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The history of
geodesy Geodesy or geodetics is the science of measuring and representing the Figure of the Earth, geometry, Gravity of Earth, gravity, and Earth's rotation, spatial orientation of the Earth in Relative change, temporally varying Three-dimensional spac ...
( /dʒiːˈɒdɪsi/) began during antiquity and ultimately blossomed during the
Age of Enlightenment The Age of Enlightenment (also the Age of Reason and the Enlightenment) was a Europe, European Intellect, intellectual and Philosophy, philosophical movement active from the late 17th to early 19th century. Chiefly valuing knowledge gained th ...
. Many early conceptions of the Earth held it to be flat, 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
Polaris Polaris is a star in the northern circumpolar constellation of Ursa Minor. It is designated α Ursae Minoris (Latinisation of names, Latinized to ''Alpha Ursae Minoris'') and is commonly called the North Star or Pole Star. With an ...
is seen lower in the sky as one travels southward.


Hellenic world


Initial developments

Though the earliest written mention of a spherical Earth comes from
ancient Greek Ancient Greek (, ; ) includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Greek ...
sources, there is no account of how the sphericity of Earth was discovered, or if it was initially simply a guess.James Evans, (1998), ''The History and Practice of Ancient Astronomy'', page 47, Oxford University Press A plausible explanation given by the historian Otto E. Neugebauer is that it was "the experience of travellers that suggested such an explanation for the variation in the observable
altitude Altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum (geodesy), datum and a point or object. The exact definition and reference datum varies according to the context (e.g., aviation, geometr ...
of the pole and the change in the area of circumpolar stars, a change that was quite drastic between Greek settlements" around the eastern
Mediterranean Sea The Mediterranean Sea ( ) is a sea connected to the Atlantic Ocean, surrounded by the Mediterranean basin and almost completely enclosed by land: on the east by the Levant in West Asia, on the north by Anatolia in West Asia and Southern Eur ...
, particularly those between the
Nile Delta The Nile Delta (, or simply , ) is the River delta, delta formed in Lower Egypt where the Nile River spreads out and drains into the Mediterranean Sea. It is one of the world's larger deltas—from Alexandria in the west to Port Said in the eas ...
and
Crimea Crimea ( ) is a peninsula in Eastern Europe, on the northern coast of the Black Sea, almost entirely surrounded by the Black Sea and the smaller Sea of Azov. The Isthmus of Perekop connects the peninsula to Kherson Oblast in mainland Ukrain ...
. Another possible explanation can be traced back to earlier
Phoenicia Phoenicians were an Ancient Semitic-speaking peoples, ancient Semitic group of people who lived in the Phoenician city-states along a coastal strip in the Levant region of the eastern Mediterranean, primarily modern Lebanon and the Syria, Syrian ...
n sailors. The first
circumnavigation Circumnavigation is the complete navigation around an entire island, continent, or astronomical object, astronomical body (e.g. a planet or natural satellite, moon). This article focuses on the circumnavigation of Earth. The first circumnaviga ...
of
Africa Africa is the world's second-largest and second-most populous continent after Asia. At about 30.3 million km2 (11.7 million square miles) including adjacent islands, it covers 20% of Earth's land area and 6% of its total surfac ...
is described as being undertaken by Phoenician explorers employed by Egyptian pharaoh
Necho II Necho II (sometimes Nekau, Neku, Nechoh, or Nikuu; Greek: Νεκώς Β'; ) of Egypt was a king of the 26th Dynasty (610–595 BC), which ruled from Sais. Necho undertook a number of construction projects across his kingdom. In his reign, accor ...
. In ''The Histories'', written 431–425 BC,
Herodotus Herodotus (; BC) was a Greek historian and geographer from the Greek city of Halicarnassus (now Bodrum, Turkey), under Persian control in the 5th century BC, and a later citizen of Thurii in modern Calabria, Italy. He wrote the '' Histori ...
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 ( ''The Histories'', 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
Parmenides Parmenides of Elea (; ; fl. late sixth or early fifth century BC) was a Pre-Socratic philosophy, pre-Socratic ancient Greece, Greek philosopher from Velia, Elea in Magna Graecia (Southern Italy). Parmenides was born in the Greek colony of Veli ...
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. Speculation and theorizing ranged from the flat disc advocated by
Homer Homer (; , ; possibly born ) was an Ancient Greece, Ancient Greek poet who is credited as the author of the ''Iliad'' and the ''Odyssey'', two epic poems that are foundational works of ancient Greek literature. Despite doubts about his autho ...
to the spherical body reportedly postulated by
Pythagoras Pythagoras of Samos (;  BC) was an ancient Ionian Greek philosopher, polymath, and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of P ...
. Anaximenes, an early Greek philosopher, believed strongly that the Earth was rectangular in shape. Some early Greek philosophers alluded to a spherical Earth, though with some ambiguity.
Pythagoras Pythagoras of Samos (;  BC) was an ancient Ionian Greek philosopher, polymath, and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of P ...
(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
sphere A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...
, but there is no evidence for this claim. Some idea of the sphericity of Earth seems to have been known to both
Parmenides Parmenides of Elea (; ; fl. late sixth or early fifth century BC) was a Pre-Socratic philosophy, pre-Socratic ancient Greece, Greek philosopher from Velia, Elea in Magna Graecia (Southern Italy). Parmenides was born in the Greek colony of Veli ...
and
Empedocles Empedocles (; ; , 444–443 BC) was a Ancient Greece, Greek pre-Socratic philosopher and a native citizen of Akragas, a Greek city in Sicily. Empedocles' philosophy is known best for originating the Cosmogony, cosmogonic theory of the four cla ...
in the 5th century BC, Charles H. Kahn, (2001), ''Pythagoras and the Pythagoreans: a brief history'', page 53. Hackett and although the idea cannot reliably be ascribed to Pythagoras, it might nevertheless have been formulated in the Pythagorean school 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
Aristotle Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...
. Efforts commenced to determine the size of the sphere.


Plato

Plato Plato ( ; Greek language, Greek: , ; born  BC, died 348/347 BC) was an ancient Greek philosopher of the Classical Greece, Classical period who is considered a foundational thinker in Western philosophy and an innovator of the writte ...
(427–347 BC) travelled to southern
Italy Italy, officially the Italian Republic, is a country in Southern Europe, Southern and Western Europe, Western Europe. It consists of Italian Peninsula, a peninsula that extends into the Mediterranean Sea, with the Alps on its northern land b ...
to study Pythagorean mathematics. When he returned to
Athens Athens ( ) is the Capital city, capital and List of cities and towns in Greece, largest city of Greece. A significant coastal urban area in the Mediterranean, Athens is also the capital of the Attica (region), Attica region and is the southe ...
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 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 ''Timaeus'', 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.


Aristotle

Aristotle Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...
(384–322 BC) was Plato's prize student and "the mind of the school". Aristotle observed "there are
star A star is a luminous spheroid of plasma (physics), plasma held together by Self-gravitation, self-gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sk ...
s seen in
Egypt Egypt ( , ), officially the Arab Republic of Egypt, is a country spanning the Northeast Africa, northeast corner of Africa and Western Asia, southwest corner of Asia via the Sinai Peninsula. It is bordered by the Mediterranean Sea to northe ...
and ..
Cyprus Cyprus (), officially the Republic of Cyprus, is an island country in the eastern Mediterranean Sea. Situated in West Asia, its cultural identity and geopolitical orientation are overwhelmingly Southeast European. Cyprus is the List of isl ...
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". Aristotle reported the circumference of the Earth (which is actually slightly over 40,000 km or 24,000 miles) to be 400,000 stadia (45,000 miles or 74,000 km). Aristotle provided physical and observational arguments supporting the idea of a spherical Earth: * Every portion of Earth tends toward the centre until by compression and convergence they form a sphere. * Travelers going south see southern constellations rise higher above the horizon. * The shadow of Earth on the Moon during a
lunar eclipse A lunar eclipse is an astronomical event that occurs when the Moon moves into the Earth's shadow, causing the Moon to be darkened. Such an alignment occurs during an eclipse season, approximately every six months, during the full moon phase, ...
is round. The concepts of symmetry, equilibrium and cyclic repetition permeated Aristotle's work. In his ''Meteorology'' he divided the world into five climatic zones: two temperate areas separated by a torrid zone near the
equator The equator is the circle of latitude that divides Earth into the Northern Hemisphere, Northern and Southern Hemisphere, Southern Hemispheres of Earth, hemispheres. It is an imaginary line located at 0 degrees latitude, about in circumferen ...
, 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. Aristotle's theory of natural place relied on a spherical Earth to explain why heavy things go down (toward what Aristotle believed was the center of the Universe), and things like
air An atmosphere () is a layer of gases that envelop an astronomical object, held in place by the gravity of the object. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A stellar atmosph ...
and
fire Fire is the rapid oxidation of a fuel in the exothermic chemical process of combustion, releasing heat, light, and various reaction Product (chemistry), products. Flames, the most visible portion of the fire, are produced in the combustion re ...
go up. In this
geocentric model In astronomy, the geocentric model (also known as geocentrism, often exemplified specifically by the Ptolemaic system) is a superseded scientific theories, superseded description of the Universe with Earth at the center. Under most geocentric m ...
, 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
celestial spheres The celestial spheres, or celestial orbs, were the fundamental entities of the cosmological models developed by Plato, Eudoxus, Aristotle, Ptolemy, Copernicus, and others. In these celestial models, the apparent motions of the fixed star ...
around a stationary Earth. Though Aristotle's theory of physics survived in the Christian world for many centuries, the heliocentric model was eventually shown to be a more correct explanation of the
Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Sola ...
than the geocentric model, and
atomic theory Atomic theory is the scientific theory that matter is composed of particles called atoms. The definition of the word "atom" has changed over the years in response to scientific discoveries. Initially, it referred to a hypothetical concept of ...
was shown to be a more correct explanation of the nature of matter than
classical element The classical elements typically refer to Earth (classical element), earth, Water (classical element), water, Air (classical element), air, Fire (classical element), fire, and (later) Aether (classical element), aether which were proposed to ...
s like earth, water, air, fire, and aether.


Archimedes

Archimedes Archimedes of Syracuse ( ; ) was an Ancient Greece, Ancient Greek Greek mathematics, mathematician, physicist, engineer, astronomer, and Invention, inventor from the ancient city of Syracuse, Sicily, Syracuse in History of Greek and Hellenis ...
() gave an upper bound for the circumference of the Earth. In proposition 2 of the First Book of his treatise '' On Floating Bodies'', 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.


Eratosthenes

Eratosthenes Eratosthenes of Cyrene (; ;  – ) was an Ancient Greek polymath: a Greek mathematics, mathematician, geographer, poet, astronomer, and music theory, music theorist. He was a man of learning, becoming the chief librarian at the Library of A ...
(276–194 BC), a Hellenistic astronomer from what is now
Cyrene, Libya Cyrene, also sometimes anglicization of names, anglicized as Kyrene, was an ancient Greeks, ancient Greek Greek colonization, colony and ancient Romans, Roman Cities of the Roman Empire, city near present-day Shahhat in northeastern Libya in Nor ...
, working in
Alexandria, Egypt Alexandria ( ; ) is the List of cities and towns in Egypt#Largest cities, second largest city in Egypt and the List of coastal settlements of the Mediterranean Sea, largest city on the Mediterranean coast. It lies at the western edge of the Nile ...
, estimated
Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...
's circumference around 240 BC, computing a value of 252,000 '' stades''. 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 ''On the Measure of the Earth'', which has not been preserved. Eratosthenes could only measure the circumference of Earth by assuming that the distance to the Sun is so great that the rays of
sunlight Sunlight is the portion of the electromagnetic radiation which is emitted by the Sun (i.e. solar radiation) and received by the Earth, in particular the visible spectrum, visible light perceptible to the human eye as well as invisible infrare ...
are practically parallel. Eratosthenes's method to calculate the
Earth's circumference Earth's circumference is the distance around Earth. Measured around the equator, it is . Measured passing through the poles, the circumference is . Treating the Earth as a sphere, its circumference would be its single most important measuremen ...
has been lost; what has been preserved is the simplified version described by
Cleomedes Cleomedes () was a Greek astronomer who is known chiefly for his book ''On the Circular Motions of the Celestial Bodies'' (Κυκλικὴ θεωρία μετεώρων), also known as ''The Heavens'' (). Placing his work chronologically His bi ...
to popularise the discovery. Cleomedes invites his reader to consider two Egyptian cities,
Alexandria Alexandria ( ; ) is the List of cities and towns in Egypt#Largest cities, second largest city in Egypt and the List of coastal settlements of the Mediterranean Sea, largest city on the Mediterranean coast. It lies at the western edge of the Nile ...
and Syene, modern Assuan: # Cleomedes assumes that the distance between Syene and Alexandria was 5,000 stadia (a figure that was checked yearly by professional bematists, ''mensores regii''); # he assumes the simplified hypothesis that Syene was precisely on the
Tropic of Cancer The Tropic of Cancer, also known as the Northern Tropic, is the Earth's northernmost circle of latitude where the Sun can be seen directly overhead. This occurs on the June solstice, when the Northern Hemisphere is tilted toward the Sun ...
, saying that at local noon on the summer
solstice A solstice is the time when the Sun reaches its most northerly or southerly sun path, excursion relative to the celestial equator on the celestial sphere. Two solstices occur annually, around 20–22 June and 20–22 December. In many countries ...
the Sun was directly overhead; # he assumes the simplified hypothesis that Syene and Alexandria are on the same meridian. Under the previous assumptions, says Cleomedes, one can measure the Sun's angle of elevation at noon of the summer solstice in Alexandria, by using a vertical rod (a gnomon) 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 7.2°, 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. Eratosthenes's 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's book. The method was based on several
surveying Surveying or land surveying is the technique, profession, art, and science of determining the land, terrestrial Plane (mathematics), two-dimensional or Three-dimensional space#In Euclidean geometry, three-dimensional positions of Point (geom ...
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's measure corresponds precisely to 252,000 stadia might be intentional, since it is a number that 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's ratio". 1,700 years after Eratosthenes,
Christopher Columbus Christopher Columbus (; between 25 August and 31 October 1451 – 20 May 1506) was an Italians, Italian explorer and navigator from the Republic of Genoa who completed Voyages of Christopher Columbus, four Spanish-based voyages across the At ...
studied Eratosthenes's 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's findings, he might have never gone west, since he did not have the supplies or funding needed for the much longer eight-thousand-plus mile voyage.


Seleucus of Seleucia

Seleucus of Seleucia (c. 190 BC), who lived in the city of
Seleucia Seleucia (; ), also known as or or Seleucia ad Tigrim, was a major Mesopotamian city, located on the west bank of the Tigris River within the present-day Baghdad Governorate in Iraq. It was founded around 305 BC by Seleucus I Nicator as th ...
in
Mesopotamia Mesopotamia is a historical region of West Asia situated within the Tigris–Euphrates river system, in the northern part of the Fertile Crescent. Today, Mesopotamia is known as present-day Iraq and forms the eastern geographic boundary of ...
, wrote that Earth is spherical (and actually orbits the Sun, influenced by the heliocentric theory of
Aristarchus of Samos Aristarchus of Samos (; , ; ) was an ancient Greek astronomer and mathematician who presented the first known heliocentric model that placed the Sun at the center of the universe, with the Earth revolving around the Sun once a year and rotati ...
).


Posidonius

A parallel later ancient measurement of the size of the Earth was made by another Greek scholar, Posidonius (c. 13551 BC), using a similar method as Eratosthenes. Instead of observing the Sun, he noted that the star
Canopus Canopus is the brightest star in the southern constellation of Carina (constellation), Carina and the list of brightest stars, second-brightest star in the night sky. It is also Bayer designation, designated α Carinae, which is Rom ...
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 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
atmospheric refraction Atmospheric refraction is the deviation of light or other electromagnetic wave from a straight line as it passes through the atmosphere due to the variation in air density as a function of height. This refraction is due to the velocity of light ...
. Posidonius furthermore expressed the distance of the Sun in Earth radii. The above-mentioned larger and smaller sizes of the Earth were those used by later Roman author Claudius Ptolemy at different times: 252,000 stadia in his '' Almagest'' and 180,000 stadia in his later '' Geographia''. 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.


Roman Empire

The idea of a spherical Earth slowly spread across the globe, and ultimately became the adopted view in all major astronomical traditions.Continuation into Roman and medieval thought: Reinhard Krüger:
Materialien und Dokumente zur mittelalterlichen Erdkugeltheorie von der Spätantike bis zur Kolumbusfahrt (1492)
Direct adoption by India: D. Pingree: "History of Mathematical Astronomy in India", ''Dictionary of Scientific Biography'', 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, , p. 463Adoption by China via European science: and In the West, the idea came to the Romans through the lengthy process of cross-fertilization with
Hellenistic civilization In classical antiquity, the Hellenistic period covers the time in Greek history after Classical Greece, between the death of Alexander the Great in 323 BC and the death of Cleopatra VII in 30 BC, which was followed by the ascendancy of the R ...
. Many Roman authors such as
Cicero Marcus Tullius Cicero ( ; ; 3 January 106 BC – 7 December 43 BC) was a Roman statesman, lawyer, scholar, philosopher, orator, writer and Academic skeptic, who tried to uphold optimate principles during the political crises tha ...
and Pliny refer in their works to the rotundity of Earth as a matter of course.Krüger, Reinhard
"Ein Versuch über die Archäologie der Globalisierung. Die Kugelgestalt der Erde und die globale Konzeption des Erdraums im Mittelalter"
''Wechselwirkungen'', Jahrbuch aus Lehre und Forschung der Universität Stuttgart, University of Stuttgart, 2007, pp. 28–52 (35–36)
Pliny also considered the possibility of an imperfect sphere "shaped like a pinecone".


Strabo

It has been suggested that seafarers probably provided the first observational evidence that Earth was not flat, based on observations of the
horizon The horizon is the apparent curve that separates the surface of a celestial body from its sky when viewed from the perspective of an observer on or near the surface of the relevant body. This curve divides all viewing directions based on whethe ...
. This argument was put forward by the geographer
Strabo Strabo''Strabo'' (meaning "squinty", as in strabismus) was a term employed by the Romans for anyone whose eyes were distorted or deformed. The father of Pompey was called "Gnaeus Pompeius Strabo, Pompeius Strabo". A native of Sicily so clear-si ...
(c. 64 BC – 24 AD), who suggested that the spherical shape of Earth was probably known to seafarers around the
Mediterranean Sea The Mediterranean Sea ( ) is a sea connected to the Atlantic Ocean, surrounded by the Mediterranean basin and almost completely enclosed by land: on the east by the Levant in West Asia, on the north by Anatolia in West Asia and Southern Eur ...
since at least the time of
Homer Homer (; , ; possibly born ) was an Ancient Greece, Ancient Greek poet who is credited as the author of the ''Iliad'' and the ''Odyssey'', two epic poems that are foundational works of ancient Greek literature. Despite doubts about his autho ...
,Hugh Thurston, ''Early Astronomy'', (New York: Springer-Verlag), p. 118. . citing a line from the ''
Odyssey The ''Odyssey'' (; ) is one of two major epics of ancient Greek literature attributed to Homer. It is one of the oldest surviving works of literature and remains popular with modern audiences. Like the ''Iliad'', the ''Odyssey'' is divi ...
'' as indicating that the poet
Homer Homer (; , ; possibly born ) was an Ancient Greece, Ancient Greek poet who is credited as the author of the ''Iliad'' and the ''Odyssey'', two epic poems that are foundational works of ancient Greek literature. Despite doubts about his autho ...
knew of this as early as the 7th or 8th century BC.
Strabo Strabo''Strabo'' (meaning "squinty", as in strabismus) was a term employed by the Romans for anyone whose eyes were distorted or deformed. The father of Pompey was called "Gnaeus Pompeius Strabo, Pompeius Strabo". A native of Sicily so clear-si ...
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.


Claudius Ptolemy

Claudius Ptolemy (90–168 AD) lived in
Alexandria Alexandria ( ; ) is the List of cities and towns in Egypt#Largest cities, second largest city in Egypt and the List of coastal settlements of the Mediterranean Sea, largest city on the Mediterranean coast. It lies at the western edge of the Nile ...
, the centre of scholarship in the 2nd century. In the '' Almagest'', 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
mountain A mountain is an elevated portion of the Earth's crust, generally with steep sides that show significant exposed bedrock. Although definitions vary, a mountain may differ from a plateau in having a limited summit area, and is usually higher t ...
s, 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. He compiled an eight-volume '' Geographia'' covering what was known about Earth. The first part of the ''Geographia'' is a discussion of the data and of the methods he used. As with the model of the Solar System in the ''Almagest'', Ptolemy put all this information into a grand scheme. He assigned coordinates to all the places and geographic features he knew, in a grid that spanned the globe (although most of this has been lost).
Latitude In geography, latitude is a geographic coordinate system, geographic coordinate that specifies the north-south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at t ...
was measured from the
equator The equator is the circle of latitude that divides Earth into the Northern Hemisphere, Northern and Southern Hemisphere, Southern Hemispheres of Earth, hemispheres. It is an imaginary line located at 0 degrees latitude, about in circumferen ...
, as it is today, but Ptolemy preferred to express it as the length of the longest day rather than degrees of arc (the length of the
midsummer Midsummer is a celebration of the season of summer, taking place on or near the date of the summer solstice in the Northern Hemisphere; the longest Daytime, day of the year. The name "midsummer" mainly refers to summer solstice festivals of Eu ...
day increases from 12h to 24h as you go from the equator to the polar circle). He put the meridian of 0
longitude Longitude (, ) is a geographic coordinate that specifies the east- west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lett ...
at the most western land he knew, the
Canary Islands The Canary Islands (; ) or Canaries are an archipelago in the Atlantic Ocean and the southernmost Autonomous communities of Spain, Autonomous Community of Spain. They are located in the northwest of Africa, with the closest point to the cont ...
. ''Geographia'' indicated the countries of " Serica" and "Sinae" (
China China, officially the People's Republic of China (PRC), is a country in East Asia. With population of China, a population exceeding 1.4 billion, it is the list of countries by population (United Nations), second-most populous country after ...
) at the extreme right, beyond the island of "Taprobane" (
Sri Lanka Sri Lanka, officially the Democratic Socialist Republic of Sri Lanka, also known historically as Ceylon, is an island country in South Asia. It lies in the Indian Ocean, southwest of the Bay of Bengal, separated from the Indian subcontinent, ...
, oversized) and the "Aurea Chersonesus" ( Southeast Asian peninsula). Ptolemy also devised and provided instructions on how to make maps both of the whole inhabited world (''oikoumenè'') and of the Roman provinces. In the second part of the ''Geographia'', he provided the necessary topographic lists, and captions for the maps. His ''oikoumenè'' spanned 180 degrees of longitude from the Canary Islands in the
Atlantic Ocean The Atlantic Ocean is the second largest of the world's five borders of the oceans, oceanic divisions, with an area of about . It covers approximately 17% of Earth#Surface, Earth's surface and about 24% of its water surface area. During the ...
to
China China, officially the People's Republic of China (PRC), is a country in East Asia. With population of China, a population exceeding 1.4 billion, it is the list of countries by population (United Nations), second-most populous country after ...
, and about 81 degrees of latitude from the Arctic to the
East Indies The East Indies (or simply the Indies) is a term used in historical narratives of the Age of Discovery. The ''Indies'' broadly referred to various lands in Eastern world, the East or the Eastern Hemisphere, particularly the islands and mainl ...
and deep into
Africa Africa is the world's second-largest and second-most populous continent after Asia. At about 30.3 million km2 (11.7 million square miles) including adjacent islands, it covers 20% of Earth's land area and 6% of its total surfac ...
. Ptolemy was well aware that he knew about only a quarter of the globe.


Late Antiquity

Knowledge of the spherical shape of Earth was received in scholarship of
Late Antiquity Late antiquity marks the period that comes after the end of classical antiquity and stretches into the onset of the Early Middle Ages. Late antiquity as a period was popularized by Peter Brown (historian), Peter Brown in 1971, and this periodiza ...
as a matter of course, in both
Neoplatonism Neoplatonism is a version of Platonic philosophy that emerged in the 3rd century AD against the background of Hellenistic philosophy and religion. The term does not encapsulate a set of ideas as much as a series of thinkers. Among the common id ...
and
Early Christianity Early Christianity, otherwise called the Early Church or Paleo-Christianity, describes the History of Christianity, historical era of the Christianity, Christian religion up to the First Council of Nicaea in 325. Spread of Christianity, Christian ...
. Calcidius's fourth-century
Latin Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...
commentary on and translation of Plato's ''Timaeus'', which was one of the few examples of Greek scientific thought that was known in the Early Middle Ages in Western Europe, discussed
Hipparchus Hipparchus (; , ;  BC) was a Ancient Greek astronomy, Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equinoxes. Hippar ...
's use of the geometrical circumstances of eclipses in '' On Sizes and Distances'' to compute the relative diameters of the Sun, Earth, and Moon. Theological doubt informed by the flat Earth model implied in the
Hebrew Bible The Hebrew Bible or Tanakh (;"Tanach"
. '' Lactantius, John Chrysostom and
Athanasius of Alexandria Athanasius I of Alexandria ( – 2 May 373), also called Athanasius the Great, Athanasius the Confessor, or, among Coptic Christians, Athanasius the Apostolic, was a Christian theologian and the 20th patriarch of Alexandria (as Athanasius ...
, but this remained an eccentric current. Learned Christian authors such as Basil of Caesarea, Ambrose and
Augustine of Hippo Augustine of Hippo ( , ; ; 13 November 354 – 28 August 430) was a theologian and philosopher of Berber origin and the bishop of Hippo Regius in Numidia, Roman North Africa. His writings deeply influenced the development of Western philosop ...
were clearly aware of the sphericity of Earth. "Flat Earthism" lingered longest in
Syriac Christianity Syriac Christianity (, ''Mšiḥoyuṯo Suryoyto'' or ''Mšiḥāyūṯā Suryāytā'') is a branch of Eastern Christianity of which formative Christian theology, theological writings and traditional Christian liturgy, liturgies are expressed in ...
, which tradition laid greater importance on a literalist interpretation of the Old Testament. Authors from that tradition, such as Cosmas Indicopleustes, 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
medieval period In the history of Europe, the Middle Ages or medieval period lasted approximately from the 5th to the late 15th centuries, similarly to the post-classical period of World history (field), global history. It began with the fall of the West ...
, "no cosmographer worthy of note has called into question the sphericity of the Earth". Such widely read encyclopedists as Macrobius and
Martianus Capella Martianus Minneus Felix Capella () was a jurist, polymath and Latin literature, Latin prose writer of late antiquity, one of the earliest developers of the system of the seven liberal arts that structured early medieval education. He was a native ...
(both 5th century AD) discussed the circumference of the sphere of the Earth, its central position in the universe, the difference of the
season A season is a division of the year based on changes in weather, ecology, and the number of daylight hours in a given region. On Earth, seasons are the result of the axial parallelism of Earth's axial tilt, tilted orbit around the Sun. In temperat ...
s in Northern and Southern Hemispheres, and many other geographical details., translated in In his commentary on
Cicero Marcus Tullius Cicero ( ; ; 3 January 106 BC – 7 December 43 BC) was a Roman statesman, lawyer, scholar, philosopher, orator, writer and Academic skeptic, who tried to uphold optimate principles during the political crises tha ...
's '' Dream of Scipio'', Macrobius described the Earth as a globe of insignificant size in comparison to the remainder of the cosmos.


Ancient India

While the textual evidence has not survived, the precision of the constants used in pre-Greek '' Vedanga'' 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 quantitative Greek astronomy text in the medieval era. Greek ethnographer Megasthenes, 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 Hellenistic culture in the east, Hellenistic astronomy filtered eastwards to
ancient India Anatomically modern humans first arrived on the Indian subcontinent between 73,000 and 55,000 years ago. The earliest known human remains in South Asia date to 30,000 years ago. Sedentism, Sedentariness began in South Asia around 7000 BCE; ...
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 Varāhamihira and
Brahmagupta Brahmagupta ( – ) was an Indian Indian mathematics, mathematician and Indian astronomy, astronomer. He is the author of two early works on mathematics and astronomy: the ''Brāhmasphuṭasiddhānta'' (BSS, "correctly established Siddhanta, do ...
, strengthened the astronomical principles. Some ideas were found possible to preserve, although in altered form.D. Pingree: "History of Mathematical Astronomy in India", ''Dictionary of Scientific Biography'', Vol. 15 (1978), pp. 533–633 (533, 554f.) "Chapter 6. Cosmology"


Aryabhata

The Indian astronomer and mathematician
Aryabhata Aryabhata ( ISO: ) or Aryabhata I (476–550 CE) was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His works include the '' Āryabhaṭīya'' (which mentions that in 3600 ' ...
(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
Sanskrit Sanskrit (; stem form ; nominal singular , ,) is a classical language belonging to the Indo-Aryan languages, Indo-Aryan branch of the Indo-European languages. It arose in northwest South Asia after its predecessor languages had Trans-cultural ...
magnum opus, ''
Āryabhaṭīya ''Aryabhatiya'' (IAST: ') or ''Aryabhatiyam'' ('), a Indian astronomy, Sanskrit astronomical treatise, is the ''Masterpiece, magnum opus'' and only known surviving work of the 5th century Indian mathematics, Indian mathematician Aryabhata. Philos ...
''. ''Aryabhatiya'' is divided into four sections: ''Gitika'', ''Ganitha'' ("mathematics"), ''Kalakriya'' ("reckoning of time") and ''Gola'' ("
celestial sphere In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, ...
"). The discovery that the Earth rotates on its own axis from west to east is described in ''Aryabhatiya'' (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: :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 east.) In the ''Aryabhatiya'', Aryabhata also estimates the circumference of the Earth. He gives this as 4967 Yojana and its diameter as 1581 yojana. The length of a Yojana varies considerably between sources (3.5 - 15 km); if a yojana is taken to be 8 km (4.97097 miles) the formula offers a circumference of , close to the current
equator The equator is the circle of latitude that divides Earth into the Northern Hemisphere, Northern and Southern Hemisphere, Southern Hemispheres of Earth, hemispheres. It is an imaginary line located at 0 degrees latitude, about in circumferen ...
ial value of .


Islamic world

Islamic astronomy was developed on the basis of a spherical Earth inherited from Hellenistic astronomy. The Islamic theoretical framework largely relied on the fundamental contributions of
Aristotle Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...
('' De caelo'') and
Ptolemy Claudius Ptolemy (; , ; ; – 160s/170s AD) was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine science, Byzant ...
('' Almagest''), both of whom worked from the premise that Earth was spherical and at the centre of the universe (
geocentric model In astronomy, the geocentric model (also known as geocentrism, often exemplified specifically by the Ptolemaic system) is a superseded scientific theories, superseded description of the Universe with Earth at the center. Under most geocentric m ...
). Early Islamic scholars recognized Earth's sphericity, leading Muslim mathematicians to develop
spherical trigonometry Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the edge (geometry), sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, ge ...
David A. King, ''Astronomy in the Service of Islam'', (Aldershot (U.K.): Variorum), 1993. in order to further mensuration and to calculate the distance and direction from any given point on Earth to
Mecca Mecca, officially Makkah al-Mukarramah, is the capital of Mecca Province in the Hejaz region of western Saudi Arabia; it is the Holiest sites in Islam, holiest city in Islam. It is inland from Jeddah on the Red Sea, in a narrow valley above ...
. This determined the ''
Qibla The qibla () is the direction towards the Kaaba in the Great Mosque of Mecca, Sacred Mosque in Mecca, which is used by Muslims in various religious contexts, particularly the direction of prayer for the salah. In Islam, the Kaaba is believed to ...
'', or Muslim direction of prayer.


Al-Ma'mun

Around 830 CE,
Caliph A caliphate ( ) is an institution or public office under the leadership of an Islamic steward with Khalifa, the title of caliph (; , ), a person considered a political–religious successor to the Islamic prophet Muhammad and a leader of ...
al-Ma'mun commissioned a group of Muslim astronomers and
geographers A geographer is a physical scientist, social scientist or humanist whose area of study is geography, the study of Earth's natural environment and human society, including how society and nature interacts. The Greek prefix "geo" means "earth" ...
to measure the distance from Tadmur (
Palmyra Palmyra ( ; Palmyrene dialect, Palmyrene: (), romanized: ''Tadmor''; ) is an ancient city in central Syria. It is located in the eastern part of the Levant, and archaeological finds date back to the Neolithic period, and documents first menti ...
) to Raqqa in modern Syria. To determine the length of one degree of
latitude In geography, latitude is a geographic coordinate system, geographic coordinate that specifies the north-south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at t ...
, by using a rope to measure the distance travelled due north or south (
meridian arc In geodesy and navigation, a meridian arc is the curve (geometry), curve between two points near the Earth's surface having the same longitude. The term may refer either to a arc (geometry), segment of the meridian (geography), meridian, or to its ...
) on flat desert land until they reached a place where the altitude of the North Pole had changed by one degree. Al-Ma'mun's arc measurement result is described in different sources as 66 2/3 miles, 56.5 miles, and 56 miles. The figure Alfraganus used based on these measurements was 56 2/3 miles, giving an Earth circumference of . 66 miles results in a calculated planetary circumference of . Another estimate given by his astronomers was 56 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.


Ibn Hazm

Andalusian
polymath A polymath or polyhistor is an individual whose knowledge spans many different subjects, known to draw on complex bodies of knowledge to solve specific problems. Polymaths often prefer a specific context in which to explain their knowledge, ...
Ibn Hazm 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).


Al-Farghānī

Al-Farghānī (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 Arabic miles) was much more accurate than the 60 Roman miles (89.7 km) given by Ptolemy.
Christopher Columbus Christopher Columbus (; between 25 August and 31 October 1451 – 20 May 1506) was an Italians, Italian explorer and navigator from the Republic of Genoa who completed Voyages of Christopher Columbus, four Spanish-based voyages across the At ...
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.


Al-Biruni

Abu Rayhan Biruni Abu Rayhan Muhammad ibn Ahmad al-Biruni (; ; 973after 1050), known as al-Biruni, was a Khwarazmian Iranian peoples, Iranian scholar and polymath during the Islamic Golden Age. He has been called variously "Father of Comparative religion, Co ...
(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 trigonometric calculations based on the angle between a
plain In geography, a plain, commonly known as flatland, is a flat expanse of land that generally does not change much in elevation, and is primarily treeless. Plains occur as lowlands along valleys or at the base of mountains, as coastal plains, and ...
and
mountain A mountain is an elevated portion of the Earth's crust, generally with steep sides that show significant exposed bedrock. Although definitions vary, a mountain may differ from a plateau in having a limited summit area, and is usually higher t ...
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 (present day Pind Dadan Khan, Pakistan). 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
law of sines In trigonometry, the law of sines (sometimes called the sine formula or sine rule) is a mathematical equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, \frac \,=\, \frac \,=\, \frac \,=\ ...
formula to calculate the curvature of the Earth.
/ref> While this was an ingenious new method, Al-Biruni was not aware of
atmospheric refraction Atmospheric refraction is the deviation of light or other electromagnetic wave from a straight line as it passes through the atmosphere due to the variation in air density as a function of height. This refraction is due to the velocity of light ...
. 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%. Biruni also made use of
algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...
to formulate trigonometric equations and used the
astrolabe An astrolabe (; ; ) is an astronomy, astronomical list of astronomical instruments, instrument dating to ancient times. It serves as a star chart and Model#Physical model, physical model of the visible celestial sphere, half-dome of the sky. It ...
to measure angles. Jim Al-Khalili, ,
BBC The British Broadcasting Corporation (BBC) is a British public service broadcaster headquartered at Broadcasting House in London, England. Originally established in 1922 as the British Broadcasting Company, it evolved into its current sta ...
According to John J. O'Connor and Edmund F. Robertson,


Al-Zarqali

By 1060, Andalusi astronomer Al-Zarqali corrects geographical data from
Ptolemy Claudius Ptolemy (; , ; ; – 160s/170s AD) was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine science, Byzant ...
and
Al-Khwarizmi Muhammad ibn Musa al-Khwarizmi , or simply al-Khwarizmi, was a mathematician active during the Islamic Golden Age, who produced Arabic-language works in mathematics, astronomy, and geography. Around 820, he worked at the House of Wisdom in B ...
, specifically by correcting Ptolemy's estimate of the longitude of the
Mediterranean Sea The Mediterranean Sea ( ) is a sea connected to the Atlantic Ocean, surrounded by the Mediterranean basin and almost completely enclosed by land: on the east by the Levant in West Asia, on the north by Anatolia in West Asia and Southern Eur ...
from 62 degrees to the correct value of 42 degrees.


Jamal-al-Din

A terrestrial globe (Kura-i-ard) was among the presents sent by the Persian Muslim astronomer Jamal-al-Din to Kublai Khan's Chinese 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 et cetera. Ho Peng Yoke remarks that "it did not seem to have any general appeal to the Chinese in those days".


Applications

Muslim scholars who held to the spherical Earth theory used it to calculate the distance and direction from any given point on Earth to
Mecca Mecca, officially Makkah al-Mukarramah, is the capital of Mecca Province in the Hejaz region of western Saudi Arabia; it is the Holiest sites in Islam, holiest city in Islam. It is inland from Jeddah on the Red Sea, in a narrow valley above ...
. Muslim mathematicians developed
spherical trigonometry Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the edge (geometry), sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, ge ...
; in the 11th century, al-Biruni used it to find the direction of Mecca from many cities and published it in ''The Determination of the Co-ordinates of Cities''. This determined the
Qibla The qibla () is the direction towards the Kaaba in the Great Mosque of Mecca, Sacred Mosque in Mecca, which is used by Muslims in various religious contexts, particularly the direction of prayer for the salah. In Islam, the Kaaba is believed to ...
, or Muslim direction of prayer.


Magnetic declination

Muslim astronomers and geographers were aware of magnetic declination by the 15th century, when the Egyptian astronomer 'Abd al-'Aziz al-Wafa'i (d. 1469/1471) measured it as 7 degrees from
Cairo Cairo ( ; , ) is the Capital city, capital and largest city of Egypt and the Cairo Governorate, being home to more than 10 million people. It is also part of the List of urban agglomerations in Africa, largest urban agglomeration in Africa, L ...
.


Medieval Europe


Greek influence

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 (
Aristotle Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...
), and via authors such as
Isidore of Seville Isidore of Seville (; 4 April 636) was a Spania, Hispano-Roman scholar, theologian and Roman Catholic Archdiocese of Seville, archbishop of Seville. He is widely regarded, in the words of the 19th-century historian Charles Forbes René de Montal ...
and the
Venerable Bede Bede (; ; 672/326 May 735), also known as Saint Bede, Bede of Jarrow, the Venerable Bede, and Bede the Venerable (), was an English monk, author and scholar. He was one of the most known writers during the Early Middle Ages, and his most fa ...
. It became increasingly traceable with the rise of
scholasticism Scholasticism was a medieval European philosophical movement or methodology that was the predominant education in Europe from about 1100 to 1700. It is known for employing logically precise analyses and reconciling classical philosophy and Ca ...
and medieval learning. Revising the figures attributed to Posidonius, another Greek philosopher determined as the Earth's circumference. This last figure was promulgated by
Ptolemy Claudius Ptolemy (; , ; ; – 160s/170s AD) was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine science, Byzant ...
through his world maps. The maps of Ptolemy strongly influenced the cartographers of the
Middle Ages In the history of Europe, the Middle Ages or medieval period lasted approximately from the 5th to the late 15th centuries, similarly to the post-classical period of global history. It began with the fall of the Western Roman Empire and ...
. It is probable that
Christopher Columbus Christopher Columbus (; between 25 August and 31 October 1451 – 20 May 1506) was an Italians, Italian explorer and navigator from the Republic of Genoa who completed Voyages of Christopher Columbus, four Spanish-based voyages across the At ...
, using such maps, was led to believe that Asia was only west of Europe. Ptolemy's view was not universal, however, and chapter 20 of Sir John Mandeville's ''Travels'' (c. 1357) supports Eratosthenes' calculation. Spread of this knowledge beyond the immediate sphere of Greco-Roman scholarship was necessarily gradual, associated with the pace of Christianisation of Europe. For example, the first evidence of knowledge of the spherical shape of Earth in
Scandinavia Scandinavia is a subregion#Europe, subregion of northern Europe, with strong historical, cultural, and linguistic ties between its constituent peoples. ''Scandinavia'' most commonly refers to Denmark, Norway, and Sweden. It can sometimes also ...
is a 12th-century Old Icelandic translation of '' Elucidarius''. A list of more than a hundred
Latin Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...
and vernacular writers from
Late Antiquity Late antiquity marks the period that comes after the end of classical antiquity and stretches into the onset of the Early Middle Ages. Late antiquity as a period was popularized by Peter Brown (historian), Peter Brown in 1971, and this periodiza ...
and the
Middle Ages In the history of Europe, the Middle Ages or medieval period lasted approximately from the 5th to the late 15th centuries, similarly to the post-classical period of global history. It began with the fall of the Western Roman Empire and ...
who were aware that Earth was spherical has been compiled by Reinhard Krüger, professor for Romance literature at the University of Stuttgart. It was not until the 16th century that his concept of the Earth's size was revised. During that period the Flemish cartographer, Mercator, made successive reductions in the size of the
Mediterranean Sea The Mediterranean Sea ( ) is a sea connected to the Atlantic Ocean, surrounded by the Mediterranean basin and almost completely enclosed by land: on the east by the Levant in West Asia, on the north by Anatolia in West Asia and Southern Eur ...
and all of Europe which had the effect of increasing the size of the Earth.


Early medieval Europe


Isidore of Seville

Bishop
Isidore of Seville Isidore of Seville (; 4 April 636) was a Spania, Hispano-Roman scholar, theologian and Roman Catholic Archdiocese of Seville, archbishop of Seville. He is widely regarded, in the words of the 19th-century historian Charles Forbes René de Montal ...
(560–636) taught in his widely read encyclopedia, ''The
Etymologies Etymology ( ) is the study of the origin and evolution of words—including their constituent units of sound and meaning—across time. In the 21st century a subfield within linguistics, etymology has become a more rigorously scientific study. ...
'', 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.


Bede the Venerable

The monk
Bede Bede (; ; 672/326 May 735), also known as Saint Bede, Bede of Jarrow, the Venerable Bede, and Bede the Venerable (), was an English monk, author and scholar. He was one of the most known writers during the Early Middle Ages, and his most f ...
(c. 672–735) wrote in his influential treatise on
computus As a moveable feast, the date of Easter is determined in each year through a calculation known as – often simply ''Computus'' – or as paschalion particularly in the Eastern Orthodox Church. Easter is celebrated on the first Sunday after th ...
, ''The Reckoning of Time'', 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." The large number of surviving manuscripts of ''The Reckoning of Time'', 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.
Ælfric of Eynsham Ælfric of Eynsham (; ; ) was an English abbot and a student of Æthelwold of Winchester, and a consummate, prolific writer in Old English of hagiography, homilies, biblical commentaries, and other genres. He is also known variously as '' ...
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." 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 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."Russell, Jeffrey B. 1991. ''Inventing the Flat Earth''. New York: Praeger Publishers. p. 87.


Anania Shirakatsi

The 7th-century
Armenian Armenian may refer to: * Something of, from, or related to Armenia, a country in the South Caucasus region of Eurasia * Armenians, the national people of Armenia, or people of Armenian descent ** Armenian diaspora, Armenian communities around the ...
scholar Anania Shirakatsi 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)".


High and late medieval Europe

During the
High Middle Ages The High Middle Ages, or High Medieval Period, was the periodization, period of European history between and ; it was preceded by the Early Middle Ages and followed by the Late Middle Ages, which ended according to historiographical convention ...
, the astronomical knowledge in Christian Europe was extended beyond what was transmitted directly from ancient authors by transmission of learning from medieval Islamic astronomy. An early student of such learning was Gerbert d'Aurillac, the later Pope Sylvester II. Saint Hildegard ( Hildegard von Bingen, 1098–1179), depicted the spherical Earth several times in her work ''Liber Divinorum Operum''. Johannes de Sacrobosco (c. 1195c. 1256 AD) wrote a famous work on Astronomy called '' Tractatus de Sphaera'', based on Ptolemy, which primarily considers the sphere of the sky. However, it contains clear proofs of Earth's sphericity in the first chapter. Many scholastic commentators on Aristotle's '' On the Heavens'' and Sacrobosco's ''Treatise on the Sphere'' unanimously agreed that Earth is spherical or round. Grant observes that no author who had studied at a
medieval university A medieval university was a corporation organized during the Middle Ages for the purposes of higher education. The first Western European institutions generally considered to be universities were established in present-day Italy, including the K ...
thought that Earth was flat. The ''Elucidarium'' of Honorius Augustodunensis (c. 1120), an important manual for the instruction of lesser clergy, which was translated into
Middle English Middle English (abbreviated to ME) is a form of the English language that was spoken after the Norman Conquest of 1066, until the late 15th century. The English language underwent distinct variations and developments following the Old English pe ...
,
Old French Old French (, , ; ) was the language spoken in most of the northern half of France approximately between the late 8th -4; we might wonder whether there's a point at which it's appropriate to talk of the beginnings of French, that is, when it wa ...
, Middle High German, Old Russian, Middle Dutch, Old Norse, Icelandic language, Icelandic, Spanish language, Spanish, and several Italian dialects, explicitly refers to a spherical Earth. Likewise, the fact that Bertold von Regensburg (mid-13th century) used the spherical Earth as an illustration in a
sermon A sermon is a religious discourse or oration by a preacher, usually a member of clergy. Sermons address a scriptural, theological, or moral topic, usually expounding on a type of belief, law, or behavior within both past and present context ...
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. Dante's ''
Divine Comedy The ''Divine Comedy'' (, ) is an Italian narrative poetry, narrative poem by Dante Alighieri, begun and completed around 1321, shortly before the author's death. It is widely considered the pre-eminent work in Italian literature and one of ...
'', written in Italian in the early 14th century, portrays Earth as a sphere, discussing implications such as the different stars visible in the Southern Hemisphere, the altered position of the Sun, and the various
time zone A time zone is an area which observes a uniform standard time for legal, Commerce, commercial and social purposes. Time zones tend to follow the boundaries between Country, countries and their Administrative division, subdivisions instead of ...
s of Earth.


Early modern period

The invention of the
telescope A telescope is a device used to observe distant objects by their emission, Absorption (electromagnetic radiation), absorption, or Reflection (physics), reflection of electromagnetic radiation. Originally, it was an optical instrument using len ...
and the
theodolite A theodolite () is a precision optical instrument for measuring angles between designated visible points in the horizontal and vertical planes. The traditional use has been for land surveying, but it is also used extensively for building and ...
and the development of logarithm tables allowed exact
triangulation In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications In surveying Specifically in surveying, triangulation involves only angle m ...
and arc measurements.


Ming China

Joseph Needham, in his ''Chinese Cosmology'' reports that
Shen Kuo Shen Kuo (; 1031–1095) or Shen Gua, courtesy name Cunzhong (存中) and Art name#China, pseudonym Mengqi (now usually given as Mengxi) Weng (夢溪翁),Yao (2003), 544. was a Chinese polymath, scientist, and statesman of the Song dynasty (960� ...
(1031–1095) used models of lunar eclipse and solar eclipse to conclude the roundness of celestial bodies. 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 Western astronomy, ultimately spread to Ming China, when
Jesuit missionaries The Society of Jesus (; abbreviation: S.J. or SJ), also known as the Jesuit Order or the Jesuits ( ; ), is a religious order of clerics regular of pontifical right for men in the Catholic Church headquartered in Rome. It was founded in 1540 ...
, who held high positions as astronomers at the imperial court, successfully challenged the Chinese belief that Earth was flat and square.Christopher Cullen, "Joseph Needham on Chinese Astronomy", ''Past and Present'', No. 87. (May 1980), pp. 39–53 (42 & 49)Christopher Cullen, "A Chinese Eratosthenes of the Flat Earth: A Study of a Fragment of Cosmology in Huai Nan Tzu 淮 南 子", ''Bulletin of the School of Oriental and African Studies'', Vol. 39, No. 1 (1976), pp. 106–127 (107–109) The ''Ge zhi cao'' (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".Needham, Joseph (1986). Science and Civilization in China: Volume 3. Taipei: Caves Books, Ltd. pp. 499. The text also pointed out that sailing ships could return to their port of origin after circumnavigating the waters of Earth. 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 accompanied by a sinocentric reinterpretation that declared the imported ideas Chinese in origin: Although mainstream Chinese science until the 17th century held the view that Earth was flat, square, and enveloped by the
celestial sphere In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, ...
, this idea was criticized by the Jin-dynasty scholar Yu Xi (fl. 307–345), who suggested that Earth could be either square or round, in accordance with the shape of the heavens. The Yuan-dynasty mathematician Li Ye (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 ''Ge zhi cao'' treatise also used the same terminology to describe the shape of Earth that the Eastern-Han scholar
Zhang Heng Zhang Heng (; AD 78–139), formerly romanization of Chinese, romanized Chang Heng, was a Chinese polymathic scientist and statesman who lived during the Han dynasty#Eastern Han (25–220 AD), Eastern Han dynasty. Educated in the capital citi ...
(78–139 AD) had used to describe the shape of the Sun and Moon (as in, that the former was as round as a
crossbow A crossbow is a ranged weapon using an Elasticity (physics), elastic launching device consisting of a Bow and arrow, bow-like assembly called a ''prod'', mounted horizontally on a main frame called a ''tiller'', which is hand-held in a similar f ...
bullet, and the latter was the shape of a ball).


Circumnavigation of the globe

The Portugal, Portuguese exploration of
Africa Africa is the world's second-largest and second-most populous continent after Asia. At about 30.3 million km2 (11.7 million square miles) including adjacent islands, it covers 20% of Earth's land area and 6% of its total surfac ...
and Asia, Christopher Columbus, Columbus's voyage to the Americas (1492) provided more direct evidence of the size and shape of the world. The first direct demonstration of Earth's sphericity came in the form of the Magellan expedition, first circumnavigation in history, an expedition captained by Portuguese explorer Ferdinand Magellan. The expedition was financed by the Spanish Crown. On August 10, 1519, the five ships under Magellan's command departed from Seville. They crossed the
Atlantic Ocean The Atlantic Ocean is the second largest of the world's five borders of the oceans, oceanic divisions, with an area of about . It covers approximately 17% of Earth#Surface, Earth's surface and about 24% of its water surface area. During the ...
, passed through what is now called the Strait of Magellan, crossed the Pacific, and arrived in Cebu, where Magellan was killed by Philippine natives in a battle. His second in command, the Spaniard Juan Sebastián Elcano, continued the expedition and, on September 6, 1522, arrived at Seville, completing the circumnavigation. Charles I of Spain, in recognition of his feat, gave Elcano a coat of arms with the motto ''Primus circumdedisti me'' (in Latin, "You went around me first"). 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 circles in Europe. The Transglobe Expedition (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.


European calculations

In the Carolingian Renaissance, Carolingian era, scholars discussed Macrobius's view of the ''antipodes''. One of them, the Irish monk Saint Dungal, Dungal, asserted that the tropical gap between our habitable region and the other habitable region to the south was smaller than Macrobius had believed. In 1505 the cosmographer and explorer Duarte Pacheco Pereira calculated the value of the degree of the
meridian arc In geodesy and navigation, a meridian arc is the curve (geometry), curve between two points near the Earth's surface having the same longitude. The term may refer either to a arc (geometry), segment of the meridian (geography), meridian, or to its ...
with a margin of error of only 4%, when the current error at the time varied between 7 and 15%. Jean Picard performed the first modern meridian arc measurement in 1669–1670. He measured a Baseline (surveying), baseline using wooden rods, a telescope (for his Angle#Angles in geography and astronomy, angular measurements), and logarithms (for computation). Giovanni Domenico Cassini, Gian Domenico Cassini then his son Jacques Cassini later continued Picard's arc (Paris meridian arc) northward to Dunkirk, France, Dunkirk and southward to the France–Spain border, Spanish border. Cassini divided the measured arc into two parts, one northward from Paris, another southward. When he computed the length of a degree from both chains, he found that the length of one degree of
latitude In geography, latitude is a geographic coordinate system, geographic coordinate that specifies the north-south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at t ...
in the northern part of the chain was shorter than that in the southern part (see illustration). This result, if correct, meant that the earth was not a sphere, but a spheroid, prolate spheroid (taller than wide). However, this contradicted computations by Isaac Newton and Christiaan Huygens. In 1659, Christiaan Huygens was the first to derive the now standard formula for the centrifugal force in his work ''De vi centrifuga''. The formula played a central role in classical mechanics and became known as the second of Newton's laws of motion. Newton's Law of universal gravitation, theory of gravitation combined with the rotation of the Earth predicted the Earth to be an spheroid, oblate spheroid (wider than tall), with a flattening of 1:230. 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 zeniths. On an oblate Earth, the meridional Meridian arc, distance corresponding to one degree of latitude will grow toward the poles, as can be Meridian arc#Meridian distance on the ellipsoid, demonstrated mathematically. The French Academy of Sciences dispatched two expeditions. One expedition (1736–37) under Pierre Louis Maupertuis was sent to Meänmaa#French Geodesic Mission, Torne Valley (near the Earth's northern pole). The French Geodesic Mission, second mission (1735–44) under Pierre Bouguer was sent to what is modern-day Ecuador, 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 reference ellipsoid. In 1787 the first precise trigonometric survey to be undertaken within Britain was the Anglo-French Survey (1784–1790), Anglo-French Survey. Its purpose was to link the Greenwich and Paris' observatories. The survey is very significant as the forerunner of the work of the Ordnance Survey which was founded in 1791, one year after William Roy's death. Johann Georg Tralles surveyed the Bernese Oberland, then the entire Canton of Bern. Soon after the Anglo-French Survey, in 1791 and 1797, he and his pupil Ferdinand Rudolph Hassler measured the base of the Grand Marais, Seeland, Grand Marais (German: ''Grosses Moos'') near Aarberg in Seeland (administrative district), Seeland. This work earned Tralles to be appointed as the representative of the Helvetic Republic on the international scientific committee meeting in Paris from 1798 to 1799 to determine the length of the ''metre''. The French Academy of Sciences had commissioned an expedition led by Jean Baptiste Joseph Delambre and Pierre Méchain, lasting from 1792 to 1799, which attempted to accurately measure the distance between a belfry in Dunkirk, Dunkerque and Montjuïc Castle (Barcelona), Montjuïc castle in Barcelona at the
longitude Longitude (, ) is a geographic coordinate that specifies the east- west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lett ...
of Panthéon, Paris Panthéon. The ''metre'' was defined as one ten-millionth of the shortest distance from the North Pole to the equator Paris meridian, passing through Paris, assuming an Earth's flattening of 1/334. The committee extrapolated from Delambre and Méchain's survey the distance from the North Pole to the Equator which was 5 130 740 toises. As the metre had to be equal to one ten-million of this distance, it was defined as 0,513074 toises or 443,296 lignes of the Toise of Peru (see below).


Asia and Americas

A discovery made in 1672–1673 by Jean Richer turned the attention of mathematicians to the deviation of the Figure of the Earth, Earth's shape from a spherical form. This astronomer, having been sent by the French Academy of Sciences, Academy of Sciences of Paris to Cayenne, in South America, for the purpose of investigating the amount of Atmospheric refraction, astronomical refraction and other astronomical objects, notably the parallax of Mars between Paris and Cayenne in order to determine the Astronomical unit, Earth-Sun distance, 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 pendulum by more than a line (about 112th 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. In South America Bouguer noticed, as did George Everest in the 19th century Great Trigonometric Survey of India, that the astronomical vertical tended to be pulled in the direction of large mountain ranges, due to the gravitational attraction of these huge piles of rock. As this vertical is everywhere perpendicular to the idealized surface of mean sea level, or the geoid, this means that the figure of the Earth is even more irregular than an ellipsoid of revolution. Thus the study of the "undulation of the geoid" became the next great undertaking in the science of studying the figure of the Earth.


19th century

In the late 19th century the International Association of Geodesy, Mitteleuropäische Gradmessung (Central European Arc Measurement) was established by several central European countries and a Central Bureau was set up at the expense of Prussia, within the Geodetic Institute at Berlin. One of its most important goals was the derivation of an international ellipsoid and a gravity formula which should be optimal not only for Europe but also for the whole world. The International Association of Geodesy, Mitteleuropäische Gradmessung was an early predecessor of the International Association of Geodesy (IAG) one of the constituent sections of the International Union of Geodesy and Geophysics (IUGG) which was founded in 1919.


Prime meridian and standard of length

In 1811 Ferdinand Rudolph Hassler 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 United States Coast and Geodetic Survey in 1878—were referred is the French ''metre,'' a copy of which Hassler had brought to the United States in 1805. The Scandinavian-Russian meridian arc or Struve Geodetic Arc, named after the German astronomer Friedrich Georg Wilhelm von Struve, 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 ''Arc du méridien de 25° 20′ entre le Danube et la Mer Glaciale mesuré depuis 1816 jusqu’en 1855''. The flattening of the Earth was estimated at 1/294.26 and the Earth's equatorial radius was estimated at 6378360.7 metres. In the early 19th century, the Paris meridian's arc was recalculated with greater precision between Shetland and the Balearic Islands by the French astronomers François Arago and Jean-Baptiste Biot. In 1821 they published their work as a fourth volume following the three volumes of "''Bases du système métrique décimal ou mesure de l'arc méridien compris entre les parallèles de Dunkerque et Barcelone''" (Basis for the decimal metric system or measurement of the meridian arc comprised between Dunkirk and Barcelona) by Jean Baptiste Joseph Delambre, Delambre and Pierre Méchain, Méchain. Louis Puissant declared in 1836 in front of the French Academy of Sciences 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 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 International Association of Geodesy in Neuchâtel Carlos Ibáñez e Ibáñez de Ibero announced Spain's contribution to the remeasurement and extension of the French meridian arc. In 1870, François Perrier (French Army officer), François Perrier was in charge of resuming the triangulation between Dunkirk and Barcelona. This new survey of the Paris meridian, Paris meridian arc, named West Europe-Africa Meridian-arc by Alexander Ross Clarke, was undertaken in France and in Algeria under the direction of François Perrier (French Army officer), François Perrier 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 Algeria, the Earth equatorial radius was 6377935 metres, the ellipticity being assumed as 1/299.15. 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 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. In 1860, the Russian Government at the instance of Otto Wilhelm von Struve, Otto Wilhelm von Sturve 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 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 Ordnance Survey 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 toise, of which the oldest physical representative was the Toise of Peru. The Toise of Peru had been constructed in 1735 for Pierre Bouguer, Bouguer and Charles Marie de La Condamine, De La Condamine as their standard of reference in the French Geodesic Mission, conducted in actual Ecuador from 1735 to 1744 in collaboration with the Spanish officers Jorge Juan y Santacilia, Jorge Juan and Antonio de Ulloa. Friedrich Bessel was responsible for the nineteenth-century investigations of the shape of the
Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...
by means of the pendulum's determination of gravity and the use of Clairaut's theorem. 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 reversible pendulum as it was used by geodesists at the end of the 19th century was largely due to the work of Bessel, because neither Johann Gottlieb Friedrich von Bohnenberger, its inventor, nor Henry Kater 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 brothers was used in Switzerland in 1865 by Emile Plantamour, Émile Plantamour 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.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, 78 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 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, Adolphe Hirsch 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 Charles Sanders Peirce would independently develop a correction formula which would make it possible to use the observations made using this type of gravimeter. As Carlos Ibáñez e Ibáñez de Ibero 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 Seconds pendulum, pendulum, 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. In 1855, the Dufour map (French: ''Carte Dufour''), the first Topographic Map of Switzerland, topographic map of Switzerland for which the metre was adopted as the unit of length, won the gold medal at the Exposition Universelle. However, the baselines for this map were measured in 1834 with three toises long measuring rods calibrated on a toise made in 1821 by Jean Nicolas Fortin for Friedrich Georg Wilhelm von Struve. The Spanish standard, a geodetic measuring device calibrated on the metre devised by Carlos Ibáñez e Ibáñez de Ibero and Frutos Saavedra Meneses, was also displayed by Jean Brunner at the Exhibition. The Spanish standard consisted of two platinum and copper rulers, each 4 metres long, forming a metallic thermometer when superimposed. As early as 1834, Bessel had used bimetallic rulers constituting a metallic thermometer, according to the method already used by Borda and Antoine Lavoisier, Lavoisier for the arc measurement between Dunkirk and Barcelona. The results of the comparisons of the four rulers that maked up the measuring devices with each other and with the standard that had been used to calibrate them were calculated meticulously by the method of least squares. Alexander Ross Clarke and Henry James published the first results of the standards' comparisons in 1867. The same year Russia, Spain and Portugal joined the International Association of Geodesy, ''Europäische Gradmessung'' and the General Conference of the association proposed the metre as a uniform length standard for the Arc Measurement and recommended the establishment of an International Bureau of Weights and Measures. The International Association of Geodesy, Europäische Gradmessung 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 Charles Sanders Peirce 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, in order to compare them and thus to have the equation of their scales. The Metre Convention was signed in 1875 in Paris and the International Bureau of Weights and Measures was created under the supervision of the International Committee for Weights and Measures. The first president of the International Committee for Weights and Measures was the Spanish geodesist Carlos Ibáñez e Ibáñez de Ibero. He also was the president of the Permanent Commission of the ''International Association of Geodesy, Europäische Gradmessung'' from 1874 to 1886. In 1886 the association changed its name to the International Association of Geodesy, International Geodetic Association and Carlos Ibáñez e Ibáñez de Ibero was reelected as president. He remained in this position until his death in 1891. During this period the International Association of Geodesy, International Geodetic Association gained worldwide importance with the joining of United States, Mexico, Chile, Argentina and Japan. In 1883 the General Conference of the International Association of Geodesy, ''Europäische Gradmessung'' had proposed to select the Prime meridian (Greenwich), Greenwich meridian as prime meridian in the hope that United States and United Kingdom of Great Britain and Ireland, Great Britain 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.


Geodesy and mathematics

In 1804 Johann Georg Tralles was made a member of the German Academy of Sciences at Berlin, Berlin Academy of Sciences. In 1810 he became the first holder of the chair of mathematics at the Humboldt University of Berlin. In the same year he was appointed secretary of the mathematics class at the Berlin Academy of Sciences. Tralles maintained an important correspondence with Friedrich Bessel, Friedrich Wilhelm Bessel and supported his appointment to the University of Königsberg. In 1809 Carl Friedrich Gauss 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 Adrien-Marie Legendre. 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 normal distribution. 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 arithmetic mean is indeed the best estimate of the location parameter by changing both the probability density 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. In 1810, after reading Gauss's work, Pierre-Simon Laplace, after proving the central limit theorem, 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 Gauss–Markov theorem. The publication in 1838 of Friedrich Bessel, Friedrich Wilhelm Bessel's ''Gradmessung in Ostpreußen'' marked a new era in the science of geodesy. Here was found the method of least squares 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 later called ''personal equation'', that several simultaneously observing persons determine slightly different values, especially recording the transition time of stars. Most of the relevant theories were then derived by the German geodesist Friedrich Robert Helmert in his famous books ''Die mathematischen und physikalischen Theorien der höheren Geodäsie'', 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 United States, US geodesist John Fillmore Hayford, Hayford derived a global ellipsoid in ~1910, based on intercontinental isostasy and an accuracy of 200 m. It was adopted by the IUGG as "international ellipsoid 1924".


See also

*Bedford Level experiment *Figure of the Earth *History of the metre *History of cadastre *History of cartography *History of hydrography *History of navigation *History of surveying *Meridian arc#History *Arc measurement#History *


Notes


Works cited

*An early version of this article was taken from the public domain source at http://www.ngs.noaa.gov/PUBS_LIB/Geodesy4Layman/TR80003A.HTM#ZZ4. * * * *


Further reading

*J. L. Greenberg: ''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.'' Cambridge : Cambridge University Press, 1995 *M .R. Hoare: ''Quest for the true figure of the Earth: ideas and expeditions in four centuries of geodesy''. Burlington, VT: Ashgate, 2004 *D. Rawlins: "Ancient Geodesy: Achievement and Corruption" 1984 (Greenwich Meridian Centenary, published in ''Vistas in Astronomy'', v.28, 255–268, 1985) *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' Experiment?", ''Archive for History of Exact Sciences'', v.26, 211–219, 1982 *C. Taisbak: "Posidonius vindicated at all costs? Modern scholarship versus the stoic earth measurer". ''Centaurus'' v.18, 253–269, 1974 * * * {{DEFAULTSORT:History Of Geodesy Geodesy Articles containing video clips History of measurement, G