1.
Greek language
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It is an independent branch of the Indo-European family of languages, native to Greece, western and northeastern Asia Minor, southern Italy, Albania and Cyprus. Greek has the longest documented history of any living language, spanning 34 centuries of written records. The alphabet was in turn the basis of the Latin, Cyrillic, Armenian, Coptic, Gothic and many other writing systems. Together with the Latin traditions of the Roman world, the study of the Greek texts and society of antiquity constitutes the discipline of Classics. During antiquity, it was a widely spoken franca in the Mediterranean world and beyond. Greek would eventually develop into Medieval Greek. The language is spoken by at least million people today in Greece, Cyprus, Italy, Albania, Turkey, the Greek diaspora. Greek roots are often used to coin new words for other languages; Greek and Latin are the predominant sources of scientific vocabulary. It has been spoken since around the 3rd millennium BC, or possibly earlier. Among the Indo-European languages, its date of earliest written attestation is matched only by the now extinct Anatolian languages. The Greek language is conventionally assumed last ancestor of all known varieties of Greek. The unity of Proto-Greek would have ended as Hellenic migrants entered the Greek peninsula sometime in the Bronze Age. Mycenaean Greek: the language of the Mycenaean civilisation. Greek is recorded on tablets dating from the 15th century BC onwards. Ancient Greek: in its various dialects, the language of the Archaic and Classical periods of the ancient Greek civilisation.
Greek language
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Idealized portrayal of Homer
Greek language
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regions where Greek is the official language
Greek language
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Greek language road sign, A27 Motorway, Greece
2.
Medieval Greek
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From the 7th century onwards, Greek was the only language in the Byzantine Empire. This stage of language is thus described as Byzantine Greek. However, this approach is rather arbitrary as it is more an assumption of political linguistic developments. Indeed, by this time the spoken language, particularly pronunciation, had already shifted towards modern forms. Medieval Greek is the link between this vernacular, known as Koine Greek, the Modern Greek language. At first, it was used for official documents, but its influence soon waned. From the beginning of the 6th century, amendments to the law were mostly written in Greek. Furthermore, parts of the Roman Corpus Iuris Civilis were gradually translated into Greek. Under the rule of Emperor Heraclius, who also assumed the Greek title Basileus in 629, Greek became the official language of the Eastern Roman Empire. This was in spite of the fact that the inhabitants of the empire still considered themselves in 1453. The number of those who were able to communicate in Greek may have been far higher. In any case, all cities of the Eastern Roman Empire were strongly influenced by the Greek language. A center of Greek culture and language, fell to the Arabs in 642. During the eighth centuries, Greek was replaced by Arabic as an official language in conquered territories such as Egypt. From the 11th century onwards, the interior of Anatolia was invaded by Seljuq Turks, who advanced westwards.
Medieval Greek
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Manuscript of the Anthology of Planudes (c.1300)
Medieval Greek
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Evolution of Greek dialects from the late Byzantine Empire through to the early 20th century. Demotic in yellow. Pontic in orange. Cappadocian in green. (Green dots indicate Cappadocian Greek speaking villages in 1910.)
3.
Ancient Greeks
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Ancient Greece was a civilization belonging to a period of Greek history from the Greek Dark Ages to c. 5th century BC to the end of antiquity. Immediately following this period was the beginning of the Early Middle Ages and the Byzantine era. Included in ancient Greece is the period of Classical Greece, which flourished during the 5th to 4th centuries BC. Classical Greece began with the era of the Persian Wars. Because of conquests by Alexander the Great of Macedonia, Hellenistic civilization flourished from Central Asia to the western end of the Mediterranean Sea. Classical Antiquity in the Mediterranean region is commonly considered to have begun in the 8th century BC and ended in the 6th century AD. Classical Antiquity in Greece is preceded by the Greek Dark Ages, archaeologically characterised by the protogeometric and geometric styles of designs on pottery. The end of the Dark Ages is also frequently dated to 776 BC, the year of the first Olympic Games. The earliest of these is the Archaic period, in which artists made larger free-standing sculptures in stiff, hieratic poses with the dreamlike "archaic smile". The Archaic period is often taken to end with the overthrow of the last tyrant of Athens and the start of Athenian Democracy in 508 BC. This period saw the Greco-Persian Wars and the Rise of Macedon. Following the Classical period was the Hellenistic period, during which Greek culture and power expanded into the Near and Middle East. This period begins with the death of Alexander and ends with the Roman conquest. Herodotus is widely known as the "father of history": his Histories are eponymous of the entire field. Herodotus was succeeded by authors such as Thucydides, Xenophon, Demosthenes, Plato and Aristotle.
Ancient Greeks
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The Parthenon, a temple dedicated to Athena, located on the Acropolis in Athens, is one of the most representative symbols of the culture and sophistication of the ancient Greeks.
Ancient Greeks
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Dipylon Vase of the late Geometric period, or the beginning of the Archaic period, c. 750 BC.
Ancient Greeks
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Political geography of ancient Greece in the Archaic and Classical periods
4.
Tralles
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Aydın, ancient Greek Tralles, is a city in and the seat of Aydın Province in Turkey's Aegean Region. Its population was 207554 in 2014. City is located along a region, famous for its productivity since ancient times. Figs remain the province's best-known crop, although other agricultural products are also grown intensively and the city has some light industry. A smaller airport, namely Aydın Airport, is located a few kilometers in the South-East of Aydın. The region of Aydın still has the densest network. The province of Aydın is also where a number of internationally known historic sites and centers of tourism are concentrated. The weather warm all round. The city was later taken over by Turks of the Aydinids, whose lands extended towards the north, who named it after Aydinid dynasty. "Aydın" meant "lucid, enlightened" in a distinct evolution of the term, came to mean "educated, intellectual" in modern Turkish. It is still a popular male name. In ancient Greek sources, the name of the city is given as Anthea and Euanthia. During the Seleucid period, it received the name Antiochia. At other times it was also called Seleucia ad Maeandrum and Erynina. In Byzantine times, it was one of the largest Aegean cities in antiquity.
Tralles
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Monument to Turkish War of Independence in Aydın.
Tralles
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A street in Aydın.
Tralles
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Aydın Archaeological Museum.
5.
Byzantine architecture
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Byzantine architecture is the architecture of the Byzantine Empire, also known as the Later Roman or Eastern Roman Empire. Early Byzantine architecture drew upon earlier elements of Roman architecture. Political and territorial changes meant that a distinct style gradually resulted in the Greek cross plan in church architecture. Most of the surviving structures are sacred with secular buildings mostly known only through contemporaneous descriptions. Prime examples of Byzantine architecture date from Justinian I's reign and survive in Ravenna and Istanbul, as well as in Sofia. Secular structures include the ruins of the Great Palace of the innovative walls of Constantinople and Basilica Cistern. A frieze in the Ostrogothic palace in Ravenna depicts an Byzantine palace. Remarkable engineering feats include the 430 m long the pointed arch of Karamagara Bridge. The period of the Macedonian dynasty, traditionally considered the epitome of Byzantine art, has not left a lasting legacy in architecture. The cross-in-square type also became predominant in the Slavic countries which were Christianized during the Macedonian period. Only national forms of architecture can be found in abundance due to this. Those styles can be also in Sicily and Veneto. The Paleologan period is well represented at Chora and St Mary Pammakaristos. Unlike their Slavic counterparts, the Paleologan architects never accented the vertical thrust of structures. As a result, there is little grandeur in the medieval architecture of Byzantium.
Byzantine architecture
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Hagia Sophia Church, Sofia, Bulgaria
Byzantine architecture
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The basilica of Sant'Apollinare Nuovo in Ravenna
Byzantine architecture
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The 11th-century monastery of Hosios Loukas in Greece is representative of the Byzantine art during the rule of the Macedonian dynasty.
Byzantine architecture
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Interior of the Hagia Sophia under renovation, showing many features of the grandest Byzantine architecture.
6.
Constantinople
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Constantinople was the capital city of the Roman/Byzantine Empire, also of the brief Latin, the later Ottoman empires. Constantinople was famed for its massive and complex defences. The first wall of the city was surrounded the city on both sea fronts. Constantinople never truly recovered from the devastation of the Fourth Crusade and the decades of misrule by the Latins. The founding myth of the city has it told that the settlement was named after the leader of the Megarian colonists, Byzas. During this time, the city was also called Roma Constantinopolitana. In the language of other peoples, Constantinople was referred to just as reverently. The medieval Vikings, who had contacts with the empire through their expansion in eastern Europe used the Old Norse name Miklagarðr, later Miklagard and Miklagarth. In Arabic, the city was sometimes called Rūmiyyat al-kubra and in Persian as Takht-e Rum. This was presumably a calque on a Greek phrase such as Βασιλέως Πόλις,'the city of the emperor'. The Turkish name for İstanbul, derives from the Greek phrase eis tin polin, meaning "into the city" or "to the city". In 1928, the Turkish alphabet was changed from Arabic script to Latin script. In time the city came to be known as Istanbul and its variations in most world languages. In Greece today, the city is still called Konstantinoúpolis/Konstantinoúpoli or simply just "the City". Apart from this, little is known about this initial settlement, except that it was abandoned by the time the Megarian colonists settled the site anew.
Constantinople
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Constantinople in the Byzantine era
Constantinople
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Map of Byzantine Constantinople
Constantinople
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Emperor Constantine I presents a representation of the city of Constantinople as tribute to an enthroned Mary and Christ Child in this church mosaic. Hagia Sophia, c. 1000
Constantinople
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Coin struck by Constantine I to commemorate the founding of Constantinople
7.
Byzantine Empire
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During most of its existence, the empire was the most powerful economic, military force in Europe. Several signal events from the 4th to 6th centuries mark the period of transition during which the Roman Empire's Greek East and Latin West divided. Constantine I reorganised the empire, legalised Christianity. Under Theodosius I, Christianity became other religious practices were proscribed. Finally, under the reign of Heraclius, the Empire's administration were restructured and adopted Greek for official use instead of Latin. The borders of the Empire evolved significantly over its existence, as it went through several cycles of recovery. During the reign of Maurice, the north stabilised. In a matter of years the Empire lost Egypt and Syria, to the Arabs. This battle opened the way for the Turks to settle as a homeland. The Empire recovered again during such that by the 12th century Constantinople was the largest and wealthiest European city. Its remaining territories were progressively annexed by the Ottomans over the 15th century. The Fall of Constantinople to the Ottoman Empire in 1453 finally ended the Byzantine Empire. The term comes from "Byzantium", the name of the city of Constantinople before it became Constantine's capital. This older name of the city would rarely be used from this point onward except in poetic contexts. However, it was not until the mid-19th century that the term came in the Western world.
Byzantine Empire
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Tremissis with the image of Justinian the Great (r. 527–565) (see Byzantine insignia)
Byzantine Empire
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Byzantine lamellar armour klivanium (Κλιβάνιον) - a predecessor of Ottoman krug mirror armour
Byzantine Empire
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The Baptism of Constantine painted by Raphael 's pupils (1520–1524, fresco, Vatican City, Apostolic Palace); Eusebius of Caesarea records that (as was common among converts of early Christianity) Constantine delayed receiving baptism until shortly before his death
Byzantine Empire
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Restored section of the Theodosian Walls.
8.
Isidore of Miletus
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He also created the comprehensive compilation of Archimedes' works. Isidore is also renowned for producing the comprehensive compilation of Archimedes' work, one copy of which survived to the present. Emperor Justinian I appointed his architects to rebuild the Hagia Sophia following his victory over protesters within the city of his Roman Empire, Constantinople. The Blues and the Greens, opposed each other in the chariot races at the Hippodrome and often resorted to violence. During the Nika Riot, more than thousand people died. The Hagia Sophia was quickly repaired. Isidore the Younger, introduced the new dome design that can be viewed in the Hagia Sophia in present-day Istanbul, Turkey. After a great earthquake in 989 ruined the dome of Hagia Sophia, the Byzantine officials summoned Trdat the Architect to Byzantium to organize repairs. The restored dome was completed by 994. Cakmak, AS; Taylor, RM; Durukal, E. "The Structural Configuration of the First Dome of Justinian's Hagia Sophia: An Investigation Based on Structural and Literary Analysis". Soil Earthquake Engineering. 29. Krautheimer, Richard. Early Christian and Byzantine Architecture.
Isidore of Miletus
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Interior panorama of the Hagia Sophia, the patriarchal basilica designed by Isidore. The influence of Archimedes' solid geometry works, which Isidore was the first to compile, is evident.
9.
Hagia Sophia
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The building was later converted into an Ottoman mosque from 29 May 1453 until 1931. It was then secularized and opened as a museum on 1 February 1935. Famous in particular for its massive dome, it is considered the epitome of Byzantine architecture and is said to have "changed the history of architecture". It remained the world's largest cathedral for nearly a thousand years, until Seville Cathedral was completed in 1520. It was designed by the Greek geometers Isidore of Miletus and Anthemius of Tralles. The church contained a large collection of relics and featured, among other things, a 15-metre silver iconostasis. In 1453, Constantinople was conquered by the Ottoman Empire under Mehmed the Conqueror, who ordered this main church of Orthodox Christianity converted into a mosque. By that point, the church had fallen into a state of disrepair. Nevertheless, the Christian cathedral made a strong impression on the new Ottoman rulers and they decided to convert it into a mosque. Islamic features -- such as four minarets -- were added. It remained a mosque until 1931, when it was closed to the public for four years. It was re-opened by the Republic of Turkey. Hagia Sophia was, as of 2014, the second-most visited museum in Turkey, attracting almost 3.3 million visitors annually. According to data released by the Turkish Culture and Tourism Ministry, Hagia Sophia was Turkey’s most visited tourist attraction in 2015. From its initial conversion until the construction of the nearby Sultan Ahmed Mosque in 1616, it was the principal mosque of Istanbul.
Hagia Sophia
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A view of Hagia Sophia, Istanbul
Hagia Sophia
Hagia Sophia
10.
Justinian I
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During his reign, Justinian sought to reconquer the lost western half of the historical Roman Empire. Because of his restoration activities, Justinian has sometimes been called the "last Roman" in modern historiography. This ambition was expressed by the partial recovery of the territories of the western Roman empire. Belisarius, swiftly conquered the Vandal kingdom in North Africa. The prefect Liberius reclaimed the south of the Iberian peninsula, establishing the province of Spania. These campaigns re-established Roman control over the western Mediterranean, increasing the Empire's annual revenue by over a solidi. During his Justinian also subdued the Tzani, a people on the east coast of the Black Sea that had never been under Roman rule before. His building program yielded such masterpieces as the church of Hagia Sophia. A devastating outbreak of bubonic plague in the early 540s marked the end of an age of splendour. Justinian was born around 482. A native speaker of Latin, he came from a family believed to have been of Illyro-Roman or Thraco-Roman origins. The cognomen Iustinianus, which he took later, is indicative of adoption by his Justin. During his reign, he founded Justiniana Prima far from his birthplace, which today is in South East Serbia. His mother was the sister of Justin. Justin, in the imperial guard before he became emperor, adopted Justinian, ensured the boy's education.
Justinian I
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Detail of a contemporary portrait mosaic in the Basilica of San Vitale, Ravenna.
Justinian I
Justinian I
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The ancient town of Tauresium, the birthplace of Justinian I, located in today's Republic of Macedonia.
Justinian I
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The Barberini Ivory, which is thought to portray either Justinian or Anastasius I
11.
Ancient Rome
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Ancient Rome was an Italic civilization that began on the Italian Peninsula as early as the 8th century BC. In its approximately 12 centuries of existence, Roman civilization shifted from a monarchy to a classical republic and then to an increasingly autocratic empire. Through assimilation, it came to dominate Southern and Western Europe, Asia Minor, parts of Northern and Eastern Europe. Rome was preponderant throughout the Mediterranean region and was one of the most powerful entities of the ancient world. Societies are known as the Greco-Roman world. Roman society has contributed to modern government, law, politics, engineering, art, literature, architecture, technology, warfare, religion, society. The Roman Empire emerged with the end of the Republic and the dictatorship of Augustus Caesar. 721 years of Roman-Persian Wars started in 92 BC with their first war against Parthia. It would have lasting effects and consequences for both empires. Under Trajan, the Empire reached its territorial peak. Republican mores and traditions started to decline during the imperial period, with civil wars becoming a prelude common to the rise of a new emperor. Splinter states, such as the Palmyrene Empire, would temporarily divide the Empire during the crisis of the 3rd century. Attacked by various migrating peoples, the western part of the empire broke up in the 5th century. This splintering is a landmark historians use to divide the ancient period of universal history from the pre-medieval "Dark Ages" of Europe. King Numitor was deposed by Amulius, while Numitor's daughter, Rhea Silvia, gave birth to the twins.
Ancient Rome
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Senātus Populus que Rōmānus
Ancient Rome
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Roman Republic
Ancient Rome
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According to legend, Rome was founded in 753 BC by Romulus and Remus, who were raised by a she-wolf.
Ancient Rome
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This bust from the Capitoline Museums is traditionally identified as a portrait of Lucius Junius Brutus.
12.
Roman law
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The historical importance of Roman law is reflected in many legal systems influenced by it. After the dissolution of the Western Roman Empire, the Roman law remained in the Eastern Roman Empire. From the 7th onward, the legal language in the East was Greek. Roman law also denotes the legal system applied until the end of the 18th century. In Germany, Roman practice remained in place longer under the Holy Roman Empire. North American common law were influenced also by Roman law, notably in their Latinate legal glossary. Also, Eastern European law was influenced by the "Farmer's Law" of the medieval legal system. It is believed that Roman Law is rooted in the Etruscan religion, emphasising ritual. The legal text is the Law of the Twelve Tables, dating from the mid-5th century BC. The plebeian tribune, C. Terentilius Arsa, proposed that the law should be written, in order to prevent magistrates from applying the law arbitrarily. According to the traditional story, ten Roman citizens were chosen to record the laws. While they were performing this task, they were given political power, whereas the power of the magistrates was restricted. These laws were regarded as unsatisfactory by the plebeians. A second decemvirate is said to have added two further tablets in 449 BC.
Roman law
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Cicero, author of the classic book The Laws, attacks Catiline for attempting a coup in the Roman Senate.
Roman law
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Ancient Rome
Roman law
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Title page of a late 16th-century edition of the Digesta, part of Emperor Justinian 's Corpus Juris Civilis
13.
Joist
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In architecture and engineering, a joist is one of the horizontal supporting members that run between foundations, walls, or beams to support a ceiling or floor. Typically, a joist has the cross section of a plank. Joists are often supported by beams laid out in repetitive patterns. The wider the span between the supporting structures, the deeper the joist will need to be if it is not to deflect under load. Lateral support called dwang, strutting also increases its strength. Many joist manufacturers supply load tables in order to allow designers to select the proper joist sizes for their projects. Joists which land on a binding joist are called bridging joists. A large beam in the ceiling of a room carrying joists is a beam. A joist may be installed flush with the bottom of the beam or sometimes below the beam. Joists left visible from below are called "naked flooring" or "articulated" and were typically planed smooth and sometimes chamfered or beaded. Joists may also be tenoned during the raising with a soffit tenon or a tusk tenon. Joists can also be joined by being slipped into mortises after the beams are in place such as a chase mortise, "short joist". Joists can have different joints on either ends such as being lodged on the other end. A reduction in the under-side of cogged joist-ends may be square, curved. Sometimes they are pinned or designed to hold under tension.
Joist
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A double floor is a floor framed with joists supported by larger timbers.
Joist
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A single floor or simple set of joists. If the joists land directly above the studs they are stacked.
Joist
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These joists land on a beam. Between some of the joists is a form of pugging used for insulation and air sealing. Image: Rijksdienst voor het Cultureel Erfgoed
14.
Thunder
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Thunder is the sound caused by lightning. Depending on the nature of the lightning, thunder can range from a sharp, loud crack to a long, low rumble. The sudden increase in temperature from lightning produces rapid expansion of the air surrounding and within a bolt of lightning. The cause of thunder has been the subject of centuries of speculation and scientific inquiry. Subsequently, other theories were proposed. By the mid-19th century, the accepted theory was that lightning produced a vacuum. The average is about 20,400 K. This heating causes a outward expansion, impacting the surrounding cooler air at a speed faster than sound would otherwise travel. Experimental studies of simulated lightning have produced results largely consistent with this model, though there is continued debate of the process. Other causes have also been proposed, relying on electrodynamic effects of the current acting on the plasma in the bolt of lightning. The shockwave in thunder is sufficient to cause injury, such as internal contusion, to individuals nearby. Thunder results when lightning strikes between cloud and ground occur during a temperature inversion. In such an inversion, the air near the ground is cooler than the higher air. The sound energy is thus concentrated in the near-ground layer. The d in Modern English thunder is now found as well in Modern Dutch donder.
Thunder
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Cumulonimbus clouds often form thunderstorms.
Thunder
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Thunder is the sound produced by lightning.
15.
Lightning
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Lightning is a sudden electrostatic discharge that occurs during an electrical storm. This discharge occurs between electrically charged regions of a cloud, between a cloud and the ground. Lightning sound in the form of thunder. This article incorporates public material from the National Oceanic and Atmospheric Administration document "Understanding Lightning: Thunderstorm Electrification". There is general agreement on some of the basic concepts of thunderstorm electrification. At that place, the combination of rapid upward air movement produces a mixture of super-cooled cloud droplets, small ice crystals, soft hail. The updraft carries very small ice crystals upward. At the same time, the graupel, denser, tends to fall or be suspended in the rising air. The differences in the movement of the cause collisions to occur. The graupel becomes negatively charged. See figure to the left. The updraft carries the positively charged ice crystals upward toward the top of the cloud. The denser graupel is either suspended in the middle of the thunderstorm cloud or falls toward the lower part of the storm. This part of the cloud is called the anvil. While this is the main process for the thunderstorm cloud, some of these charges can be redistributed by air movements within the storm.
Lightning
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A lightning flash during a thunderstorm
Lightning
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Lightning in Belfort, France
Lightning
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View of lightning from an airplane flying above a system.
Lightning
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A lightning strike from cloud to ground in the California, Mojave Desert
16.
Gunpowder
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Gunpowder, also known as black powder, is the earliest known chemical explosive. It is a mixture of sulfur, charcoal, nitrate. The saltpeter is an oxidizer. Formulations used in blasting rock are called blasting powder. Gunpowder is still used in antique firearms because modern propellants are too powerful and could break the already fragile barrels. This discovery led in China. In the centuries following the Chinese discovery, gunpowder weapons began appearing in the Muslim world, India. The technology spread through the Middle East or Central Asia, then into Europe. The earliest Western accounts of gunpowder appear in texts written by English philosopher Roger Bacon in the 13th century. The hypothesis that gunpowder was used by ancient Hindus was first mentioned by some Sanskrit scholars. The most ardent protagonists were Nathaniel Halhad, Johann Backmann, Gustav Oppert. However due to lack of sufficient proof, these theories have not been widely accepted. Gunpowder has a hazard class of 1.1 D. It has a point of approximately 427 -- 464 ° C. The specific point may vary based on the specific composition of the gunpowder.
Gunpowder
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Black powder for muzzleloading rifles and pistols in FFFG granulation size. U.S. Quarter (diameter 24 mm) for comparison.
Gunpowder
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A Mongol bomb thrown against a charging Japanese samurai during the Mongol invasions of Japan after founding the Yuan Dynasty, 1281.
Gunpowder
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Yuan Dynasty hand cannon dated to 1288.
Gunpowder
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Chinese Ming Dynasty (1368-1644) matchlock firearms
17.
Greek mathematics
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Greek mathematicians were united by language. Greek mathematics of the period following Alexander the Great is sometimes called Hellenistic mathematics. The word "mathematics" itself derives from the ancient Greek μάθημα, meaning "subject of instruction". The origin of Greek mathematics is not well documented. The earliest advanced civilizations in Greece and in Europe were the Minoan and later Mycenaean civilization, both of which flourished during the 2nd millennium BC. While these civilizations were capable of advanced engineering, including four-story palaces with beehive tombs, they left behind no mathematical documents. Though no direct evidence is available, it is generally thought that the neighboring Babylonian and Egyptian civilizations had an influence on the younger Greek tradition. Historians traditionally place the beginning of Greek mathematics proper to the age of Thales of Miletus. Despite this, it is generally agreed that Thales is the first of the seven wise men of Greece. Thales' theorem and theorem are attributed to Thales. It is for this reason that Thales is often hailed as the true mathematician. Thales is also thought to be the earliest known man in history to whom specific mathematical discoveries have been attributed. Another important figure in the development of Greek mathematics is Pythagoras of Samos. Like Thales, Pythagoras also traveled to Egypt and Babylon, then under the rule of Nebuchadnezzar, but settled in Croton, Magna Graecia. And since in antiquity it was customary to give all credit to the master, Pythagoras himself was given credit for the discoveries made by his order.
Greek mathematics
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Statue of Euclid in the Oxford University Museum of Natural History
Greek mathematics
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An illustration of Euclid 's proof of the Pythagorean Theorem
Greek mathematics
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The Antikythera mechanism, an ancient mechanical calculator.
18.
Burning Glass
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Burning mirrors achieve a similar effect by using reflecting surfaces to focus the light. They were used for burning materials in closed glass vessels where the products of combustion could be trapped for analysis. The glass was a useful contrivance in the days before electrical ignition was easily achieved. The technology of the glass has been known since antiquity. Vases filled with water used to start fires were known in the ancient world. Burning lenses were used to light sacred fires in temples. Plutarch refers to a burning mirror made of joined metal mirrors installed at the temple of the Vestal Virgins. Aristophanes mentions The Clouds. "Strepsiades. Have you ever seen a transparent stone at the druggists', with which you may kindle fire?" The sacred fire in the classic temples as the Olympic torch had to be pure and to come directly from the gods. For this they used the sun's rays focused with lenses and not impure triggers. The renowned mathematician, was said to have used a burning glass as a weapon in 212 BC, when Syracuse was besieged by Marcus Claudius Marcellus. The Roman fleet was supposedly incinerated, though Archimedes was slain. The legend of Archimedes gave rise until the late 17th century.
Burning Glass
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A replica (on a smaller scale) of the burning lens owned by Joseph Priestley, in his laboratory
Burning Glass
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Close-up view of a flat Fresnel lens. These thin, light weight, non fragile and low cost lens can be used as burning-glass in emergency situations.
19.
Ellipse
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As such, it is a generalization of a circle, a special type of an ellipse having both focal points at the same location. Ellipses are the closed type of conic section: a curve resulting from the intersection of a cone by a plane. Ellipses have many similarities of conic sections: parabolas and hyperbolas, both of which are open and unbounded. The cross section of a cylinder is an ellipse, unless the section is parallel to the axis of the cylinder. This ratio is called the eccentricity of the ellipse. Ellipses are common in physics, engineering. The same is true for all other systems having two astronomical bodies. The shapes of stars are often well described by ellipsoids. It is also the simplest figure formed when the horizontal and vertical motions are sinusoids with the same frequency. A similar effect leads to elliptical polarization of light in optics. ἔλλειψις, was given by Apollonius of Perga in his Conics, emphasizing the connection of the curve with "application of areas". Ellipses have two perpendicular axes about which the ellipse is symmetric. Due to this symmetry, these axes intersect at the center of the ellipse. The larger of these two axes, which corresponds on the ellipse, is called the major axis. The smaller distance between antipodal points on the ellipse, is called the minor axis.
Ellipse
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Drawing an ellipse with two pins, a loop, and a pen
Ellipse
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An ellipse obtained as the intersection of a cone with an inclined plane.
20.
Apollonius of Perga
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Apollonius of Perga was a Greek geometer and astronomer noted for his writings on conic sections. His innovative terminology, especially in the field of conics, influenced many later scholars including Ptolemy, Francesco Maurolico, Johannes Kepler, Isaac Newton, René Descartes. Apollonius gave the ellipse, the hyperbola their modern names. Ptolemy describes Apollonius' theorem in the Almagest XII.1. Apollonius also researched the history, for which he is said to have been called Epsilon. The crater Apollonius on the Moon is named in his honor. He is one of the ancient geometers. The degree of originality of the Conics can best be judged from Apollonius's own prefaces. Books i–iv he describes as an "elementary introduction" containing essential principles, while the other books are specialized investigations in particular directions. Allusions such as Euclid's four Books on Conics, show a debt not only to Euclid but also to Conon and Nicoteles. The way the cone is cut does not matter. It is the form of the fundamental property that leads him to give their names: parabola, ellipse, hyperbola. Thus Books v–vii are clearly original. He further developed relations between the corresponding ordinates that are equivalent to rhetorical equations of curves. Curves were not determined by equations.
Apollonius of Perga
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Pages from the 9th century Arabic translation of the Conics
Apollonius of Perga
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Parabola connection with areas of a square and a rectangle, that inspired Apollonius of Perga to give the parabola its current name.
21.
Directrix (conic section)
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In mathematics, a conic section is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the ellipse. The type of conic is determined by the value of the eccentricity. Some geometric properties can be studied as algebraic conditions. In the Euclidean plane, the conic sections share many properties. The commonality becomes evident. Further extension, by expanding the real coordinates to admit complex coordinates, provides the means to see this unification algebraically. The conic sections have provided a rich source of interesting and beautiful results in Euclidean geometry. A conic is the curve obtained as the intersection of a plane, called the cutting plane, with the surface of a double cone. Planes that pass through the vertex of the cone will intersect the cone of intersecting lines. Some authors do not consider them to be conics at all. Unless otherwise stated, we shall assume that "conic" refers to a non-degenerate conic. There are three types of conics, the ellipse, hyperbola. The circle is a special kind of ellipse, although historically it had been considered as a fourth type. The ellipse arise when the intersection of the cone and plane is a closed curve.
Directrix (conic section)
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Table of conics, Cyclopaedia, 1728
Directrix (conic section)
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Types of conic sections: 1. Parabola 2. Circle and ellipse 3. Hyperbola
Directrix (conic section)
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Diagram from Apollonius' Conics, in a 9th century Arabic translation
Directrix (conic section)
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The paraboloid shape of Archeocyathids produces conic sections on rock faces
22.
Parabola
–
It fits any of several superficially different mathematical descriptions which can all be proved to define curves of exactly the same shape. One description of a parabola involves a line. The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from the focus. A third description is algebraic. A parabola is a graph of a quadratic function, y = x2, for example. The perpendicular to the directrix and passing through the focus is called the "axis of symmetry". The point on the parabola that intersects the axis of symmetry is the point where the parabola is most sharply curved. The distance between the focus, measured along the axis of symmetry, is the "focal length". The "latus rectum" is the chord of the parabola which passes through the focus. Parabolas can open up, down, right, or in some other arbitrary direction. Any parabola can be rescaled to fit exactly on any other parabola --, all parabolas are geometrically similar. Conversely, light that originates from a source at the focus is reflected into a parallel beam, leaving the parabola parallel to the axis of symmetry. The same effects occur with other forms of energy. This reflective property is the basis of practical uses of parabolas.
Parabola
–
Parabolic compass designed by Leonardo da Vinci
Parabola
–
Part of a parabola (blue), with various features (other colours). The complete parabola has no endpoints. In this orientation, it extends infinitely to the left, right, and upward.
Parabola
–
A bouncing ball captured with a stroboscopic flash at 25 images per second. Note that the ball becomes significantly non-spherical after each bounce, especially after the first. That, along with spin and air resistance, causes the curve swept out to deviate slightly from the expected perfect parabola.
Parabola
–
Parabolic trajectories of water in a fountain.
23.
Mathematics in medieval Islam
–
Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics and Indian mathematics. Arabic works also played an important role during the 10th to 12th centuries. The study of algebra, which itself is derived from "reunion of broken parts", flourished during the Islamic golden age. A scholar in the House of Wisdom in Baghdad, is along with the Greek mathematician Diophantus, known as the father of algebra. Unlike Diophantus, gives general solutions for the equations he deals with. Al-Khwarizmi's algebra was rhetorical, which means that the equations were written out in full sentences. This was unlike the algebraic work of Diophantus, syncopated, meaning that some symbolism is used. The transition to symbolic algebra, where only symbols are used, can be seen in the work of Ibn al-Banna' al-Marrakushi and Abū al-Ḥasan ʿAlī al-Qalaṣādī. It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics, essentially geometry. Algebra was a unifying theory which allowed irrational numbers, geometrical magnitudes, etc. to all be treated as "algebraic objects". Other mathematicians during this time period expanded on the algebra of Al-Khwarizmi. Omar Khayyam, along with Sharaf al-Dīn al-Tūsī, found several solutions of the cubic equation. Omar Khayyam found the geometric solution of a cubic equation. Omar Khayyám wrote the Treatise on Demonstration of Problems of Algebra going beyond the Algebra of al-Khwārizmī.
Mathematics in medieval Islam
–
A page from the The Compendious Book on Calculation by Completion and Balancing by Al-Khwarizmi.
Mathematics in medieval Islam
–
Engraving of Abū Sahl al-Qūhī 's perfect compass to draw conic sections.
Mathematics in medieval Islam
–
The theorem of Ibn Haytham.
24.
Book of Optics
–
Alhazen's work extensively affected the development of optics in Europe between 1650. Before the writing of the Book of Optics there were two types of theories of vision that were held in contention. One was the extramission or theory. The striking of the rays on the object allow the viewer to perceive things such as the color, size of the object. Al-Haytham held the theory of vision, offering many reasons against the extramission theory. Secondary light is the light that comes from accidental objects. Accidental light can only exist if there is a source of primary light. Both secondary light travel in straight lines. Opaque objects can become luminous bodies themselves which radiate secondary light. Al-Haytham presents many experiments in Optics that uphold his claims about its transmission. Through experimentation Book concludes that color can not exist without air. As objects radiate light in straight lines in all directions, the eye must also be hit with this light over its outer surface. Al-Haytham solved this problem using his theory of refraction. According to al-Haytham, this causes them to be weakened. Book claimed that all the rays other than the one that hits the eye perpendicularly are not involved in vision.
Book of Optics
–
Cover page for Ibn al-Haytham's Book of Optics
Book of Optics
–
Front page of the Latin Opticae Thesaurus, which included Alhazen's Book of Optics, showing rainbows, parabolic mirrors, distorted images caused by refraction in water, and other optical effects.
25.
Dara (Mesopotamia)
–
Dara or Daras was an important East Roman fortress city in northern Mesopotamia on the border with the Sassanid Empire. The former bishopric remains a Catholic titular see. The Turkish village of Oğuz, Mardin Province, occupies its location. During the Anastasian War in 502–506, the Roman armies fared badly against the Sassanid Persians. Workers from all over Mesopotamia were gathered and worked with great haste. It took the name became the seat of the Roman dux Mesopotamiae. Thus Byzantine Emperor Justinian I was compelled to undertake extensive repairs to the city, afterwards renaming Iustiniana Nova. The inner wall raised by a new storey, doubling its height to about 20 m. A moat dug out and filled with water. Justinian's engineers also diverted the nearby river Cordes towards the city by a canal. The river now flowed through the city, ensuring ample supply. In addition, two new churches were constructed, the "Great Church", one dedicated to St Bartholomew. It was taken again after a nine-month siege, recovered again for the Roman Empire by Heraclius. Finally captured by the Arabs, the city then lost its military significance, declined and was eventually abandoned. Dara became the site of massacre during the Armenian Genocide.
Dara (Mesopotamia)
–
Ruins of rock-cut building in Daraa
26.
International Standard Book Number
–
The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each variation of a book. For example, an e-book, a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned after 1 January 2007, 10 digits long if assigned before 2007. The method of assigning an ISBN varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated based upon the 9-digit Standard Book Numbering created in 1966. The 10-digit ISBN format was published in 1970 as international standard ISO 2108. The International Standard Serial Number, identifies periodical publications such as magazines; and the International Standard Music Number covers for musical scores. The ISBN configuration of recognition was generated in 1967 in the United Kingdom by Emery Koltay. The 10-digit ISBN format was published as international standard ISO 2108. The United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978. An SBN may be converted by prefixing the digit "0". This can be converted to ISBN 0-340-01381-8; the digit does not need to be re-calculated. Since 1 ISBNs have contained 13 digits, a format, compatible with "Bookland" European Article Number EAN-13s.
International Standard Book Number
–
A 13-digit ISBN, 978-3-16-148410-0, as represented by an EAN-13 bar code
27.
Public domain
–
Works in the public domain are those whose exclusive intellectual property rights have expired, have been forfeited, or are inapplicable. Examples for works actively dedicated by their authors are reference implementations of cryptographic algorithms, NIH's ImageJ, the CIA's World Factbook. As rights vary, a work may be subject to rights in one country and be in the public domain in another. The res nullius was defined as things not yet appropriated. The res communes was defined as "things that could be commonly enjoyed by mankind, such as air, sunlight and ocean." When the early copyright law was first established in Britain with the Statute of Anne in 1710, public domain did not appear. However, similar concepts were developed in the eighteenth century. Instead of "public domain" they used terms such as propriété publique to describe works that were not covered by copyright law. The phrase "fall in the public domain" can be traced to mid-nineteenth century France to describe the end of term. In this historical context Paul Torremans describes copyright as a "little reef of private right jutting up from the ocean of the public domain." Because law is different from country to country, Pamela Samuelson has described the public domain as being "different sizes at different times in different countries". However, the usage of the term domain can be more granular, including for example uses of works in copyright permitted by copyright exceptions. Such a definition regards work in copyright as limitation on ownership. The materials that compose our cultural heritage must be free for all living to use no less than matter necessary for biological survival." Edgar Huntly, Wieland and Sky-Walk by Charles Brockden Brown Camilla, Evelina and Cecilia by Frances Burney Jonathan Dickinson's Journal by Jonathan Dickinson.
Public domain
–
Newton's own copy of his Principia, with hand-written corrections for the second edition
Public domain
–
L.H.O.O.Q. (1919). Derivative work by the Dadaist Marcel Duchamp based on the Mona Lisa.
28.
University of St Andrews
–
The University of St Andrews is a British public research university in St Andrews, Fife, Scotland. It is the oldest of the four ancient universities of Scotland and the third oldest university in the English-speaking world. St Andrews was founded between 1413, when the Avignon Antipope Benedict XIII issued a papal bull to a small group of Augustinian clergy. St Andrews is made up including 18 academic schools organised into four faculties. The university occupies historic and modern buildings located throughout the town. The academic year is divided into Candlemas. In time, over one-third of the town's population is either a staff student of the university. It is ranked behind Oxbridge. The Times Higher Education World Universities Ranking names St Andrews among the world's Top 50 universities for Social Sciences, Arts and Humanities. St Andrews has the highest student satisfaction amongst all multi-faculty universities in the United Kingdom. St Andrews has affiliated faculty, including eminent mathematicians, scientists, theologians, politicians. Six Nobel Laureates are amongst St Andrews' alumni and former staff: two in Chemistry and Physiology or Medicine, one each in Peace and Literature. A charter of privilege was bestowed by the Bishop of Henry Wardlaw, on 28 February 1411. King James I of Scotland confirmed the charter of the university in 1432. Subsequent kings supported the university with King James V "confirming privileges of the university" in 1532.
University of St Andrews
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College Hall, within the 16th century St Mary's College building
University of St Andrews
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University of St Andrews shield
University of St Andrews
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St Salvator's Chapel in 1843
University of St Andrews
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The "Gateway" building, built in 2000 and now used for the university's management department
29.
Anaxagoras
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Anaxagoras was a Pre-Socratic Greek philosopher. Born in Clazomenae in Asia Minor, Anaxagoras was the first to bring philosophy to Athens. He introduced the concept of Nous as an ordering force, which separated out the original mixture, homogeneous, or nearly so. He also gave scientific accounts of natural phenomena. Anaxagoras is believed to have enjoyed some wealth and political influence in Asia Minor. However, he supposedly surrendered this out of a fear that they would hinder his search for knowledge. A sentence, denoted by Maximus, as being "possessed of sought-after wisdom!" Although a Greek, he may have been a soldier of the Persian army when Clazomenae was suppressed during the Ionian Revolt. In early manhood he went to Athens, rapidly becoming the centre of Greek culture. There he is said to have remained for thirty years. The poet Euripides derived from him an enthusiasm for science and humanity. Anaxagoras brought philosophy and the spirit of scientific inquiry to Athens. He was the first to explain that the moon shines by reflecting the sun's light. Disturbances in this air sometimes causes earthquakes. These speculations made him vulnerable to a charge of impiety.
Anaxagoras
–
Anaxagoras; part of a fresco in the portico of the National University of Athens.
Anaxagoras
–
Anaxagoras, depicted as a medieval scholar in the Nuremberg Chronicle
30.
Archytas
–
Archytas was an Ancient Greek philosopher, mathematician, astronomer, statesman, strategist. Famous for being the reputed founder of mathematical mechanics, as well as a good friend of Plato. Archytas was the son of Mnesagoras or Histiaeus. For a while, he was a teacher of mathematics to Eudoxus of Cnidus. Eudoxus' student was Menaechmus. As a Pythagorean, Archytas believed that not geometry, could provide a basis for satisfactory proofs. Archytas is believed to be the founder of mathematical mechanics. This machine, which its inventor called The pigeon, may have been pivot for its flight. Archytas also wrote some lost works, as he was included in the list of the twelve authors of works of mechanics. Thomas Winter has suggested that the pseudo-Aristotelian Mechanical Problems misattributed. Archytas named the harmonic mean, important later in projective geometry and number theory, though he did not invent it. According to Eutocius, Archytas solved the problem of doubling the cube in his manner with a geometric construction. Hippocrates of Chios before, reduced this problem to finding mean proportionals. The Archytas curve, which he used in his solution of the cube problem, is named after him. Militarily, Archytas appears to have been the dominant figure in Tarentum in his generation, somewhat comparable to Pericles in Athens a half-century earlier.
Archytas
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Bust from the Villa of the Papyri in Herculaneum, once identified as Archytas, now thought to be Pythagoras
31.
Aristarchus of Samos
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Like Anaxagoras before him, he suspected that the stars were just other bodies like the Sun, albeit further away from Earth. His astronomical ideas were often rejected in favor of the incorrect geocentric theories of Aristotle and Ptolemy. Copernicus had attributed the heliocentric theory to Aristarchus. This is the common account as you have heard from astronomers. Since stellar parallax is only detectable with telescopes, his accurate speculation was unprovable at the time. It is a common misconception that the heliocentric view was held as sacrilegious by the contemporaries of Aristarchus. This is due to Gilles Ménage's translation of a passage from Plutarch's On the Apparent Face in the Orb of the Moon. The resulting misconception of an isolated and persecuted Aristarchus is still transmitted today. Still, no stellar parallax was observed, Plato, Aristotle and Ptolemy preferred the geocentric model, held as true throughout the Middle Ages. The heliocentric theory was successfully revived by Copernicus, after which Johannes Kepler described planetary motions with greater accuracy with his three laws. Isaac Newton later gave a theoretical explanation based on laws of gravitational attraction and dynamics. The only surviving work usually attributed to Aristarchus, On the Sizes and Distances of the Sun and Moon, is based on a geocentric world view. The discrepancy may come from a misinterpretation of what unit of measure was meant by a certain Greek term in Aristarchus' text. Aristarchus claimed that at half moon, the angle between the Sun and Moon was 87°. Aristarchus is known to have also studied light and vision.
Aristarchus of Samos
–
Statue of Aristarchos of Samos at the Aristotle University of Thessaloniki
Aristarchus of Samos
–
Aristarchus's 3rd-century BC calculations on the relative sizes of (from left) the Sun, Earth and Moon, from a 10th-century AD Greek copy
32.
Archimedes
–
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. He was also one of the first to apply mathematics to physical phenomena, founding statics, including an explanation of the principle of the lever. He is credited with designing innovative machines, such as his screw pump, defensive war machines to protect his native Syracuse from invasion. Archimedes died during the Siege of Syracuse when he was killed despite orders that he should not be harmed. Unlike his inventions, the mathematical writings of Archimedes were little known in antiquity. The date of birth is based by the Byzantine Greek historian John Tzetzes that Archimedes lived for 75 years. In The Sand Reckoner, Archimedes gives his father's name as Phidias, an astronomer about whom nothing is known. Plutarch wrote in his Parallel Lives that Archimedes was related to the ruler of Syracuse. This work has been lost, leaving the details of his life obscure. It is unknown, for instance, whether he ever had children. During his youth, Archimedes may have studied in Alexandria, Egypt, where Conon of Samos and Eratosthenes of Cyrene were contemporaries. He referred as his friend while two of his works have introductions addressed to Eratosthenes. According to the popular account given by Plutarch, Archimedes was contemplating a mathematical diagram when the city was captured. He declined, saying that he had to finish working on the problem.
Archimedes
–
Archimedes Thoughtful by Fetti (1620)
Archimedes
–
Cicero Discovering the Tomb of Archimedes by Benjamin West (1805)
Archimedes
–
Artistic interpretation of Archimedes' mirror used to burn Roman ships. Painting by Giulio Parigi.
Archimedes
–
A sphere has 2/3 the volume and surface area of its circumscribing cylinder including its bases. A sphere and cylinder were placed on the tomb of Archimedes at his request. (see also: Equiareal map)
33.
Autolycus of Pitane
–
Autolycus of Pitane was a Greek astronomer, mathematician, geographer. The crater Autolycus was named in his honour. Autolycus was born within Ionia, Asia Minor. Autolycus is known to have taught Arcesilaus. Another On Risings and Settings of celestial bodies. Autolycus' works were translated in the sixteenth century. On the Moving Sphere is believed to be the oldest mathematical treatise from ancient Greece, completely preserved. All mathematical works prior to Autolycus' Sphere are taken from later summaries, commentaries, or descriptions of the works. In Europe, it was brought back during the crusades in the 12th century, translated back into Latin. In his Sphere, Autolycus studied the characteristics and movement of a sphere. The theorem statement is clearly enunciated, finally a concluding remark is made. Moreover, it gives indications of what theorems were well known in his day. The second book is actually an expansion of higher quality. He wrote that "any star which sets always rises and sets at the same point in the horizon." Autolycus was a strong supporter of Eudoxus' theory of homocentric spheres.
Autolycus of Pitane
–
De sphaera quae movetur liber
34.
Bion of Abdera
Bion of Abdera
–
v
35.
Chrysippus
–
Chrysippus of Soli was a Greek Stoic philosopher. He was a native of Soli, Cilicia, but moved to Athens as a young man, where he became a pupil of Cleanthes in the Stoic school. When Cleanthes died, around 230 BC, Chrysippus became the third head of the school. Chrysippus excelled in logic, the theory of knowledge, ethics and physics. He created an original system of propositional logic in order to better understand the workings of the universe and role of humanity within it. He adhered to a deterministic view of fate, but nevertheless sought a role for personal freedom in thought and action. He initiated the success of Stoicism as one of the most influential philosophical movements for centuries in the Greek and Roman world. Chrysippus, the son of Apollonius of Tarsus, was born at Soli, Cilicia. He was slight in stature, is reputed to have trained as a long-distance runner. While still young, he lost his substantial inherited property when it was confiscated to the king's treasury. Chrysippus moved to Athens, where he became the disciple of Cleanthes, then the head of the Stoic school. He is believed to have attended the courses of Arcesilaus and his successor Lacydes, in the Platonic Academy. Chrysippus threw himself eagerly into the study of the Stoic system. His reputation for learning among his contemporaries was considerable. He succeeded Cleanthes as head of the Stoic school when Cleanthes died, in around 230 BC.
Chrysippus
–
Roman copy of a Hellenistic bust of Chrysippus (British Museum)
Chrysippus
–
A partial marble bust of Chrysippus that is a Roman copy of a Hellenistic original (Louvre Museum).
Chrysippus
–
Cleromancy in ancient Greece. Chrysippus accepted divination as part of the causal chain of fate.
Chrysippus
–
Greek amphora depicting Euripides ' Medea. Chrysippus regarded Medea as a prime example of how bad judgments could give rise to irrational passions.
36.
Ctesibius
–
Ctesibius or Ktesibios or Tesibius was a Greek inventor and mathematician in Alexandria, Ptolemaic Egypt. He wrote the first treatises on the science of compressed air and its uses in pumps. This, On pneumatics earned the title of "father of pneumatics." None of his written work has survived, including his Memorabilia, a compilation of his research, cited by Athenaeus. Ctesibius was probably the first head of the Museum of Alexandria. Very little is known of his life but his inventions were well known. It is said that his first career was as a barber. During his time as a barber, he invented a counterweight-adjustable mirror. His other inventions include a organ, considered the precursor of the modern pipe organ, improved the water clock or clepsydra. The principle of the siphon has also been attributed to him. According to Diogenes Laertius, Ctesibius was miserably poor. Proclus and Hero of Alexandria also mention him. Landels, J.G.. Engineering in the ancient world. Berkeley: Univ. of California Press.
Ctesibius
–
Ctesibius' water clock, as visualized by the 17th-century French architect Claude Perrault
37.
Democritus
–
Democritus was an influential Ancient Greek pre-Socratic philosopher primarily remembered today for his formulation of an atomic theory of the universe. Democritus was born around 460 BCE although, some thought it was BCE. His exact contributions are difficult to disentangle from those of his mentor Leucippus, as they are often mentioned together in texts. Largely ignored in ancient Athens, Democritus is said to have been disliked so much by Plato that the latter wished all of his books burned. He was nevertheless well known to his northern-born Aristotle. Many consider Democritus to be the "father of modern science". None of his writings have survived; only fragments are known from his vast body of work. Democritus was said to be born in an Ionian colony of Teos, although some called him a Milesian. It was said that Democritus's father was from a noble family and so wealthy that he received Xerxes on his march through Abdera. Democritus spent the inheritance which his father left him on travels into distant countries, to satisfy his thirst for knowledge. He traveled to Asia, was even said to have reached India and Ethiopia. It is known that he wrote on Babylon and Meroe; he visited Egypt, Diodorus Siculus states that he lived there for five years. Himself declared that among his contemporaries none had made greater journeys, met more scholars than himself. He particularly mentions the Egyptian mathematicians, whose knowledge he praises. Theophrastus, too, spoke of him as a man who had seen many countries.
Democritus
–
Democritus
Democritus
–
Democritus by Hendrick ter Brugghen, 1628.
Democritus
–
Rembrandt, The Young Rembrandt as Democritus the Laughing Philosopher (1628-1629).
Democritus
–
Democritus meditating on the seat of the soul by Léon-Alexandre Delhomme (1868).
38.
Diophantus
–
These texts deal with solving algebraic equations. This led to tremendous advances in number theory, the study of Diophantine equations and of Diophantine approximations remain important areas of mathematical research. Diophantus coined the term παρισότης to refer to an approximate equality. Diophantus was the Greek mathematician who recognized fractions as numbers; thus he allowed rational numbers for the solutions. In modern use, Diophantine equations are usually algebraic equations with integer coefficients, for which integer solutions are sought. Diophantus also made advances in mathematical notation. Little is known about the life of Diophantus. He lived to 298. Much of our knowledge of the life of Diophantus is derived from a 5th-century Greek anthology of number games and puzzles created by Metrodorus. One of the problems states:'Here lies Diophantus,' the wonder behold. The dear child of sage After attaining half the measure of his father's life fate took him. After consoling his fate by the science of numbers for four years, he ended his life.' However, the accuracy of the information cannot be independently confirmed. The Arithmetica is the major work of Diophantus and the most prominent work on algebra in Greek mathematics. It is a collection of problems giving numerical solutions of both determinate and indeterminate equations.
Diophantus
–
Title page of the 1621 edition of Diophantus' Arithmetica, translated into Latin by Claude Gaspard Bachet de Méziriac.
Diophantus
–
Problem II.8 in the Arithmetica (edition of 1670), annotated with Fermat's comment which became Fermat's Last Theorem.
39.
Eratosthenes
–
Eratosthenes of Cyrene was a Greek mathematician, geographer, poet, astronomer, music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexandria. He invented the discipline of geography, including the terminology used today. His calculation was remarkably accurate. He was also the first to calculate the tilt of the Earth's axis. Additionally, Eratosthenes invented the day. Eratosthenes created the first map of the world, incorporating meridians based on the geographic knowledge of his era. Eratosthenes was the founder of scientific chronology; he endeavored to revise the dates of the political events from the conquest of Troy. In theory, Eratosthenes introduced the sieve of an efficient method of identifying prime numbers. He was a figure of influence in many fields. According to an entry in the Suda, his critics scorned him, calling Beta because he always came in all his endeavors. Eratosthenes yearned to understand the complexities of the entire world. The son of Aglaos, Eratosthenes was born in 276 BC in Cyrene. Under the economy prospered based largely on the export of horses and silphium, a plant used for rich medicine. Cyrene became a place of cultivation, where knowledge blossomed.
Eratosthenes
–
19th-century reconstruction of Eratosthenes' map of the known world, c. 194 BC
Eratosthenes
–
Eratosthenes
Eratosthenes
–
The Burning of the Library at Alexandria in 391 AD, an illustration from "Hutchinsons History of the Nations", c. 1910
40.
Euclid
–
Euclid, sometimes called Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "father of geometry". He was active in Alexandria during the reign of Ptolemy I. In the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, rigor. Euclid is the anglicized version of the Greek Εὐκλείδης, which means "renowned, glorious". Very original references to Euclid survive, so little is known about his life. The place and circumstances of both his birth and death are unknown and may only be estimated roughly relative to other people mentioned with him. He is usually referred to as" ὁ στοιχειώτης". The historical references to Euclid were written centuries after he lived by Proclus c. 450 AD and Pappus of Alexandria c. 320 AD. Proclus introduces Euclid only briefly in his Commentary on the Elements. This anecdote is questionable since it is similar to a story told about Alexander the Great. 247–222 BC. A detailed biography of Euclid is given by Arabian authors, mentioning, for example, a town of Tyre. This biography is generally believed to be completely fictitious. However, there is little evidence in its favor.
Euclid
–
Euclid by Justus van Gent, 15th century
Euclid
–
One of the oldest surviving fragments of Euclid's Elements, found at Oxyrhynchus and dated to circa AD 100 (P. Oxy. 29). The diagram accompanies Book II, Proposition 5.
Euclid
–
Statue in honor of Euclid in the Oxford University Museum of Natural History
41.
Hero of Alexandria
–
Heron of Alexandria was a Greek mathematician and engineer, active in his native city of Alexandria, Roman Egypt. His work is representative of the Hellenistic scientific tradition. Heron published a well recognized description of a steam-powered device called an aeolipile. Among his most famous inventions was a windwheel, constituting the earliest instance of wind harnessing on land. He is said to have been a follower of the atomists. Some of his ideas were derived from the works of Ctesibius. Some of his works were preserved in Arabic manuscripts. Heron described the construction of the aeolipile, the first-recorded steam engine. It was created almost two millennia before the industrial revolution. Some historians have conflated the two inventions to assert that the aeolipile was capable of useful work. This was included in his list of inventions in his book Optics. When the coin was deposited, it fell upon a pan attached to a lever. The lever opened up a valve which let some flow out. An organ, marking the first instance of wind powering a machine in history. The sound of thunder was produced onto a hidden drum.
Hero of Alexandria
–
Hero's wind-powered organ (reconstruction)
Hero of Alexandria
–
Hero
42.
Hipparchus
–
Hipparchus of Nicaea was a Greek astronomer, geographer, mathematician. He is considered the founder of trigonometry but is most famous for his incidental discovery of precession of the equinoxes. Hipparchus was born in Nicaea, Bithynia, probably died on the island of Rhodes. He is known to have been a working astronomer at least from 162 to 127 BC. Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity. He was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. For this he certainly made perhaps the mathematical techniques accumulated over centuries from Mesopotamia. He developed trigonometry and constructed trigonometric tables, he solved several problems of spherical trigonometry. With his solar and lunar theories and his trigonometry, he may have been the first to develop a reliable method to predict solar eclipses. Relatively little of Hipparchus's direct work survives into modern times. Although he wrote at least fourteen books, only his commentary on the popular astronomical poem by Aratus was preserved by later copyists. There is a strong tradition that Hipparchus was born in Nicaea, in the ancient district of Bithynia, in what today is the country Turkey. His date was calculated based on clues in his work. Hipparchus must have lived some time after 127 BC because he analyzed and published his observations from that year. Hipparchus obtained information from Alexandria as well as Babylon, but it is not known when or if he visited these places.
Hipparchus
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Hipparchus as he appears in " The School of Athens " by Raphael.
43.
Hippasus
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Hippasus of Metapontum, was a Pythagorean philosopher. Little is known about his life or his beliefs, but he is sometimes credited with the discovery of the existence of irrational numbers. The discovery of irrationality is not specifically ascribed to Hippasus by any ancient writer. Some modern scholars though have suggested that he discovered the irrationality of √2, believed to have been discovered around the time that he lived. Little is known about the life of Hippasus. He may have lived in the late 5th century BC, about a century after the time of Pythagoras. Hippasus is recorded under the city of Sybaris in Iamblichus list of each city's Pythagoreans. Memory was the most valued faculty. According to one statement, Hippasus left no writings, according to another he was the author of the Mystic Discourse, written to bring Pythagoras into disrepute. Hippasus is sometimes credited with the discovery of the existence of irrational numbers, following which he was drowned at sea. Pythagoreans preached that all numbers could be expressed as the ratio of integers, the discovery of irrational numbers is said to have shocked them. However, the evidence linking the discovery to Hippasus is confused. Pappus merely says that the knowledge of irrational numbers originated in the Pythagorean school, that the member who first divulged the secret perished by drowning. Iamblichus gives a series of inconsistent reports. Iamblichus clearly states that the drowning at sea was a punishment from the gods for impious behaviour.
Hippasus
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Hippasus of Metapontum
44.
Hippocrates of Chios
–
Hippocrates of Chios was an ancient Greek mathematician, geometer, astronomer, who lived c. 470 – c. 410 BCE. He was born on the isle of Chios, where he originally was a merchant. After some misadventures he went to Athens, possibly for litigation. There he grew into a leading mathematician. On Chios, Hippocrates may have been a pupil of the astronomer Oenopides of Chios. The reductio ad argument has been traced to him. Only a famous, fragment of Hippocrates' Elements is existent, embedded in the work of Simplicius. In this fragment the area is calculated of some Hippocratic lunes -- see Lune of Hippocrates. The strategy apparently was to divide a circle into a number of crescent-shaped parts. If it were possible to calculate the area of each of those parts, then the area of the circle as a whole would be known too. Only much later was it proven that this approach had no chance of success, because the factor pi is transcendental. In the century after Hippocrates at least four other mathematicians wrote their own Elements, steadily improving logical structure. In this way Hippocrates' pioneering work laid the foundation for Euclid's Elements, to remain the standard textbook for many centuries. Two other contributions by Hippocrates in the field of mathematics are noteworthy. He found a way to tackle the problem of ` duplication of the cube', the problem of how to construct a root.
Hippocrates of Chios
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The Lune of Hippocrates. Partial solution of the " Squaring the circle " task, suggested by Hippocrates. The area of the shaded figure is equal to the area of the triangle ABC. This is not a complete solution of the task (the complete solution is proven to be impossible with compass and straightedge).
45.
Hypatia
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Hypatia, often called Hypatia of Alexandria, was a Greek mathematician, astronomer, philosopher in Egypt, then a part of the Byzantine Empire. She was the head of the Neoplatonic school at Alexandria, where she taught philosophy and astronomy. The mathematician and philosopher Hypatia of Alexandria was the only daughter of the mathematician Theon of Alexandria. She was educated in Athens. However, not all Christians were as hostile towards her: some Christians even used Hypatia as symbolic of Virtue. Neither did she feel abashed in going to an assembly of men. For all men on account of her extraordinary dignity and virtue admired her the more. Together with the references by the pagan philosopher Damascius, these are the extant records left by Hypatia's pupils at the Platonist school of Alexandria. Hypatia was murdered during an episode of city-wide anger stemming from the Bishop of Alexandria. Her death is symbolic for some historians. Of the many accounts of Hypatia's death, the most complete is the one written around 415 by Socrates of Constantinople and included in the Historia Ecclesiastica. The edict angered Christians as well as Jews. At one such gathering, a Christian follower of Cyril, applauded the new regulations. Many people felt that Hierax was attempting to incite the crowd into sedition. Orestes reacted swiftly and violently out of what Scholasticus suspected was "jealousy the growing power of the bishops… encroached on the jurisdiction of the authorities".
Hypatia
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"Death of the philosopher Hypatia, in Alexandria" from Vies des savants illustres, depuis l'antiquité jusqu'au dix-neuvième siècle, 1866, by Louis Figuier.
Hypatia
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"Hypatia", at the Haymarket Theatre, January 1893
Hypatia
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Cameron 's 1867 photograph Hypatia
46.
Menelaus of Alexandria
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Menelaus of Alexandria was a Greek mathematician and astronomer, the first to recognize geodesics on a curved surface as natural analogs of straight lines. Ptolemy also mentions, in his Almagest, two astronomical observations made in January of the year 98. These were occultations of the stars Spica and Beta Scorpii by the moon, a few nights apart. Ptolemy used these observations to confirm precession of a phenomenon, discovered in the 2nd century BCE. Sphaerica is the only book that has survived, in an Arabic translation. Composed of three books, it deals with its application in astronomical calculations. It was later translated by the sixteenth century astronomer and mathematician Francesco Maurolico. The lunar crater Menelaus is named after him. Ivor Bulmer-Thomas. "Menelaus of Alexandria." Dictionary of Scientific Biography 9:296-302. "d'Alexandrie", in R. Goulet, Dictionnaire des Philosophes Antiques, vol. IV, 2005, p. 456-464. O'Connor, John J.; Robertson, Edmund F. "Menelaus of Alexandria", MacTutor History of Mathematics archive, University of St Andrews. Halley's Latin Translation from the Arabic and Hebrew Versions at Google Books
Menelaus of Alexandria
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Contents
Menelaus of Alexandria
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Sphaericorum libri tres
47.
Nicomedes (mathematician)
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Nicomedes was an ancient Greek mathematician. Almost nothing is known apart from references in his works. Studies have stated that Nicomedes was died in about 210 BC. But, we do because he criticized Eratosthenes' method of doubling the cube. Consequently, it is believed that Nicomedes lived before Apollonius of Perga. In the course of his investigations, Nicomedes created the conchoid of Nicomedes; a discovery, contained in his famous work entitled On conchoid lines. Nicomedes discovered three distinct types of conchoids, now unknown. T. L. Heath, A History of Greek Mathematics. G. J. Toomer, Biography in Dictionary of Scientific Biography. O'Connor, John J.; Robertson, Edmund F. "Nicomedes", MacTutor History of Mathematics archive, University of St Andrews.
Nicomedes (mathematician)
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Conchoids of line with common center.
48.
Pappus of Alexandria
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Nothing is known of his life, except that he had a son named Hermodorus, was a teacher in Alexandria. Collection, his best-known work, is a compendium of mathematics in eight volumes, the bulk of which survives. It covers a wide range of topics, including recreational mathematics, doubling the polyhedra. Pappus flourished in the 4th century AD. In a period of general stagnation in mathematical studies, he stands out as a remarkable exception. "In this respect the fate of Pappus strikingly resembles that of Diophantus." The Suda states that Pappus was of the same age as Theon of Alexandria, who flourished in the reign of Emperor Theodosius I. This works out as October 18, 320 AD, so Pappus must have flourished c. 320 AD. The Suda enumerates other works of Pappus: Χωρογραφια οἰκουμενική, commentary on the 4 books of Ptolemy's Almagest, Ποταμοὺς τοὺς ἐν Λιβύῃ, Ὀνειροκριτικά. Pappus himself mentions another commentary of his own on the Ἀνάλημμα of Diodorus of Alexandria. Pappus also wrote commentaries on Euclid's Elements, on Ptolemy's Ἁρμονικά. These discoveries form, in fact, a text upon which Pappus enlarges discursively. The portions of Collection which has survived can be summarized as follows. We can only conjecture that the lost Book I, like Book II, was concerned with arithmetic, Book III being clearly introduced as beginning a new subject. The whole of Book II discusses a method of multiplication from an unnamed book by Apollonius of Perga.
Pappus of Alexandria
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Title page of Pappus's Mathematicae Collectiones, translated into Latin by Federico Commandino (1589).
Pappus of Alexandria
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Mathematicae collectiones, 1660
49.
Philolaus
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Philolaus was a Greek Pythagorean and Presocratic philosopher. He argued that at the foundation of everything is the part played by the limiting and limitless, which combine together in a harmony. He is also credited with originating the theory that the Earth was not the center of the universe. According to August Böckh, who cites Nicomachus, Philolaus was the successor of Pythagoras. Philolaus is variously reported as being born in either Croton, or Tarentum, or Metapontum — all part of Magna Graecia. It is most likely that he came from Croton. He may have fled the second burning of the Pythagorean meeting-place around 454 BCE, after which he migrated to Greece. According to Plato's Phaedo, he was the instructor of Simmias and Cebes at Thebes, around the time the Phaedo takes place, in 399 BCE. This would make him a contemporary of Socrates, agrees with the statement that Philolaus and Democritus were contemporaries. The various reports about his life are scattered among the writings of much later writers and are of dubious value in reconstructing his life. He apparently lived for some time at Heraclea, where he was the pupil of Aresas, or Arcesus. The pupils of Philolaus were said to have included Xenophilus, Phanto, Echecrates, Diocles and Polymnastus. Diogenes Laërtius speaks of Philolaus composing one book, but elsewhere he speaks of three books, as do Aulus Gellius and Iamblichus. It might have been one treatise divided into three books. Plato is said to have procured a copy of his book from which, it was later claimed, Plato composed much of his Timaeus.
Philolaus
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Philolaus book, (Charles Peter Mason, 1870)
Philolaus
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Medieval woodcut by Franchino Gaffurio, depicting Pythagoras and Philolaus conducting musical investigations.
50.
Porphyry (philosopher)
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Porphyry of Tyre was a Neoplatonic philosopher, born in Tyre, in the Roman Empire. He published the Enneads, the only collection of the work of his teacher Plotinus. His commentary on Euclid's Elements was used by Pappus of Alexandria. He also wrote many works himself on a wide variety of topics. In Latin translation it was the standard textbook on logic throughout the Middle Ages. Porphyry was born in Tyre. Under Longinus he studied rhetoric. At one point he became suicidal. On the advice of Plotinus he went to live in Sicily for five years to recover his mental health. On returning to Rome, he completed an edition of the writings of Plotinus together with a biography of his teacher. The two men differed publicly on the issue of theurgy. In his later years, he married Marcella, an enthusiastic student of philosophy. The date of his death is uncertain. Porphyry is best known for his contributions to philosophy. In medieval textbooks, the all-important Arbor porphyriana illustrates his logical classification of substance.
Porphyry (philosopher)
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Porphire Sophiste, in a French 16th-century engraving
Porphyry (philosopher)
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Imaginary debate between Averroes (1126–1198 AD) and Porphyry (234–c. 305 AD). Monfredo de Monte Imperiali Liber de herbis, 14th century.
51.
Posidonius
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Posidonius "of Apameia" or "of Rhodes", was a Greek Stoic philosopher, politician, astronomer, geographer, historian and teacher native to Apamea, Syria. He was acclaimed as the greatest polymath of his age. His vast body of work exists today only in fragments. Writers such as Strabo and Seneca provide most of the information, from history, about his life. Posidonius, nicknamed "the Athlete", was born to a Greek family in Apamea, a Hellenistic city on the river Orontes in northern Syria. Posidonius completed his higher education in Athens, where he was a student of the aged Panaetius, the head of the Stoic school. But soon Posidonius was involved in heated debates with many Stoic philosophers of the school. The incidents concerning Posidonius's conflict and final break up with the Stoics are mentioned by Galen in his book On the Doctrines of Plato and Hippocrates. Posidonius settled around 95 BCE in a maritime state which became a citizen. In Rhodes, Posidonius actively took part in political life, his high standing is apparent from the offices he held. He attained the highest public office as one of the Prytaneis of Rhodes. Posidonius served during the Marian and Sullan era. Along with other Greek intellectuals, Posidonius favored Rome as the stabilizing power in a turbulent world. His connections to the Roman class were also important to his scientific research. His entry into government provided Posidonius with powerful connections to facilitate his travels to far away places, even beyond Roman control.
Posidonius
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Bust of Posidonius from the Naples National Archaeological Museum
Posidonius
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Posidonius's method for calculating the circumference of the earth, relied on the altitude of the star Canopus
Posidonius
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World map according to ideas by Posidonius (150-130 BCE), drawn in 1628 by cartographers Petrus Bertius and Melchior Tavernier. Many of the details could not have been known to Posidonius; rather, Bertius and Tavernier show Posidonius's ideas about the positions of the continents.
Posidonius
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Posidonius, depicted as a medieval scholar in the Nuremberg Chronicle
52.
Ptolemy
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Claudius Ptolemy was a Greek writer, known as a mathematician, astronomer, geographer, astrologer, poet of a single epigram in the Greek Anthology. He lived in the city of Alexandria in the Roman province of Egypt, held Roman citizenship. Beyond that, reliable details of his life are known. His birthplace has been given as Ptolemais Hermiou in the Thebaid by the 14th-century astronomer Theodore Meliteniotes. Ptolemy wrote several scientific treatises, three of which were of importance to later Byzantine, Islamic and European science. The first is the astronomical treatise now known as the Almagest, although it was originally then known as the "Great Treatise". The second is the Geography, a thorough discussion of the geographic knowledge of the Greco-Roman world. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the natural philosophy of his day. This is sometimes more commonly known as the Tetrabiblos from the Greek meaning "Four Books" or by the Latin Quadripartitum. If, as was common, this was the emperor, citizenship would have been granted between AD 68. The astronomer would also have had a praenomen, which remains unknown. Ptolemaeus is a Greek name. It is of Homeric form. All the kings after him, until Egypt became a Roman province in 30 BC, were also Ptolemies. Abu Ma ` shar recorded a belief that a different member of this royal line "attributed it to Ptolemy".
Ptolemy
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Engraving of a crowned Ptolemy being guided by the muse Astronomy, from Margarita Philosophica by Gregor Reisch, 1508. Although Abu Ma'shar believed Ptolemy to be one of the Ptolemies who ruled Egypt after the conquest of Alexander the title ‘King Ptolemy’ is generally viewed as a mark of respect for Ptolemy's elevated standing in science.
Ptolemy
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Early Baroque artist's rendition
Ptolemy
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A 15th-century manuscript copy of the Ptolemy world map, reconstituted from Ptolemy's Geography (circa 150), indicating the countries of " Serica " and "Sinae" (China) at the extreme east, beyond the island of "Taprobane" (Sri Lanka, oversized) and the "Aurea Chersonesus" (Malay Peninsula).
Ptolemy
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Prima Europe tabula. A C15th copy of Ptolemy's map of Britain
53.
Pythagoras
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Pythagoras of Samos was an Ionian Greek philosopher, mathematician, the putative founder of the movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so little reliable information is known about him. He travelled, visiting Egypt and Greece, maybe India. Around 530 BC, there established some kind of school or guild. In 520 BC, he returned to Samos. Pythagoras made influential contributions in the late 6th century BC. He is best known for the Pythagorean theorem which bears his name. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his successors. Some accounts mention that numbers were important. Burkert states that Aristoxenus and Dicaearchus are the most important accounts. Aristotle had written a separate work On the Pythagoreans, no longer extant. However, the Protrepticus possibly contains parts of On the Pythagoreans. Dicaearchus, Aristoxenus, Heraclides Ponticus had written on the same subject. According to Clement of Alexandria, Pythagoras was a disciple of Soches, Plato of Sechnuphis of Heliopolis. Herodotus, other early writers agree that Pythagoras was the son of Mnesarchus, born on a Greek island in the eastern Aegean called Samos.
Pythagoras
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Bust of Pythagoras of Samos in the Capitoline Museums, Rome.
Pythagoras
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Bust of Pythagoras, Vatican
Pythagoras
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A scene at the Chartres Cathedral shows a philosopher, on one of the archivolts over the right door of the west portal at Chartres, which has been attributed to depict Pythagoras.
Pythagoras
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Croton on the southern coast of Magna Graecia (Southern Italy), to which Pythagoras ventured after feeling overburdened in Samos.
54.
Simplicius of Cilicia
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Simplicius of Cilicia was a disciple of Ammonius Hermiae and Damascius, was one of the last of the Neoplatonists. He wrote extensively on the works of Aristotle. His works have preserved much information about earlier philosophers which would have otherwise been lost. Simplicius was consequently one of the last members of the Neoplatonist school. The school had its headquarters in Athens. It became the centre of the last efforts to maintain Hellenistic religion against the encroachments of Christianity. Imperial edicts enacted in the 5th century against paganism gave legal protection against personal maltreatment. In the 528 the emperor Justinian ordered that pagans should be removed from government posts. Some were robbed of their property, some put to death. The order specified that if they did not within three months convert to Christianity, they were to be banished from the Empire. In addition, it was forbidden any longer to teach jurisprudence in Athens. But they were disappointed in their hopes. Of the subsequent fortunes of the seven philosophers we learn nothing. We know about where Simplicius lived and taught. As to his personal history, especially his migration to Persia, no definite allusions are to be found in the writings of Simplicius.
Simplicius of Cilicia
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Commentary on Aristotle's De Caelo by Simplicius. This 14th-century manuscript is signed by a former owner, Basilios Bessarion.
55.
Sporus of Nicaea
Sporus of Nicaea
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v
56.
Thales of Miletus
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Aristotle reported Thales's hypothesis that the nature of matter was a single substance: water. In mathematics, Thales used geometry to calculate the heights of pyramids and the distance of ships from the shore. He is the known individual to use deductive reasoning applied by deriving four corollaries to Thales' theorem. He is the first known individual to whom a mathematical discovery has been attributed. Apollodorus of Athens, writing during the 2nd BCE, thought Thales was born about the year 625 BCE. The dates of Thales' life are roughly established by a datable events mentioned in the sources. According to Herodotus, Thales predicted the solar eclipse of May 28, 585 BC. Nevertheless, several years later, anxious for family, he adopted his nephew Cybisthus. Thales involved himself in many activities, taking the role of an innovator. Some say that he left no writings, others say that he wrote On the Solstice and On the Equinox. Thales identifies the Milesians as Athenian colonists. Thales' principal occupation was engineering. He was aware of the existence of the lodestone, was the first to be connected to knowledge of this in history. According to Aristotle, Thales thought lodestones had souls, because of the fact of iron being attracted to them. Several anecdotes suggest Thales was not solely a philosopher, but also involved in business.
Thales of Miletus
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Thales of Miletus
Thales of Miletus
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An olive mill and an olive press dating from Roman times in Capernaum, Israel.
Thales of Miletus
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Total eclipse of the Sun
Thales of Miletus
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The Ionic Stoa on the Sacred Way in Miletus
57.
Theodosius of Bithynia
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Theodosius of Bithynia was a Greek astronomer and mathematician who wrote the Sphaerics, a book on the geometry of the sphere. Born in Bithynia, Theodosius is cited by Vitruvius as having invented a sundial suitable for any place on Earth. His Sphaerics may have been based on a work by Eudoxus of Cnidus. Francesco Maurolico translated his works in the 16th century. Ivor Bulmer-Thomas, "Theodosius of Bithynia," Dictionary of Scientific Biography 13:319–320. Also on line "Theodosius of Bithynia." Complete Dictionary of Scientific Biography. 2008. Encyclopedia.com. 25 Mar. 2015. Chisholm, Hugh, ed.. "Theodosius of Tripolis". Encyclopædia Britannica. 26. Cambridge University Press.
Theodosius of Bithynia
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v
58.
Xenocrates
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Xenocrates of Chalcedon was a Greek philosopher, mathematician, leader of the Platonic Academy from 339/8 to 314/3 BC. His teachings followed those of Plato, which he attempted to define more closely, often with mathematical elements. Xenocrates distinguished a third compounded of the two, to which correspond respectively, sense, intellect and opinion. Unity and duality he considered to be gods which rule the universe, the soul is a self-moving number. There are daemonical powers, intermediate between the mortal, which consist in conditions of the soul. He held that mathematical objects and the Platonic Ideas are identical, unlike Plato who distinguished them. In Ethics, Xenocrates taught that external goods can enable it to effect its purpose. Xenocrates was a native of Chalcedon. By the most probable calculation he was born 396/5 BC, died 314/3 BC at the age of 82. Moving in early youth, Xenocrates became the pupil of Aeschines Socraticus, but subsequently joined himself to Plato, whom he accompanied in 361. Upon his master's death, he paid a visit with Aristotle to Hermias of Atarneus. In 339/8 BC, Xenocrates succeeded Speusippus in the presidency of the school, defeating his competitors Menedemus of Pyrrha and Heraclides Ponticus by a few votes. On three occasions he was member of an Athenian legation, once to Philip, twice to Antipater. Xenocrates resented the Macedonian influence then dominant at Athens. In 314/3, Xenocrates died after tripping over a pot in his house.
Xenocrates
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Xenocrates
Xenocrates
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Xenocrates, depicted as a medieval scholar in the Nuremberg Chronicle
59.
Zeno of Elea
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Zeno of Elea was a pre-Socratic Greek philosopher of Magna Graecia and a member of the Eleatic School founded by Parmenides. Aristotle called the inventor of the dialectic. He is best known for his paradoxes, which Bertrand Russell has described as "immeasurably profound". Little is known for certain about Zeno's life. According to Diogenes Laertius, Zeno conspired to overthrow Nearchus the tyrant. Eventually, Zeno was arrested and tortured. When Nearchus leaned in to listen to the secret, Zeno bit his ear. The tyrant lost that part of his body." Within Men of the Same Name, Demetrius said it was the nose, instead. Zeno may have also interacted with other tyrants. According to Laertius, Heraclides Lembus, within his Satyrus, said these events occurred against Diomedon instead of Nearchus. This would be impossible as Phalaris had died before Zeno was even born. According to Plutarch, Zeno attempted to kill the tyrant Demylus. After failing, he had, "with his own teeth bit off his tongue, he spit it in the tyrant’s face." Although ancient writers refer to the writings of Zeno, none of his works survive intact.
Zeno of Elea
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Zeno shows the Doors to Truth and Falsity (Veritas et Falsitas). Fresco in the Library of El Escorial, Madrid.
Zeno of Elea
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Achilles and the tortoise
60.
Almagest
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The Almagest is the critical source of information on ancient Greek astronomy. It has also been valuable to students of mathematics because it documents Hipparchus's work, lost. Ptolemy set up a public inscription in 147 or 148. The late N. T. Hamilton found that the version of Ptolemy's models set out in the Canopic Inscription was earlier than the version in the Almagest. Hence it can not have been completed before about 150, a century after Ptolemy began observing. The Syntaxis Mathematica or Almagest consists of thirteen sections, called books. An example illustrating how the Syntaxis was organized is given below. It is a Latin edition printed in 1515 at Venice by Petrus Lichtenstein. Then follows an explanation of chords with table of chords; observations of the obliquity of the ecliptic; and an introduction to spherical trigonometry. There is also a study of the angles made by the ecliptic with tables. Book III covers the motion of the Sun. Ptolemy begins explaining the theory of epicycles. Book VI covers solar and lunar eclipses. Books VII and VIII cover the motions of the fixed stars, including precession of the equinoxes. They also contain a catalogue of 1022 stars, described by their positions in the constellations.
Almagest
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Ptolemy's Almagest became an authoritative work for many centuries.
Almagest
Almagest
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Picture of George Trebizond's Latin translation of Almagest
61.
Archimedes Palimpsest
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It was overwritten with a Christian religious text by 13th-century monks. A copy of this text was made around 950 AD, again in the Byzantine Empire, by an anonymous scribe. This medieval Byzantine manuscript then traveled to Jerusalem, likely sometime after the Crusader sack of Constantinople in 1204. There, in 1229, the original Archimedes codex was washed, with at least six other parchment manuscripts, including one with works of Hypereides. The palimpsest remained near Jerusalem through at least the 16th century at the isolated Greek Orthodox monastery of Mar Saba. At some point before 1840 the palimpsest was brought back by the Greek Orthodox Patriarchate of Jerusalem to their library in Constantinople. In 1899 the Greek scholar Papadopoulos-Kerameus produced a catalog of the library's manuscripts and included a transcription of several lines of the partially visible underlying text. Upon seeing these lines Johan Heiberg, the world's authority on Archimedes, realized that the work was by Archimedes. When Heiberg studied the palimpsest in Constantinople in 1906, he confirmed that the palimpsest included works by Archimedes thought to have been lost. Shortly thereafter Archimedes' Greek text was translated into English by T. L. Heath. Before that it was not widely known among mathematicians, physicists or historians. The manuscript was still in the Greek Orthodox Patriarchate of Jerusalem's library in Constantinople in 1920. Sometime between 1930 the palimpsest was acquired by a "traveler to the Orient who lived in Paris." Stored secretly for years in Marie's cellar the palimpsest suffered damage from water and mold. These gold leaf portraits nearly obliterated the text underneath them, x-ray fluorescence imaging at Stanford would later be required to reveal it.
Archimedes Palimpsest
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A typical page from the Archimedes Palimpsest. The text of the prayer book is seen from top to bottom, the original Archimedes manuscript is seen as fainter text below it running from left to right
Archimedes Palimpsest
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Discovery reported in the New York Times on July 16, 1907
Archimedes Palimpsest
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After imaging a page from the palimpsest, the original Archimedes text is now seen clearly
Archimedes Palimpsest
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Ostomachion is a dissection puzzle in the Archimedes Palimpsest (shown after Suter from a different source; this version must be stretched to twice the width to conform to the Palimpsest)
62.
Arithmetica
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Arithmetica is an Ancient Greek text on mathematics written by the mathematician Diophantus in the 3rd century AD. It is a collection of 130 algebraic problems giving numerical solutions of indeterminate equations. Equations in the book are called Diophantine equations. The method for solving these equations is known as Diophantine analysis. Most of the Arithmetica problems lead to quadratic equations. In Book 3, Diophantus solves problems of finding values which make two linear expressions simultaneously into cubes. In book 4, he finds rational powers between given numbers. He also noticed that numbers of 3 can not be the sum of two squares. Diophantus also appears to know that every number can be written as the sum of four squares. The Greek manuscripts that survived to the present contain no more than six books. The four books are thought to have been translated by Qusta ibn Luqa. Norbert Schappacher has written: resurfaced around 1971 in a copy from 1198 AD. Arithmetica became known to mathematicians in the Islamic world in the tenth century when Abu'l-Wefa translated it into Arabic. Muhammad ibn Mūsā al-Khwārizmī Diophantus Alexandrinus, Pierre de Fermat, Claude Gaspard Bachet de Meziriac, et De numeris multangulis liber unus. Cum comm.
Arithmetica
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Cover of the 1621 edition, translated into Latin from Greek by Claude Gaspard Bachet de Méziriac.
63.
Euclid's Elements
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Euclid's Elements is a mathematical and geometric treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt circa 300 BC. It is a collection of definitions, postulates, mathematical proofs of the propositions. The books cover the ancient Greek version of elementary number theory. It is the oldest extant axiomatic deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science. According to Proclus, the term "element" was used to describe a theorem that helps furnishing proofs of many other theorems. The element in the Greek language is the same as letter. This suggests that theorems in the Elements should be seen as standing as letters to language. Euclid's Elements has been referred to as the most influential textbook ever written. Scholars believe that the Elements is largely a collection of theorems proven by other mathematicians, supplemented by some original work. The Heiberg manuscript, is from a Byzantine workshop around 900 and is the basis of modern editions. Papyrus Oxyrhynchus 29 only contains the statement of one proposition. Although known to, for instance, Cicero, no record exists of the text having been translated prior to Boethius in the fifth or sixth century. The Arabs received the Elements around 760; this version was translated into Arabic under Harun al Rashid circa 800. The Byzantine scholar Arethas commissioned the copying of the extant Greek manuscripts of Euclid in the late ninth century.
Euclid's Elements
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The frontispiece of Sir Henry Billingsley's first English version of Euclid's Elements, 1570
Euclid's Elements
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A fragment of Euclid's "Elements" on part of the Oxyrhynchus papyri
Euclid's Elements
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An illumination from a manuscript based on Adelard of Bath 's translation of the Elements, c. 1309–1316; Adelard's is the oldest surviving translation of the Elements into Latin, done in the 12th-century work and translated from Arabic.
Euclid's Elements
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Euclidis – Elementorum libri XV Paris, Hieronymum de Marnef & Guillaume Cavelat, 1573 (second edition after the 1557 ed.); in-8, 350, (2)pp. THOMAS-STANFORD, Early Editions of Euclid's Elements, n°32. Mentioned in T.L. Heath's translation. Private collection Hector Zenil.
64.
On the Sizes and Distances (Aristarchus)
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This work calculates the sizes of the Sun and Moon, well as their distances from the Earth in terms of Earth's radius. The book was presumably preserved by students of Pappus of Alexandria's course in mathematics, although there is no evidence of this. The editio princeps was published by John Wallis in 1688, using medieval manuscripts compiled by Sir Henry Savile. The earliest Latin translation was made by Giorgio Valla in 1488. There is also a 1572 Latin commentary by Frederico Commandino. The work's method relied on several observations: The apparent size of the Sun and the Moon in the sky. The rest of the article details a reconstruction of Aristarchus' method and results. From the trigonometry, we can calculate that S L = 1 cos φ = sec φ. φ is extremely close to 90 °. Aristarchus determined φ to be a thirtieth of a quadrant less than a right angle: in 87 °. Using geometrical analysis in the style of Euclid, Aristarchus determined that 18 < S L < 20. In other words, the distance to the Sun was somewhere between 20 times greater than the distance to the Moon. This value was accepted by astronomers for the next thousand years, until the invention of the telescope permitted a more precise estimate of solar parallax. The appearance of these equations can be simplified using = d / ℓ and x = s / ℓ. These formulae are likely a good approximation to those of Aristarchus.
On the Sizes and Distances (Aristarchus)
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Aristarchus's 3rd century BC calculations on the relative sizes of, from left, the Sun, Earth and Moon, from a 10th-century CE Greek copy
65.
On Sizes and Distances
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On Sizes and Distances is a text by the ancient Greek astronomer Hipparchus. Some of its contents have been preserved in the works of Ptolemy and his commentator Pappus of Alexandria. Modern historians have attempted to reconstruct the methods of Hipparchus using the available texts. Most of what is known about Hipparchus' text comes from two ancient sources: Ptolemy and Pappus. Their accounts have proven less useful in reconstructing the procedures of Hipparchus. In Almagest 11, Ptolemy writes: Now Hipparchus made such an examination principally from the sun. First, he assumes the sun to show the least perceptible parallax to find its distance. But with respect to the sun, not only the amount of its parallax, but also whether it shows any parallax at all is altogether doubtful. This passage gives a general outline of what Hipparchus provides no details. Ptolemy clearly did not agree with the methods employed by Hipparchus, thus did not go into any detail. The works of Hipparchus were still extant when Pappus wrote his commentary in the 4th century. He fills in some of the details that Ptolemy omits: Now, Hipparchus made such an examination principally from the sun, not accurately. In the first book "On Sizes and Distances" it is assumed that the earth has the ratio of a center to the sun. And by means of the eclipse adduced by him... Hence the mean is 77...
On Sizes and Distances
66.
Problem of Apollonius
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In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane. This solution does not use only straightedge and compass constructions. Viète's approach, which uses simpler limiting cases to solve more complicated ones, is considered a plausible reconstruction of Apollonius' method. This has applications in positioning systems such as LORAN. Later mathematicians introduced algebraic methods, which transform a geometric problem into algebraic equations. These developments provide a classification of solutions according to 33 essentially different configurations of the given circles. Apollonius' problem has stimulated further work. Generalizations beyond have been studied. The configuration of three mutually tangent circles has received particular attention. René Descartes gave a formula relating the radii of the given circles, now known as Descartes' theorem. Solutions to Apollonius' problem are sometimes called Apollonius circles, although the term is also used for other types of circles associated with Apollonius. The property of tangency is defined as follows. Two geometrical objects are said to intersect if they have a point in common. In practice, two distinct circles are tangent if they intersect at only one point; if they intersect at two points, they are not tangent. The same holds true for a circle.
Problem of Apollonius
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Figure 1: A solution (in pink) to Apollonius' problem. The given circles are shown in black.
67.
Squaring the circle
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Squaring the circle is a problem proposed by ancient geometers. It may be taken to ask whether specified axioms of Euclidean geometry concerning the existence of lines and circles entail the existence of such a square. Approximate squaring to any given non-perfect accuracy, in contrast, is possible in a finite number of steps, since there are rational numbers arbitrarily close to π. The expression "squaring the circle" is sometimes used as a metaphor for trying to do the impossible. Methods to approximate the area of a given circle with a square were known already to Babylonian mathematicians. Indian mathematicians also found an approximate method, though less accurate, documented in the Sulba Sutras. Archimedes showed that the value of pi lay between 1/7 and 10/71. See Numerical approximations of π for more on the history. The first known Greek to be associated with the problem was Anaxagoras, who worked on it while in prison. Hippocrates of Chios squared certain lunes, in the hope that it would lead to a solution — see Lune of Hippocrates. Even then there were skeptics—Eudemus argued that magnitudes cannot be divided up without limit, so the area of the circle will never be used up. The problem was even mentioned in Aristophanes's play The Birds. It is believed that Oenopides was the first Greek who required a plane solution. James Gregory attempted a proof of its impossibility in Vera Circuli et Hyperbolae Quadratura in 1667. Although his proof was faulty, it was the first paper to attempt to solve the problem using algebraic properties of pi.
Squaring the circle
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Squaring the circle: the areas of this square and this circle are both equal to π. In 1882, it was proven that this figure cannot be constructed in a finite number of steps with an idealized compass and straightedge.
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Doubling the cube
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Doubling the cube, also known as the Delian problem, is an ancient geometric problem. As with the related problems of squaring the circle and trisecting the angle, doubling the cube is now known to be impossible. However, the nonexistence of a solution was finally proven by Pierre Wantzel in 1837. The impossibility of doubling the cube is therefore equivalent to the statement that 3√2 is not a constructible number. This implies that the degree of the field extension generated by a constructible point must be a power of 2. The field extension generated by 3√2, however, is of degree 3. We begin with the segment defined in the plane. We are required to construct a line segment defined by two points separated by a distance of 3√2. Therefore, the degree of the field extension corresponding to each new coordinate is 2 or 1. By Gauss's Lemma, p is also irreducible over ℚ, is thus a minimal polynomial over ℚ for 3√2. The field extension ℚ:ℚ is therefore of degree 3. The oracle responded that they must double the size of the altar to Apollo, a regular cube. This may be why the problem is referred to in the 350s BC by the author of the pseudo-Platonic Sisyphus as still unsolved. However another version of the story says that all three found solutions but they were too abstract to be of practical value. Menaechmus' original solution involves the intersection of two conic curves.
Doubling the cube
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Contents
69.
Angle trisection
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Angle trisection is a classical problem of compass and straightedge constructions of ancient Greek mathematics. It concerns equal to one third of a given arbitrary angle, using only two tools: an unmarked straightedge, a compass. The problem as stated is generally impossible to solve, as shown by Pierre Wantzel in 1837. However, although there is no way to trisect an angle in general with a straightedge, some special angles can be trisected. For example, it is relatively straightforward to trisect a right angle. It is possible to trisect an arbitrary angle by using tools other than straightedge and compass. For example, neusis construction, also known to ancient Greeks, involves simultaneous rotation of a marked straightedge, which can not be achieved with the original tools. Other techniques were developed by mathematicians over the centuries. These "solutions" are simply incorrect. Three problems proved elusive, specifically, trisecting the angle, squaring the circle. Pierre Wantzel published a proof of the impossibility of classically trisecting an arbitrary angle in 1837. Wantzel's proof, restated in modern terminology, uses the abstract algebra of a topic now typically combined with Galois theory. From a solution of these two problems, one may pass to a solution of the other by a compass and straightedge construction. The triple-angle formula gives an expression relating the cosines of its trisection: cos θ = 4cos3 − 3cos. This equivalence reduces the geometric problem to a purely algebraic problem.
Angle trisection
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Rulers. The displayed ones are marked — an ideal straightedge is un-marked
Angle trisection
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Angles may be trisected via a Neusis construction, but this uses tools outside the Greek framework of an unmarked straightedge and a compass.
Angle trisection
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compasses
70.
Cyrene, Libya
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Cyrene was an ancient Greek and Roman city near present-day Shahhat, Libya. It was most important of the five Greek cities in the region. It gave the classical name Cyrenaica that it has retained to modern times. Cyrene lies in a lush valley in the Jebel Akhdar uplands. The city was named after Kyre, which the Greeks consecrated to Apollo. It was also a famous school of philosophy in the 3rd century BC, founded by Aristippus, a disciple of Socrates. It was then nicknamed the "Athens of Africa". The Oracle had offered the advice to find a new city in Libya. Not knowing how to get to Libya they sent a messenger to Crete to find someone to lead them on their journey. They found a dealer in purple dyes named Corobius. He had once traveled across from Libya called Platea. After two years of settling the colony they went back to the Oracle to get advice. The Oracle had repeated his advice to move directly to the country of Libya instead of across to Libya. So they moved to a place called Aziris. They were settled into what is now Cyrene.
Cyrene, Libya
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The ruins of Cyrene
Cyrene, Libya
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Apollo Kitharoidos from Cyrene. Roman statue from the 2nd century AD now in the British Museum.
Cyrene, Libya
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Detail of the Cyrene bronze head in the British Museum (300 BC).
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Library of Alexandria
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The Royal Library of Alexandria or Ancient Library of Alexandria in Alexandria, Egypt, was one of the largest and most significant libraries of the ancient world. It was dedicated to the nine goddesses of the arts. The library was part of a larger institution called the Musaeum of Alexandria, where many of the most famous thinkers of the ancient world studied. The library was created by Ptolemy I Soter, the successor of Alexander the Great. Most of the books were kept as papyrus scrolls. Estimates range from 40,000 to 400,000 at its height. Sources differ on when it occurred. The library may in truth have suffered several fires over many years. After the main library was destroyed, scholars used a "library" in a temple known as the Serapeum, located in another part of the city. The library may have finally been destroyed in AD 642. The library itself is known to have had a cataloguing department. A hall contained shelves for the collections of papyrus scrolls known as bibliothekai. According to popular description, an inscription above the shelves read: The place of the cure of the soul. The library was but one part of the Musaeum of Alexandria, which functioned as a sort of institute. In addition to the library, even a zoo containing exotic animals.
Library of Alexandria
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The Great Library of Alexandria, O. Von Corven, 19th century
Library of Alexandria
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This Latin inscription regarding Tiberius Claudius Balbilus of Rome (d. c. AD 79) mentions the "ALEXANDRINA BYBLIOTHECE" (line eight).
Library of Alexandria
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The Burning of the Library at Alexandria in 391 AD, an illustration from 'Hutchinsons History of the Nations', c. 1910
Library of Alexandria
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5th century scroll which illustrates the destruction of the Serapeum by Theophilus
72.
Platonic Academy
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The Academy was founded by Plato in ca. 387 BC in Athens. Aristotle studied there before founding his own school, the Lyceum. The Academy persisted throughout the Hellenistic period until coming to an end after the death of Philo of Larissa in 83 BC. The Platonic Academy has been cited by historians as the first higher institution in the Western world. Among the religious observances that took place at the Akademeia was a torchlit race from altars within the city to Prometheus' altar in the Akademeia. Funeral games also took place from Athens to the Hekademeia and then back to the polis. The road to Akademeia was lined with the gravestones of Athenians. The site of the Academy is located near Colonus, approximately, 1.5 km north of Athens' Dipylon gates. The site was rediscovered in modern Akadimia Platonos neighbourhood; considerable excavation has been accomplished and visiting the site is free. Today can visit the archaeological site of the Academy located on either side of the Cratylus street in the area of Colonos and Plato's Academy. According to Debra Nails, Speusippus "joined the group in about 390 BC". She claims, "It is not until Eudoxus of Cnidos arrives in the mid-380s BC that Eudemus recognizes a formal Academy." Originally, the location of the meetings was on Plato's property often as it was the nearby Academy gymnasium; this remained so throughout the fourth century. Though the Academic club was exclusive, not open to the public, it did not, during at least Plato's time, charge fees for membership. Therefore, there was not at that time a "school" in the sense of a clear distinction between teachers and students, or even a formal curriculum.
Platonic Academy
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Plato from The School of Athens by Raphael, 1509
Platonic Academy
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Ancient road to the Academy.
Platonic Academy
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Map of Ancient Athens. The Academy is north of Athens.
Platonic Academy
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The School of Athens by Raphael (1509–1510), fresco at the Apostolic Palace, Vatican City.
73.
Virtual International Authority File
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The Virtual International Authority File is an international authority file. It operated by the Online Computer Library Center. The project was initiated by the US Library of Congress. The aim is to link the national authority files to a virtual authority file. In this file, identical records from the different sets are linked together. The data are available for research and data exchange and sharing. Reciprocal updating uses the Open Archives Initiative protocol. The file numbers are incorporated into Wikidata. VIAF's clustering algorithm is run every month. Integrated Authority File International Standard Name Identifier Wikipedia's authority control template for articles Official website
Virtual International Authority File
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Screenshot 2012
74.
Integrated Authority File
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The Integrated Authority File or GND is an international authority file for the organisation of personal names, subject headings and corporate bodies from catalogues. It is used mainly increasingly also by archives and museums. The GND is managed with various regional library networks in German-speaking Europe and other partners. The GND falls under the Creative Commons Zero license. The GND specification provides a hierarchy of high-level sub-classes, useful in library classification, an approach to unambiguous identification of single elements. It also comprises an ontology intended for knowledge representation in the semantic web, available in the RDF format.
Integrated Authority File
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GND screenshot
75.
Anthemius of Tralles
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Anthemius of Tralles was a Greek from Tralles who worked as a geometer and architect in Constantinople, the capital of the Byzantine Empire. With Isidore of Miletus, he designed the Hagia Sophia for Justinian I. Anthemius was one of the five sons of Stephanus of Tralles, a physician. His brothers were Metrodorus. In addition to his familiarity with steam, some dubious authorities credited Anthemius with a knowledge of other explosive compound. Anthemius was a capable mathematician. This work was later known to Arab mathematicians such as Alhazen. Eutocius's commentary on Apollonius's Conics was dedicated to Anthemius. As an architect, Anthemius is best known for his work designing the Hagia Sophia. He is also said to have repaired the flood defenses at Daras. Other Anthemiuses "Anthemius", Encyclopædia Britannica, 9th ed. Vol. II, New York: Charles Scribner's Sons, 1878, p. 103. "Anthemius", Encyclopædia Britannica, 11th ed. Vol. II, Cambridge: Cambridge University Press, 1911, p. 93. Boyer, Carl Benjamin, A History of Mathematics, John Wiley & Sons, ISBN 0-471-54397-7. Editions of Anthemius's "On Burning-Glasses": Dupuy, L. Περί παραδόξων μηχανημάτων. Histoire de l'Academie des Instrumentistes, XLII.
Anthemius of Tralles
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The Hagia Sophia in cross section.