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Archytas (subgenus)
Archytas (; el, Ἀρχύτας; 435/410–360/350 BC) was an Ancient Greek mathematician, music theorist, statesman, and strategist from the ancient city of Taras (Tarentum) in Southern Italy. He was a scientist and philosopher affiliated with the Pythagorean school and famous for being the reputed founder of mathematical mechanics and a friend of Plato. As a Pythagorean, Archytas believed that arithmetic (logistic), rather than geometry, provided the basis for satisfactory proofs, and developed the most famous argument for the infinity of the universe in antiquity. Life Archytas was born in Tarentum, a Greek city in the Italian Peninsula that was part of Magna Graecia, and was the son of Hestiaeus. He was presumably taught by Philolaus, and taught mathematics to Eudoxus of Cnidus and to Eudoxus' student, Menaechmus. Politically and militarily, Archytas appears to have been the dominant figure in Tarentum in his generation, somewhat comparable to Pericles in Athens a hal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Western Philosophy
Western philosophy encompasses the philosophical thought and work of the Western world. Historically, the term refers to the philosophical thinking of Western culture, beginning with the ancient Greek philosophy of the pre-Socratics. The word ''philosophy'' itself originated from the Ancient Greek (φιλοσοφία), literally, "the love of wisdom" grc, φιλεῖν , "to love" and σοφία '' sophía'', "wisdom"). History Ancient The scope of ancient Western philosophy included the problems of philosophy as they are understood today; but it also included many other disciplines, such as pure mathematics and natural sciences such as physics, astronomy, and biology (Aristotle, for example, wrote on all of these topics). Pre-Socratics The pre-Socratic philosophers were interested in cosmology; the nature and origin of the universe, while rejecting mythical answers to such questions. They were specifically interested in the (the cause or first principle) of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic
Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms, which are highly important to the field of mathematical logic today. History The prehistory of arithmetic is limited to a small number of artifacts, which may indicate the conception of addition and subtraction, the best-known being the Ishango bone from central Africa, dating from somewhere between 20,000 and 18,000 BC, although its interpretation is disputed. The earliest written records indicate the Egyptians and Babylonians used all the elementary arithmetic operations: addition, subtraction, multiplication, and division, as early as 2000 BC. These artifacts do not always reveal the specific process used for solving problems, but t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Republic (Plato)
The ''Republic'' ( grc-gre, Πολῑτείᾱ, Politeia; ) is a Socratic dialogue, authored by Plato around 375 BCE, concerning justice (), the order and character of the just city-state, and the just man. It is Plato's best-known work, and one of the world's most influential works of philosophy and political theory, both intellectually and historically. In the dialogue, Socrates discusses the meaning of justice and whether the just man is happier than the unjust man with various Athenians and foreigners.In ancient times, the book was alternately titled ''On Justice'' (not to be confused with the spurious dialogue of the same name). They consider the natures of existing regimes and then propose a series of different, hypothetical cities in comparison, culminating in Kallipolis (Καλλίπολις), a utopian city-state ruled by a philosopher-king. They also discuss ageing, love, theory of forms, the immortality of the soul, and the role of the philosopher and of p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosopher King
The philosopher king is a hypothetical ruler in whom political skill is combined with philosophical knowledge. The concept of a city-state ruled by philosophers is first explored in Plato's ''Republic'', written around 375 BC. Plato argued that the ideal state – one which ensured the maximum possible happiness for all its citizens – could only be brought into being by a ruler possessed of absolute knowledge, obtained through philosophical study. From the Middle Ages onwards, Islamic and Jewish authors expanded on the theory, adapting it to suit their own conceptions of the perfect ruler. Several historical figures, including Alexander the Great and Marcus Aurelius, have been described by ancient and modern writers as embodying the philosopher king ideal. In the ''Republic'' The ''Republic'' is a Socratic dialogue, in which the character of Socrates is made a mouthpiece for Plato's ideas. In the first two books, Socrates is challenged to give a definition of justice, which h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syracuse, Sicily
Syracuse ( ; it, Siracusa ; scn, Sarausa ), ; grc-att, wikt:Συράκουσαι, Συράκουσαι, Syrákousai, ; grc-dor, wikt:Συράκοσαι, Συράκοσαι, Syrā́kosai, ; grc-x-medieval, Συρακοῦσαι, Syrakoûsai, ; el, label=Modern Greek language, Modern Greek, Συρακούσες, Syrakoúses, . is a historic city on the Italy, Italian island of Sicily, the capital of the Italian province of Syracuse. The city is notable for its rich Greek and Roman history, Greek culture, culture, amphitheatres, architecture, and as the birthplace of the pre-eminent mathematician and engineer Archimedes. This 2,700-year-old city played a key role in ancient times, when it was one of the major powers of the Mediterranean world. Syracuse is located in the southeast corner of the island of Sicily, next to the Gulf of Syracuse beside the Ionian Sea. It is situated in a drastic rise of land with depths being close to the city offshore although the city itself is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dionysius The Younger
Dionysius the Younger ( el, Διονύσιος ὁ Νεώτερος, 343 BC), or Dionysius II, was a Greek politician who ruled Syracuse, Sicily from 367 BC to 357 BC and again from 346 BC to 344 BC. Biography Dionysius II of Syracuse was the son of Dionysius the Elder and Doris of Locri. When his father died in 367 BC, Dionysius, who was at the time under thirty years old, and completely inexperienced in public affairs, inherited the supreme power and began ruling under the supervision of his uncle, Dion, whose disapproval of the young Dionysius's lavishly dissolute lifestyle compelled him to invite his teacher Plato to visit Syracuse. Together they attempted to restructure the government to be more moderate, with Dionysius as the archetypal philosopher-king (see the ''Seventh Letter'' of Plato). However, under the influence of opponents of Dion's reforms, Dionysius conspired with the historian Philistus and banished his uncle, taking complete power in 366 BC. Without Dion, D ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seventh Letter (Plato)
The ''Seventh Letter of Plato'' is an epistle that tradition has ascribed to Plato. It is by far the longest of the epistles of Plato and gives an autobiographical account of his activities in Sicily as part of the intrigues between Dion and Dionysius of Syracuse for the tyranny of Syracuse. It also contains an extended philosophical interlude concerning the possibility of writing true philosophical works and the theory of forms.R. G. Bury, Prefatory note to "Epistle VII" in ''Plato IX'', Loeb Classical Library (Cambridge, MA: Harvard University Press, 1929): 463–75. Assuming that the letter is authentic, it was written after Dion was assassinated by Calippus in 353 BC and before the latter was in turn overthrown a year later. Authenticity Of all the letters attributed to Plato, the ''Seventh Letter'' is widely considered the only one that might be authentic. R. Ledger defends its authenticity on the basis of computer analysis.R. Ledger, ''Re-counting Plato: A Computer A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strategos
''Strategos'', plural ''strategoi'', Linguistic Latinisation, Latinized ''strategus'', ( el, στρατηγός, pl. στρατηγοί; Doric Greek: στραταγός, ''stratagos''; meaning "army leader") is used in Greek language, Greek to mean military General officer, general. In the Hellenistic world and the Byzantine Empire, Eastern Roman Empire the term was also used to describe a military governor. In the modern Hellenic Army, it is the highest officer rank. Etymology ''Strategos'' is a compound of two Greek words: ''stratos'' and ''agos''. ''Stratos'' (στρατός) means "army", literally "that which is spread out", coming from the proto-Indo-European root *stere- "to spread". ''Agos'' (ἀγός) means "leader", from ''agein'' (ἄγειν) "to lead", from the proto-Ιndo-Εuropean root *ag- "to drive, draw out or forth, move”. Classical Greece Athens In its most famous attestation, in Classical Athens, the office of ''strategos'' existed already in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Athens
Athens ( ; el, Αθήνα, Athína ; grc, Ἀθῆναι, Athênai (pl.) ) is both the capital and largest city of Greece. With a population close to four million, it is also the seventh largest city in the European Union. Athens dominates and is the capital of the Attica region and is one of the world's oldest cities, with its recorded history spanning over 3,400 years and its earliest human presence beginning somewhere between the 11th and 7th millennia BC. Classical Athens was a powerful city-state. It was a centre for the arts, learning and philosophy, and the home of Plato's Academy and Aristotle's Lyceum. It is widely referred to as the cradle of Western civilization and the birthplace of democracy, largely because of its cultural and political influence on the European continent—particularly Ancient Rome. In modern times, Athens is a large cosmopolitan metropolis and central to economic, financial, industrial, maritime, political and cultural life in Gre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pericles
Pericles (; grc-gre, Περικλῆς; c. 495 – 429 BC) was a Greek politician and general during the Golden Age of Athens. He was prominent and influential in Athenian politics, particularly between the Greco-Persian Wars and the Peloponnesian War, and was acclaimed by Thucydides, a contemporary historian, as "the first citizen of Athens".Thucydides, 2.65 Pericles turned the Delian League into an Athenian empire and led his countrymen during the first two years of the Peloponnesian War. The period during which he led Athens, roughly from 461 to 429 BC, is sometimes known as the "Age of Pericles", but the period thus denoted can include times as early as the Persian Wars or as late as the following century. Pericles promoted the arts and literature, and it is principally through his efforts that Athens acquired the reputation of being the educational and cultural center of the ancient Greek world. He started an ambitious project that generated most of the surviving stru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
