle, relying more on Pliny. With the end of the Western Roman Empire , Western Europe entered

11175-409: The Sun orbits the Earth and illuminates the other side when it is night on this side. See French translation of De Natura Rerum . In his other work Etymologies , there are also affirmations that the sphere of the sky has Earth in its center and the sky being equally distant on all sides. Other researchers have argued these points as well. "The work remained unsurpassed until the thirteenth century and

11324-561: The accuracy of the figure of the Earth. The primary utility of this improved accuracy was to provide geographical and gravitational data for the inertial guidance systems of ballistic missiles . This funding also drove the expansion of geoscientific disciplines, fostering the creation and growth of various geoscience departments at many universities. These developments benefited many civilian pursuits as well, such as weather and communication satellite control and GPS location-finding, which would be impossible without highly accurate models for

11473-413: The air because of their flatness". Xenophanes (c. 500 BC) thought that the Earth was flat, with its upper side touching the air, and the lower side extending without limit. Belief in a flat Earth continued into the 5th century BC. Anaxagoras (c. 450 BC) agreed that the Earth was flat, and his pupil Archelaus believed that the flat Earth was depressed in the middle like a saucer, to allow for

11622-580: The angle of the North Star , which he incorrectly interpreted as having varying diurnal motion . The theory of a slightly pear-shaped Earth arose when data was received from the U.S.'s artificial satellite Vanguard 1 in 1958. It was found to vary in its long periodic orbit, with the Southern Hemisphere exhibiting higher gravitational attraction than the Northern Hemisphere. This indicated

11771-441: The assembly of demos in the agora which is lying in the middle of the city. The same rational way of thought led him to introduce the abstract apeiron (indefinite, infinite, boundless, unlimited ) as an origin of the universe, a concept that is probably influenced by the original Chaos (gaping void, abyss, formless state) from which everything else appeared in the mythical Greek cosmogony . It also takes notice of

11920-429: The basis of physical theory and observational evidence that the Earth was spherical, and reported an estimate of its circumference . The Earth's circumference was first determined around 240 BC by Eratosthenes . By the 2nd century AD, Ptolemy had derived his maps from a globe and developed the system of latitude , longitude , and climes . His Almagest was written in Greek and only translated into Latin in

12069-406: The beginning or first principle to be an endless, unlimited primordial mass ( apeiron ), subject to neither old age nor decay, that perpetually yielded fresh materials from which everything we perceive is derived. He proposed the theory of the apeiron in direct response to the earlier theory of his teacher, Thales, who had claimed that the primary substance was water. The notion of temporal infinity

12218-497: The circular surface of the Earth, is the begetter of all life and possibly of all gods." The Pyramid Texts and Coffin Texts of ancient Egypt show a similar cosmography; Nun (the Ocean) encircled nbwt ("dry lands" or "Islands"). The Israelites also imagined the Earth to be a disc floating on water with an arched firmament above it that separated the Earth from the heavens. The sky was

12367-451: The cosmic order is not monarchic but geometric , and that this causes the equilibrium of the Earth, which is lying in the centre of the universe. This is the projection on nature of a new political order and a new space organized around a centre which is the static point of the system in the society as in nature. In this space there is isonomy (equal rights) and all the forces are symmetrical and transferable. The decisions are now taken by

12516-679: The countless worlds. This theory places Anaximander close to the Atomists and the Epicureans who, more than a century later, also claimed that an infinity of worlds appeared and disappeared. In the timeline of the Greek history of thought , some thinkers conceptualized a single world (Plato, Aristotle, Anaxagoras and Archelaus ), while others instead speculated on the existence of a series of worlds, continuous or non-continuous ( Anaximenes , Heraclitus , Empedocles and Diogenes ). Anaximander attributed some phenomena, such as thunder and lightning, to

12665-472: The discovery that the Earth had a significant third degree zonal spherical harmonic in its gravitational field using Vanguard 1 satellite data. Based on further satellite geodesy data, Desmond King-Hele refined the estimate to a 45 m (148 ft) difference between north and south polar radii, owing to a 19 m (62 ft) "stem" rising in the North Pole and a 26 m (85 ft) depression in

12814-496: The distance of the Sun by measuring the length of noontime shadows at different latitudes, a method similar to Eratosthenes' measurement of the circumference of the Earth, but the Zhoubi Suanjing assumes that the Earth is flat. Pythagoras in the 6th century BC and Parmenides in the 5th century BC stated that the Earth is spherical , and this view spread rapidly in the Greek world. Around 330 BC, Aristotle maintained on

12963-593: The element of origin was often revisited afterwards, notably by Aristotle, and by the Greek tragedian Euripides : "what comes from earth must return to earth." Friedrich Nietzsche , in his Philosophy in the Tragic Age of the Greeks , stated that Anaximander viewed "... all coming-to-be as though it were an illegitimate emancipation from eternal being, a wrong for which destruction is the only penance." Physicist Max Born , in commenting upon Werner Heisenberg 's arriving at

13112-407: The elements arise.'⁠—Aristotle Physics. F, 5 204 b 22 (Ritter and Preller (1898) Historia Philosophiae Graecae, section 16 b)." Anaximander maintains that all dying things are returning to the element from which they came ( apeiron ). The one surviving fragment of Anaximander's writing deals with this matter. Simplicius transmitted it as a quotation, which describes the balanced and mutual changes of

13261-439: The elements: Whence things have their origin, Thence also their destruction happens, According to necessity; For they give to each other justice and recompense For their injustice In conformity with the ordinance of Time. Simplicius mentions that Anaximander said all these "in poetic terms", meaning that he used the old mythical language. The goddess Justice ( Dike ) keeps the cosmic order. This concept of returning to

13410-559: The ellipsoid in the vicinity of a given point is the Earth's osculating sphere . Its radius equals Earth's Gaussian radius of curvature , and its radial direction coincides with the geodetic normal direction. The center of the osculating sphere is offset from the center of the ellipsoid, but is at the center of curvature for the given point on the ellipsoid surface. This concept aids the interpretation of terrestrial and planetary radio occultation refraction measurements and in some navigation and surveillance applications. Determining

13559-451: The ellipsoid is. When flattening appears as one of the defining quantities in geodesy, generally it is expressed by its reciprocal. For example, in the WGS 84 spheroid used by today's GPS systems, the reciprocal of the flattening 1 / f {\displaystyle 1/f} is set to be exactly 298.257 223 563 . The difference between a sphere and a reference ellipsoid for Earth

13708-539: The encircling ocean is repeated far later in Quintus Smyrnaeus ' Posthomerica (4th century AD), which continues the narration of the Trojan War. Several pre-Socratic philosophers believed that the world was flat: Thales (c. 550 BC) according to several sources, and Leucippus (c. 440 BC) and Democritus (c. 460–370 BC) according to Aristotle. Thales thought that the Earth floated in water like

13857-443: The equator r e {\displaystyle r_{e}} is smaller than the polar where a {\displaystyle a} is the distance from the center of the ellipsoid to the equator (semi-major axis), and b {\displaystyle b} is the distance from the center to the pole. (semi-minor axis) The possibility that the Earth's equator is better characterized as an ellipse rather than

14006-405: The exact figure of the Earth is not only a geometric task of geodesy, but also has geophysical considerations. According to theoretical arguments by Newton, Leonhard Euler , and others, a body having a uniform density of 5,515 kg/m that rotates like the Earth should have a flattening of 1:229. This can be concluded without any information about the composition of Earth's interior . However,

14155-465: The existence of humans living in the antipodes. In any case, there is no record of any further action having been taken against Vergilius. He was later appointed bishop of Salzburg and was canonised in the 13th century. A possible non-literary but graphic indication that people in the Middle Ages believed that the Earth (or perhaps the world) was a sphere is the use of the orb ( globus cruciger ) in

14304-399: The explorers travelled. Its position directly overhead at noon gave evidence for crossing the equator. These apparent solar motions in detail were more consistent with north–south curvature and a distant Sun, than with any flat-Earth explanation. The ultimate demonstration came when Ferdinand Magellan's expedition completed the first global circumnavigation in 1521. Antonio Pigafetta , one of

14453-432: The fact that the Sun does not rise and set at the same time for everyone. Hecataeus of Miletus believed that the Earth was flat and surrounded by water. Herodotus in his Histories ridiculed the belief that water encircled the world, yet most classicists agree that he still believed Earth was flat because of his descriptions of literal "ends" or "edges" of the Earth. The ancient Norse and Germanic peoples believed in

14602-461: The few survivors of the voyage, recorded the loss of a day in the course of the voyage, giving evidence for east–west curvature. Figure of the Earth In geodesy , the figure of the Earth is the size and shape used to model planet Earth . The kind of figure depends on application, including the precision needed for the model. A spherical Earth is a well-known historical approximation that

14751-400: The figure of the Earth. The models for the figure of the Earth vary in the way they are used, in their complexity, and in the accuracy with which they represent the size and shape of the Earth. The simplest model for the shape of the entire Earth is a sphere. The Earth's radius is the distance from Earth's center to its surface, about 6,371 km (3,959 mi). While "radius" normally

14900-456: The figure of the universe." Arnobius , another eastern Christian writing sometime around 305 AD, described the round Earth: "In the first place, indeed, the world itself is neither right nor left. It has neither upper nor lower regions, nor front nor back. For whatever is round and bounded on every side by the circumference of a solid sphere, has no beginning or end ..." The influential theologian and philosopher Saint Augustine , one of

15049-521: The first Greek philosophers believed made up the universe in fact represent the primordial forces imagined in earlier ways of thinking. Their collision produced what the mythical tradition had called cosmic harmony. In the old cosmogonies – Hesiod (8th – 7th century BC) and Pherecydes (6th century BC) – Zeus establishes his order in the world by destroying the powers which were threatening this harmony (the Titans ). Anaximander claimed that

15198-574: The first to introduce this name of the material cause. He says it is neither water nor any other of the so-called elements, but a substance different from them which is infinite" [apeiron, or ἄπειρον ] "from which arise all the heavens and the worlds within them.—Phys, Op. fr. 2 (Dox. p. 476; R. P. 16)." Burnet's quote from the "First Book" is his translation of Theophrastos' Physic Opinion fragment 2 as it appears in p. 476 of Historia Philosophiae Graecae (1898) by Ritter and Preller and section 16 of Doxographi Graeci (1879) by Diels. By ascribing

15347-526: The flat-Earth model. In the early 4th century BC, Plato wrote about a spherical Earth. By about 330 BC, his former student Aristotle had provided strong empirical evidence for a spherical Earth. Knowledge of the Earth's global shape gradually began to spread beyond the Hellenistic world . By the early period of the Christian Church, the spherical view was widely held, with some notable exceptions. In contrast, ancient Chinese scholars consistently describe

15496-494: The four Great Church Fathers of the Western Church , similarly objected to the "fable" of antipodes: But as to the fable that there are Antipodes, that is to say, men on the opposite side of the Earth, where the sun rises when it sets to us, men who walk with their feet opposite ours that is on no ground credible. And, indeed, it is not affirmed that this has been learned by historical knowledge, but by scientific conjecture, on

15645-526: The geographer Eratosthenes , Anaximander was the first to publish a map of the world . The map probably inspired the Greek historian Hecataeus of Miletus to draw a more accurate version. Strabo viewed both as the first geographers after Homer . Maps were produced in ancient times, also notably in Egypt , Lydia , the Middle East , and Babylon . Only some small examples survived until today. The unique example of

15794-481: The geoid. The angle between the plumb line which is perpendicular to the geoid (sometimes called "the vertical") and the perpendicular to the ellipsoid (sometimes called "the ellipsoidal normal") is defined as the deflection of the vertical . It has two components: an east–west and a north–south component. Simpler local approximations are possible. The local tangent plane is appropriate for analysis across small distances. The best local spherical approximation to

15943-467: The gnomon itself cannot be attributed to Anaximander because its use, as well as the division of days into twelve parts, came from the Babylonians . It is they, according to Herodotus ' Histories (II, 109), who gave the Greeks the art of time measurement. It is likely that he was not the first to determine the solstices, because no calculation is necessary. On the other hand, equinoxes do not correspond to

16092-402: The gravity potential is equal everywhere and to which the direction of gravity is always perpendicular. The latter is particularly important because optical instruments containing gravity-reference leveling devices are commonly used to make geodetic measurements. When properly adjusted, the vertical axis of the instrument coincides with the direction of gravity and is, therefore, perpendicular to

16241-479: The ground that the Earth is suspended within the concavity of the sky, and that it has as much room on the one side of it as on the other: hence they say that the part that is beneath must also be inhabited. But they do not remark that, although it be supposed or scientifically demonstrated that the world is of a round and spherical form, yet it does not follow that the other side of the Earth is bare of water; nor even, though it be bare, does it immediately follow that it

16390-421: The idea that humans had to spend part of this transition inside the mouths of big fish to protect themselves from the Earth's climate until they could come out in open air and lose their scales. He thought that, considering humans' extended infancy, we could not have survived in the primeval world in the same manner we do presently. Both Strabo and Agathemerus (later Greek geographers) claim that, according to

16539-426: The idea that the elementary particles of quantum mechanics are to be seen as different manifestations, different quantum states, of one and the same "primordial substance,"' proposed that this primordial substance be called apeiron . Anaximander was the first to conceive a mechanical model of the world. In his model, the Earth floats very still in the centre of the infinite, not supported by anything. It remains "in

16688-415: The infinity of outer space surrounding the Earth and that the latter could be either square or round, in accordance to the shape of the heavens. When Chinese geographers of the 17th century, influenced by European cartography and astronomy, showed the Earth as a sphere that could be circumnavigated by sailing around the globe, they did so with formulaic terminology previously used by Zhang Heng to describe

16837-420: The intervention of elements, rather than to divine causes. In his system, thunder results from the shock of clouds hitting each other; the loudness of the sound is proportionate with that of the shock. Thunder without lightning is the result of the wind being too weak to emit any flame, but strong enough to produce a sound. A flash of lightning without thunder is a jolt of the air that disperses and falls, allowing

16986-466: The introduction of European astronomy in the 17th century. The English sinologist Cullen emphasizes the point that there was no concept of a round Earth in ancient Chinese astronomy: Chinese thought on the form of the Earth remained almost unchanged from early times until the first contacts with modern science through the medium of Jesuit missionaries in the seventeenth century. While the heavens were variously described as being like an umbrella covering

17135-414: The larger semidiameter pointing to 15° W longitude (and also 180-degree away). Following work by Picard, Italian polymath Giovanni Domenico Cassini found that the length of a degree was apparently shorter north of Paris than to the south, implying the Earth to be egg -shaped. In 1498, Christopher Columbus dubiously suggested that the Earth was pear-shaped based on his disparate mobile readings of

17284-496: The lunar wheel, whose fire was less intense, eighteen (or nineteen) times. Its hole could change shape, thus explaining lunar phases . The stars and the planets, located closer, followed the same model. Anaximander was the first astronomer to consider the Sun as a huge mass, and consequently, to realize how far from Earth it might be, and the first to present a system where the celestial bodies turned at different distances. Furthermore, according to Diogenes Laertius (II, 2), he built

17433-428: The measured flattening is 1:298.25, which is closer to a sphere and a strong argument that Earth's core is extremely compact. Therefore, the density must be a function of the depth, ranging from 2,600 kg/m at the surface (rock density of granite , etc.), up to 13,000 kg/m within the inner core. Also with implications for the physical exploration of the Earth's interior is the gravitational field , which

17582-458: The measurement of time and associates him with the introduction in Greece of the gnomon. In Lacedaemon , he participated in the construction, or at least in the adjustment, of sundials to indicate solstices and equinoxes . Indeed, a gnomon required adjustments from a place to another because of the difference in latitude . In his time, the gnomon was simply a vertical pillar or rod mounted on

17731-463: The mechanics of celestial bodies in relation to the Earth. In physics, his postulation that the indefinite (or apeiron ) was the source of all things, led Greek philosophy to a new level of conceptual abstraction . His knowledge of geometry allowed him to introduce the gnomon in Greece. He created a map of the world that contributed greatly to the advancement of geography . Anaximander was involved in

17880-561: The middle of the 8th century, discussed or taught some geographical or cosmographical ideas that St Boniface found sufficiently objectionable that he complained about them to Pope Zachary . The only surviving record of the incident is contained in Zachary's reply, dated 748, where he wrote: As for the perverse and sinful doctrine which he (Virgil) against God and his own soul has uttered – if it shall be clearly established that he professes belief in another world and other men existing beneath

18029-502: The middle point between the positions during solstices, as the Babylonians thought. As the Suda seems to suggest, it is very likely that with his knowledge of geometry, he became the first Greek to determine accurately the equinoxes. In his philosophical work De Divinatione (I, 50, 112), Cicero states that Anaximander convinced the inhabitants of Lacedaemon to abandon their city and spend

18178-439: The mutual changes between the four elements. Origin, then, must be something else unlimited in its source, that could create without experiencing decay, so that genesis would never stop. The Refutation attributed to Hippolytus of Rome (I, 5), and the later 6th century Byzantine philosopher Simplicius of Cilicia , attribute to Anaximander the earliest use of the word apeiron ( ἄπειρον "infinite" or "limitless") to designate

18327-470: The nature of the antipodes , and how it is possible to keep the ocean in a curved shape. The Vedic texts depict the cosmos in many ways. One of the earliest Indian cosmological texts pictures the Earth as one of a stack of flat disks. In the Vedic texts, Dyaus (heaven) and Prithvi (Earth) are compared to wheels on an axle , yielding a flat model. They are also described as bowls or leather bags, yielding

18476-467: The opposites found in nature — for example, water can only be wet, never dry — and therefore cannot be the one primary substance; nor could any of the other candidates. He postulated the apeiron as a substance that, although not directly perceptible to us, could explain the opposites he saw around him. "If Thales had been right in saying that water was the fundamental reality, it would not be easy to see how anything else could ever have existed. One side of

18625-650: The opposition, the cold and moist, would have had its way unchecked, and the warm and dry would have been driven from the field long ago. We must, then, have something not itself one of the warring opposites, something more primitive, out of which they arise, and into which they once more pass away." Anaximander explains how the four elements of ancient physics ( air , earth , water and fire ) are formed, and how Earth and terrestrial beings are formed through their interactions. Unlike other Pre-Socratics, he never defines this principle precisely, and it has generally been understood (e.g., by Aristotle and by Saint Augustine ) as

18774-431: The original principle. He was the first philosopher to employ, in a philosophical context, the term archē ( ἀρχή ), which until then had meant beginning or origin. "That Anaximander called this something by the name of Φύσις is the natural interpretation of what Theophrastos says; the current statement that the term ἀρχή was introduced by him appears to be due to a misunderstanding." And "Hippolytos, however,

18923-633: The point of view of his own system, these may be justified; but we shall have to remember in other cases that, when he seems to attribute an idea to some earlier thinker, we are not bound to take what he says in an historical sense." For Anaximander, the principle of things, the constituent of all substances, is nothing determined and not an element such as water in Thales' view. Neither is it something halfway between air and water, or between air and fire, thicker than air and fire, or more subtle than water and earth. Anaximander argues that water cannot embrace all of

19072-452: The primary substance could be one of these particular things. His argument seems to be preserved by Aristotle, who has the following passage in his discussion of the Infinite: "Further, there cannot be a single, simple body which is infinite, either, as some hold, one distinct from the elements, which they then derive from it, or without this qualification. For there are some who make this. (i.e.

19221-411: The radius of the Earth was given by Eratosthenes about 240 BC, with estimates of the accuracy of Eratosthenes's measurement ranging from −1% to 15%. The Earth is only approximately spherical, so no single value serves as its natural radius. Distances from points on the surface to the center range from 6,353 km (3,948 mi) to 6,384 km (3,967 mi). Several different ways of modeling

19370-675: The regalia of many kingdoms and of the Holy Roman Empire. It is attested from the time of the Christian late-Roman emperor Theodosius II (423) throughout the Middle Ages; the Reichsapfel was used in 1191 at the coronation of emperor Henry VI . However the word orbis means "circle", and there is no record of a globe as a representation of the Earth since ancient times in the west until that of Martin Behaim in 1492. Additionally it could well be

19519-404: The room be quite large. But if you take an apple and hang it close to the flame, so near that it is heated, the apple will darken nearly half the room or even more. However, if you hang the apple near the wall, it will not get hot; the candle will light up the whole house; and the shadow on the wall where the apple hangs will be scarcely half as large as the apple itself. From this you may infer that

19668-495: The same place because of its indifference", a point of view that Aristotle considered ingenious, in On the Heavens . Its curious shape is that of a cylinder with a height one-third of its diameter. The flat top forms the inhabited world. Carlo Rovelli suggests that Anaximander took the idea of the Earth's shape as a floating disk from Thales , who had imagined the Earth floating in water,

19817-516: The sea long ago, born trapped in a spiny bark, but as they got older, the bark would dry up and animals would be able to break it. The 3rd century Roman writer Censorinus reports: Anaximander of Miletus considered that from warmed up water and earth emerged either fish or entirely fishlike animals. Inside these animals, men took form and embryos were held prisoners until puberty; only then, after these animals burst open, could men and women come out, now able to feed themselves. Anaximander put forward

19966-408: The sea, when they had formed and made firm the Earth together, and laid the sea in a ring round. about her; and it may well seem a hard thing to most men to cross over it." The late Norse Konungs skuggsjá , on the other hand, explains Earth's shape as a sphere: If you take a lighted candle and set it in a room, you may expect it to light up the entire interior, unless something should hinder, though

20115-443: The seasons. The doxographer and theologian Aetius attributes to Pythagoras the exact measurement of the obliquity. According to Simplicius, Anaximander already speculated on the plurality of worlds , similar to atomists Leucippus and Democritus , and later philosopher Epicurus . These thinkers supposed that worlds appeared and disappeared for a while, and that some were born when others perished. They claimed that this movement

20264-412: The seventeenth century; this surprising fact might be the starting-point for a re-examination of the apparent facility with which the idea of a spherical Earth found acceptance in fifth-century BC Greece. Further examples cited by Needham supposed to demonstrate dissenting voices from the ancient Chinese consensus actually refer without exception to the Earth being square, not to it being flat. Accordingly,

20413-403: The shape of the Earth if they considered the question at all. Hermann of Reichenau (1013–1054) was among the earliest Christian scholars to estimate the circumference of Earth with Eratosthenes ' method. Thomas Aquinas (1225–1274), the most widely taught theologian of the Middle Ages, believed in a spherical Earth and took for granted that his readers also knew the Earth is round. Lectures in

20562-417: The size and shape of the Earth in the area of the survey. The actual measurements made on the surface of the Earth with certain instruments are however referred to the geoid. The ellipsoid is a mathematically defined regular surface with specific dimensions. The geoid, on the other hand, coincides with that surface to which the oceans would conform over the entire Earth if free to adjust to the combined effect of

20711-481: The spherical shape of the Sun and Moon (i.e. that they were as round as a crossbow bullet). As noted in the book Huainanzi , in the 2nd century BC, Chinese astronomers effectively inverted Eratosthenes ' calculation of the curvature of the Earth to calculate the height of the Sun above the Earth. By assuming the Earth was flat, they arrived at a distance of 100 000   li (approximately 200 000  km ). The Zhoubi Suanjing also discusses how to determine

20860-580: The stars were nearest to the Earth, then the Moon, and the Sun farthest away. His scheme is compatible with the Indo-Iranian philosophical traditions contained in the Iranian Avesta and the Indian Upanishads . At the origin, after the separation of hot and cold, a ball of flame appeared that surrounded Earth like bark on a tree. This ball broke apart to form the rest of the Universe. It resembled

21009-562: The subsurface. [REDACTED] This article incorporates text from this source, which is in the public domain : Defense Mapping Agency (1983). Geodesy for the Layman (Report). United States Air Force. Anaximander Little of his life and work is known today. According to available historical documents, he is the first philosopher known to have written down his studies, although only one fragment of his work remains. Fragmentary testimonies found in documents after his death provide

21158-442: The triaxiality and 3.0 for the pear shape. It was stated earlier that measurements are made on the apparent or topographic surface of the Earth and it has just been explained that computations are performed on an ellipsoid. One other surface is involved in geodetic measurement: the geoid. In geodetic surveying, the computation of the geodetic coordinates of points is commonly performed on a reference ellipsoid closely approximating

21307-488: The view that Augustine shared the common view of his contemporaries that the Earth is spherical, in line with his endorsement of science in De Genesi ad litteram . C. P. E. Nothaft, responding to writers like Leo Ferrari who described Augustine as endorsing a flat Earth, says that "...other recent writers on the subject treat Augustine’s acceptance of the earth’s spherical shape as a well-established fact". Diodorus of Tarsus ,

21456-579: The western part of Europe. Europe's view of the shape of the Earth in Late Antiquity and the Early Middle Ages may be best expressed by the writings of early Christian scholars: Bishop Isidore of Seville (560–636) taught in his widely read encyclopedia, the Etymologies , diverse views such as that the Earth "resembles a wheel" resembling Anaximander in language and the map that he provided. This

21605-445: Was eternal, "for without movement, there can be no generation, no destruction". In addition to Simplicius, Hippolytus reports Anaximander's claim that from the infinite comes the principle of beings, which themselves come from the heavens and the worlds (several doxographers use the plural when this philosopher is referring to the worlds within, which are often infinite in quantity). Cicero writes that he attributes different gods to

21754-410: Was familiar to the Greek mind from remote antiquity in the religious concept of immortality, and Anaximander's description was in terms appropriate to this conception. This archē is called "eternal and ageless". (Hippolytus (?), Refutation , I,6,I;DK B2) " Aristotle puts things in his own way regardless of historical considerations, and it is difficult to see that it is more of an anachronism to call

21903-487: Was no evidence for their existence. Isidore's T and O map , which was seen as representing a small part of a spherical Earth, continued to be used by authors through the Middle Ages, e.g. the 9th-century bishop Rabanus Maurus , who compared the habitable part of the northern hemisphere ( Aristotle 's northern temperate clime) with a wheel. At the same time, Isidore's works also gave the views of sphericity, for example, in chapter 28 of De Natura Rerum , Isidore claims that

22052-715: Was regarded as the summit of all knowledge. It became an essential part of European medieval culture. Soon after the invention of typography it appeared many times in print." However, "The Scholastics – later medieval philosophers, theologians, and scientists – were helped by the Arabic translators and commentaries, but they hardly needed to struggle against a flat-Earth legacy from the early middle ages (500–1050). Early medieval writers often had fuzzy and imprecise impressions of both Ptolemy and Aristotle and relied more on Pliny, but they felt (with one exception), little urge to assume flatness." St Vergilius of Salzburg (c. 700–784), in

22201-480: Was widely interpreted as referring to a disc-shaped Earth. An illustration from Isidore's De Natura Rerum shows the five zones of the Earth as adjacent circles. Some have concluded that he thought the Arctic and Antarctic zones were adjacent to each other. He did not admit the possibility of antipodes, which he took to mean people dwelling on the opposite side of the Earth, considering them legendary and noting that there

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