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Euclidean geometry is an example of ], in that it proceeds logically from axioms describing basic properties of geometric objects such as points and lines, to propositions about those objects. This is in contrast to ], introduced almost 2,000 years later by ], which uses ] to express geometric properties by means of ]s. | Euclidean geometry is an example of ], in that it proceeds logically from axioms describing basic properties of geometric objects such as points and lines, to propositions about those objects. This is in contrast to ], introduced almost 2,000 years later by ], which uses ] to express geometric properties by means of ]s. | ||
====Euclid's Elements=== | |||
]' ({{lang-grc-gre|Στοιχεῖα}} {{transliteration|grc|Stoikheîa}}) is a ] ] consisting of 13 books attributed to the ancient ] ] {{circa}} 300 BC. It is a collection of definitions, ], ] (]s and ]), and ]s of the propositions. The books cover plane and solid ], elementary ], and ] lines. ''Elements'' is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of ] and modern ], and its logical rigor was not surpassed until the 19th century. | |||
Euclid's ''Elements'' has been referred to as the most successful{{efn|{{harvnb|Wilson|2006|p=278}} states, "Euclid's Elements subsequently became the basis of all mathematical education, not only in the Roman and Byzantine periods, but right down to the mid-20th century, and it could be argued that it is the most successful textbook ever written."}}{{efn|{{harvnb|Boyer|1991|p=100}} notes, "As teachers at the school he called a band of leading scholars, among whom was the author of the most fabulously successful mathematics textbook ever written – the ''Elements'' (''Stoichia'') of Euclid".}} and influential{{efn|{{harvnb|Boyer|1991|p=119}} notes, "The ''Elements'' of Euclid not only was the earliest major Greek mathematical work to come down to us, but also the most influential textbook of all times. The first printed versions of the ''Elements'' appeared at Venice in 1482, one of the very earliest of mathematical books to be set in type; it has been estimated that since then at least a thousand editions have been published. Perhaps no book other than the Bible can boast so many editions, and certainly no mathematical work has had an influence comparable with that of Euclid's ''Elements''".}} ] ever written. It was one of the very earliest mathematical works to be printed after the ] and has been estimated to be second only to the ] in the number of editions published since the first printing in 1482,{{sfn|Boyer|1991|p=100}} the number reaching well over one thousand.{{efn|{{harvnb|Bunt|Jones|Bedient |1988|p=142}} state, "the ''Elements'' became known to Western Europe via the Arabs and the Moors. There, the ''Elements'' became the foundation of mathematical education. More than 1000 editions of the ''Elements'' are known. In all probability, it is, next to the ''Bible'', the most widely spread book in the civilization of the Western world."}} For centuries, when the ] was included in the curriculum of all university students, knowledge of at least part of Euclid's ''Elements'' was required of all students. Not until the 20th century, by which time its content was universally taught through other school textbooks, did it cease to be considered something all educated people had read.{{Citation needed|reason=Sweeping claim|date=April 2023}} | |||
==Greek artists== | ==Greek artists== |
Revision as of 15:24, 2 February 2024
Modern Influence of Ancient Greece refers to the influence of Ancient Greece on later periods of history, from Medieval times up to the current modern era. Greek culture and philosophy has a disproprtionate influence on modern society and its core culture, in comparison to other ancient societies of similar settings.
Background
Classics
Classics is the study of classical antiquity. In the Western world, classics traditionally refers to the study of Classical Greek and Roman literature and their related original languages, Ancient Greek and Latin. Classics also includes Greco-Roman philosophy, history, archaeology, anthropology, art, mythology and society as secondary subjects.
In Western civilization, the study of the Greek and Roman classics was traditionally considered to be the foundation of the humanities and has traditionally been the cornerstone of a typical elite European education.
Greek philosophers
Overview and background
Ancient Greek philosophy arose in the 6th century BC. Philosophy was used to make sense of the world using reason. It dealt with a wide variety of subjects, including astronomy, epistemology, mathematics, political philosophy, ethics, metaphysics, ontology, logic, biology, rhetoric and aesthetics. Greek philosophy continued throughout the Hellenistic period and later evolved into Roman philosophy.
Greek philosophy has influenced much of Western culture since its inception, and can be found in many aspects of public education. Alfred North Whitehead once noted: "The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato". Clear, unbroken lines of influence lead from ancient Greek and Hellenistic philosophers to Roman philosophy, Early Islamic philosophy, Medieval Scholasticism, the European Renaissance and the Age of Enlightenment.
Greek philosophy was influenced to some extent by the older wisdom literature and mythological cosmogonies of the ancient Near East, though the extent of this influence is widely debated. The classicist Martin Litchfield West states, "contact with oriental cosmology and theology helped to liberate the early Greek philosophers' imagination; it certainly gave them many suggestive ideas. But they taught themselves to reason. Philosophy as we understand it is a Greek creation".
Subsequent philosophic tradition was so influenced by Socrates as presented by Plato that it is conventional to refer to philosophy developed prior to Socrates as pre-Socratic philosophy. The periods following this, up to and after the wars of Alexander the Great, are those of "Classical Greek" and "Hellenistic philosophy", respectively.
Socrates
Socrates ; (c. 470–399 BC) was a Greek philosopher from Athens who is credited as the founder of Western philosophy and among the first moral philosophers of the ethical tradition of thought. An enigmatic figure, Socrates authored no texts and is known mainly through the posthumous accounts of classical writers, particularly his students Plato and Xenophon. These accounts are written as dialogues, in which Socrates and his interlocutors examine a subject in the style of question and answer; they gave rise to the Socratic dialogue literary genre. Contradictory accounts of Socrates make a reconstruction of his philosophy nearly impossible, a situation known as the Socratic problem.
Plato's dialogues are among the most comprehensive accounts of Socrates to survive from antiquity. They demonstrate the Socratic approach to areas of philosophy including epistemology and ethics. The Platonic Socrates lends his name to the concept of the Socratic method, and also to Socratic irony. The Socratic method of questioning, or elenchus, takes shape in dialogue using short questions and answers, epitomized by those Platonic texts in which Socrates and his interlocutors examine various aspects of an issue or an abstract meaning, usually relating to one of the virtues, and find themselves at an impasse, completely unable to define what they thought they understood. Socrates is known for proclaiming his total ignorance; he used to say that the only thing he was aware of was his ignorance, seeking to imply that the realization of our ignorance is the first step in philosophizing.
Socrates exerted a strong influence on philosophers in later antiquity and has continued to do so in the modern era. He was studied by medieval and Islamic scholars and played an important role in the thought of the Italian Renaissance, particularly within the humanist movement. Interest in him continued unabated, as reflected in the works of Søren Kierkegaard and Friedrich Nietzsche. Depictions of Socrates in art, literature, and popular culture have made him a widely known figure in the Western philosophical tradition.
Pythagoras
Pythagoras of Samos (c. 570 – c. 495 BC) was an ancient Ionian Greek philosopher, polymath and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, the West in general. Knowledge of his life is clouded by legend. Modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, around 530 BC, he travelled to Croton in southern Italy, where he founded a school in which initiates were sworn to secrecy and lived a communal, ascetic lifestyle. This lifestyle entailed a number of dietary prohibitions, traditionally said to have included aspects of vegetarianism.
The teaching most securely identified with Pythagoras is metempsychosis, or the "transmigration of souls", which holds that every soul is immortal and, upon death, enters into a new body. He may have also devised the doctrine of musica universalis, which holds that the planets move according to mathematical equations and thus resonate to produce an inaudible symphony of music. Scholars debate whether Pythagoras developed the numerological and musical teachings attributed to him, or if those teachings were developed by his later followers, particularly Philolaus of Croton. Following Croton's decisive victory over Sybaris in around 510 BC, Pythagoras's followers came into conflict with supporters of democracy, and Pythagorean meeting houses were burned. Pythagoras may have been killed during this persecution, or he may have escaped to Metapontum and died there.
In antiquity, Pythagoras was credited with many mathematical and scientific discoveries, including the Pythagorean theorem, Pythagorean tuning, the five regular solids, the Theory of Proportions, the sphericity of the Earth, and the identity of the morning and evening stars as the planet Venus. It was said that he was the first man to call himself a philosopher ("lover of wisdom") and that he was the first to divide the globe into five climatic zones. Classical historians debate whether Pythagoras made these discoveries, and many of the accomplishments credited to him likely originated earlier or were made by his colleagues or successors. Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were important, but it is debated to what extent, if at all, he actually contributed to mathematics or natural philosophy.
Pythagoras influenced Plato, whose dialogues, especially his Timaeus, exhibit Pythagorean teachings. Pythagorean ideas on mathematical perfection also impacted ancient Greek art. His teachings underwent a major revival in the first century BC among Middle Platonists, coinciding with the rise of Neopythagoreanism. Pythagoras continued to be regarded as a great philosopher throughout the Middle Ages and his philosophy had a major impact on scientists such as Nicolaus Copernicus, Johannes Kepler, and Isaac Newton. Pythagorean symbolism was used throughout early modern European esotericism, and his teachings as portrayed in Ovid's Metamorphoses influenced the modern vegetarian movement.
Plato
Plato (428/427 or 424/423 – 348 BC) was an ancient Greek philosopher born in Athens during the Classical period. In Athens, Plato founded the Academy, a philosophical school where he taught the philosophical doctrines that would later become known as Platonism. Plato, or Platon, was a pen name derived, apparently, from the nickname given to him by his wrestling coach – allegedly a reference to his physical girth. According to Alexander Polyhistor, quoted by Diogenes Laërtius, his actual name was Aristocles, son of Ariston, of the deme (suburb) Collytus, in Athens.
Along with his teacher, Socrates, and student Aristotle, Plato is a central figure in the history of philosophy. Unlike the work of nearly all of his contemporaries, Plato's entire body of work is believed to have survived intact for over 2,400 years. Although their popularity has fluctuated, Plato's works have consistently been read and studied. Through Neoplatonism Plato also greatly influenced both Christian (through e.g. Augustine of Hippo) and Islamic philosophy (through e.g. Al-Farabi, Al-Kindi). In modern times, Alfred North Whitehead famously said: "the safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato."
Platonism
Platonism is the philosophy of Plato and philosophical systems closely derived from it, though contemporary Platonists do not necessarily accept all doctrines of Plato. Platonism had a profound effect on Western thought. In its most basic fundamentals, Platonism affirms the existence of abstract objects, which are asserted to exist in a third realm distinct from both the sensible external world and from the internal world of consciousness, and is the opposite of nominalism. This can apply to properties, types, propositions, meanings, numbers, sets, truth values, and so on (see abstract object theory). Philosophers who affirm the existence of abstract objects are sometimes called Platonists; those who deny their existence are sometimes called nominalists. The terms "Platonism" and "nominalism" also have established senses in the history of philosophy. They denote positions that have little to do with the modern notion of an abstract object.
In a narrower sense, the term might indicate the doctrine of Platonic realism, a form of mysticism. The central concept of Platonism, a distinction essential to the Theory of Forms, is the distinction between the reality which is perceptible but unintelligible, associated with the flux of Heraclitus and studied by the likes of science, and the reality which is imperceptible but intelligible, associated with the unchanging being of Parmenides and studied by the likes of mathematics. Geometry was the main motivation of Plato, and this also shows the influence of Pythagoras. The Forms are typically described in dialogues such as the Phaedo, Symposium and Republic as perfect archetypes of which objects in the everyday world are imperfect copies. Aristotle's Third Man Argument is its most famous criticism in antiquity.
In the Republic the highest form is identified as the Form of the Good, the source of all other Forms, which could be known by reason. In the Sophist, a later work, the Forms being, sameness and difference are listed among the primordial "Great Kinds". Plato established the academy, and in the 3rd century BC, Arcesilaus adopted academic skepticism, which became a central tenet of the school until 90 BC when Antiochus added Stoic elements, rejected skepticism, and began a period known as Middle Platonism.
In the 3rd century AD, Plotinus added additional mystical elements, establishing Neoplatonism, in which the summit of existence was the One or the Good, the source of all things; in virtue and meditation the soul had the power to elevate itself to attain union with the One. Many Platonic notions were adopted by the Christian church which understood Plato's Forms as God's thoughts (a position also known as divine conceptualism), while Neoplatonism became a major influence on Christian mysticism in the West through Saint Augustine, Doctor of the Catholic Church, who was heavily influenced by Plotinus' Enneads, and in turn were foundations for the whole of Western Christian thought. Many ideas of Plato were incorporated by the Roman Catholic Church.
Aristotle
Aristotle (384–322 BCE) was an Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology and the arts. As the founder of the Peripatetic school of philosophy in the Lyceum in Athens, he began the wider Aristotelian tradition that followed, which set the groundwork for the development of modern science.
Aristotle's views profoundly shaped medieval scholarship. The influence of his physical science extended from late antiquity and the Early Middle Ages into the Renaissance, and was not replaced systematically until the Enlightenment and theories such as classical mechanics were developed. He influenced Judeo-Islamic philosophies during the Middle Ages, as well as Christian theology, especially the Neoplatonism of the Early Church and the scholastic tradition of the Catholic Church.
Aristotle was revered among medieval Muslim scholars as "The First Teacher", and among medieval Christians like Thomas Aquinas as simply "The Philosopher", while the poet Dante called him "the master of those who know". His works contain the earliest known formal study of logic, and were studied by medieval scholars such as Peter Abelard and Jean Buridan. Aristotle's influence on logic continued well into the 19th century. In addition, his ethics, though always influential, gained renewed interest with the modern advent of virtue ethics.
Plutarch
Plutarch c. AD 46 – after AD 119) was a Greek Middle Platonist philosopher, historian, biographer, essayist, and priest at the Temple of Apollo in Delphi. He is known primarily for his Parallel Lives, a series of biographies of illustrious Greeks and Romans, and Moralia, a collection of essays and speeches.
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Shakespeare: Metamorphosis – Plutarch's "Lives" (1579), Senate House Library |
Plutarch's writings had an enormous influence on English and French literature. Shakespeare paraphrased parts of Thomas North's translation of selected Lives in his plays, and occasionally quoted from them verbatim.
Jean-Jacques Rousseau quotes from Plutarch in the 1762 Emile, or On Education, a treatise on the education of the whole person for citizenship. Rousseau introduces a passage from Plutarch in support of his position against eating meat: "'You ask me', said Plutarch, 'why Pythagoras abstained from eating the flesh of beasts...'"
Ralph Waldo Emerson and the Transcendentalists were greatly influenced by the Moralia and in his glowing introduction to the five-volume, 19th-century edition, he called the Lives "a bible for heroes". He also opined that it was impossible to "read Plutarch without a tingling of the blood; and I accept the saying of the Chinese Mencius: 'A sage is the instructor of a hundred ages. When the manners of Loo are heard of, the stupid become intelligent, and the wavering, determined.'"
Montaigne's Essays draw extensively on Plutarch's Moralia and are consciously modelled on the Greek's easygoing and discursive inquiries into science, manners, customs and beliefs. Essays contains more than 400 references to Plutarch and his works.
James Boswell quoted Plutarch on writing lives, rather than biographies, in the introduction to his own Life of Samuel Johnson. Other admirers included Ben Jonson, John Dryden, Alexander Hamilton, John Milton, Edmund Burke, Joseph De Maistre, Mark Twain, Louis L'amour, and Francis Bacon, as well as such disparate figures as Cotton Mather and Robert Browning.
Plutarch's influence declined in the 19th and 20th centuries, but it remains embedded in the popular ideas of Greek and Roman history. One of his most famous quotes was one that he included in one of his earliest works. "The world of man is best captured through the lives of the men who created history."
Greek historians and academics
Thucydides
'Thucydides (c. 460 – c. 400 BC) was an Athenian historian and general. His History of the Peloponnesian War recounts the fifth-century BC war between Sparta and Athens until the year 411 BC. Thucydides has been dubbed the father of "scientific history" by those who accept his claims to have applied strict standards of impartiality and evidence-gathering and analysis of cause and effect, without reference to intervention by the gods, as outlined in his introduction to his work.
He also has been called the father of the school of political realism, which views the political behavior of individuals and the subsequent outcomes of relations between states as ultimately mediated by, and constructed upon, fear and self-interest. His text is still studied at universities and military colleges worldwide. The Melian dialogue is regarded as a seminal text of international relations theory, while his version of Pericles' Funeral Oration is widely studied by political theorists, historians, and students of the classics.
More generally, Thucydides developed an understanding of human nature to explain behavior in such crises as plagues, massacres, and wars.
Greek scientists
Mathematics
Mathematics of Ancient GreeksGreek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly from the late 7th century BC to the 6th century AD, around the shores of the Mediterranean. Greek mathematicians lived in cities spread over the entire region, from Anatolia to Italy and North Africa, but were united by Greek culture and the Greek language. The development of mathematics as a theoretical discipline and the use of deductive reasoning in proofs is an important difference between Greek mathematics and those of preceding civilizations.
Archimedes
Archimedes of Syracuse c. 287 – c. 212 BC) was an Ancient Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Considered the greatest mathematician of ancient history, and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems. These include the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral.
Archimedes' other mathematical achievements include deriving an approximation of pi, defining and investigating the Archimedean spiral, and devising a system using exponentiation for expressing very large numbers. He was also one of the first to apply mathematics to physical phenomena, working on statics and hydrostatics. Archimedes' achievements in this area include a proof of the law of the lever, the widespread use of the concept of center of gravity, and the enunciation of the law of buoyancy known as Archimedes' principle.He is also credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion.
Archimedes died during the siege of Syracuse, when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting Archimedes' tomb, which was surmounted by a sphere and a cylinder that Archimedes requested be placed there to represent his mathematical discoveries.
Unlike his inventions, Archimedes' mathematical writings were little known in antiquity. Mathematicians from Alexandria read and quoted him, but the first comprehensive compilation was not made until c. 530 AD by Isidore of Miletus in Byzantine Constantinople, while commentaries on the works of Archimedes by Eutocius in the 6th century opened them to wider readership for the first time.
The relatively few copies of Archimedes' written work that survived through the Middle Ages were an influential source of ideas for scientists during the Renaissance and again in the 17th century, while the discovery in 1906 of previously lost works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results.
Euclid
Euclid fl. 300 BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved new innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics.
Very little is known of Euclid's life, and most information comes from the scholars Proclus and Pappus of Alexandria many centuries later. Medieval Islamic mathematicians invented a fanciful biography, and medieval Byzantine and early Renaissance scholars mistook him for the earlier philosopher Euclid of Megara. It is now generally accepted that he spent his career in Alexandria and lived around 300 BC, after Plato's students and before Archimedes. There is some speculation that Euclid studied at the Platonic Academy and later taught at the Musaeum; he is regarded as bridging the earlier Platonic tradition in Athens with the later tradition of Alexandria.
In the Elements, Euclid deduced the theorems from a small set of axioms. He also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigour. In addition to the Elements, Euclid wrote a central early text in the optics field, Optics, and lesser-known works including Data and Phaenomena. Euclid's authorship of two other texts—On Divisions of Figures, Catoptrics—has been questioned. He is thought to have written many now lost works.
Euclidean geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.
The Elements begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language.
For more than two thousand years, the adjective "Euclidean" was unnecessary because Euclid's axioms seemed so intuitively obvious (with the possible exception of the parallel postulate) that theorems proved from them were deemed absolutely true, and thus no other sorts of geometry were possible. Today, however, many other self-consistent non-Euclidean geometries are known, the first ones having been discovered in the early 19th century. An implication of Albert Einstein's theory of general relativity is that physical space itself is not Euclidean, and Euclidean space is a good approximation for it only over short distances (relative to the strength of the gravitational field).
Euclidean geometry is an example of synthetic geometry, in that it proceeds logically from axioms describing basic properties of geometric objects such as points and lines, to propositions about those objects. This is in contrast to analytic geometry, introduced almost 2,000 years later by René Descartes, which uses coordinates to express geometric properties by means of algebraic formulas.
=Euclid's Elements
Euclid's Elements' (Template:Lang-grc-gre Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century.
Euclid's Elements has been referred to as the most successful and influential textbook ever written. It was one of the very earliest mathematical works to be printed after the invention of the printing press and has been estimated to be second only to the Bible in the number of editions published since the first printing in 1482, the number reaching well over one thousand. For centuries, when the quadrivium was included in the curriculum of all university students, knowledge of at least part of Euclid's Elements was required of all students. Not until the 20th century, by which time its content was universally taught through other school textbooks, did it cease to be considered something all educated people had read.
Greek artists
Euripides
Euripides (c. 480 – c. 406 BC) was a tragedian of classical Athens. Along with Aeschylus and Sophocles, he is one of the three ancient Greek tragedians for whom any plays have survived in full. Some ancient scholars attributed ninety-five plays to him, but the Suda says it was ninety-two at most. Of these, eighteen or nineteen have survived more or less complete (Rhesus is suspect). There are many fragments (some substantial) of most of his other plays. More of his plays have survived intact than those of Aeschylus and Sophocles together, partly because his popularity grew as theirs declined—he became, in the Hellenistic Age, a cornerstone of ancient literary education, along with Homer, Demosthenes, and Menander.
Euripides is identified with theatrical innovations that have profoundly influenced drama down to modern times, especially in the representation of traditional, mythical heroes as ordinary people in extraordinary circumstances. This new approach led him to pioneer developments that later writers adapted to comedy, some of which are characteristic of romance. He also became "the most tragic of poets", focusing on the inner lives and motives of his characters in a way previously unknown. He was "the creator of ... that cage which is the theatre of Shakespeare's Othello, Racine's Phèdre, of Ibsen and Strindberg," in which "imprisoned men and women destroy each other by the intensity of their loves and hates". But he was also the literary ancestor of comic dramatists as diverse as Menander and George Bernard Shaw.
His contemporaries associated him with Socrates as a leader of a decadent intellectualism. Both were frequently lampooned by comic poets such as Aristophanes. Socrates was eventually put on trial and executed as a corrupting influence. Ancient biographies hold that Euripides chose a voluntary exile in old age, dying in Macedonia, but recent scholarship casts doubt on these sources.
Greek culture
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Notes
- "The dates of his life cannot be fixed exactly, but assuming the approximate correctness of the statement of Aristoxenus (ap. Porph. V.P. 9) that he left Samos to escape the tyranny of Polycrates at the age of forty, we may put his birth round about 570 BC, or a few years earlier. The length of his life was variously estimated in antiquity, but it is agreed that he lived to a fairly ripe old age, and most probably he died at about seventy-five or eighty."
- Cicero, Tusculan Disputations, 5.3.8–9 (citing Heraclides Ponticus fr. 88 Wehrli), Diogenes Laërtius 1.12, 8.8, Iamblichus VP 58. Burkert attempted to discredit this ancient tradition, but it has been defended by C. J. De Vogel, Pythagoras and Early Pythagoreanism (1966), pp. 97–102, and C. Riedweg, Pythagoras: His Life, Teaching, And Influence (2005), p. 92.
- "...the subject of philosophy, as it is often conceived – a rigorous and systematic examination of ethical, political, metaphysical, and epistemological issues, armed with a distinctive method – can be called his invention."
- Wilson 2006, p. 278 harvnb error: no target: CITEREFWilson2006 (help) states, "Euclid's Elements subsequently became the basis of all mathematical education, not only in the Roman and Byzantine periods, but right down to the mid-20th century, and it could be argued that it is the most successful textbook ever written."
- Boyer 1991, p. 100 notes, "As teachers at the school he called a band of leading scholars, among whom was the author of the most fabulously successful mathematics textbook ever written – the Elements (Stoichia) of Euclid".
- Boyer 1991, p. 119 notes, "The Elements of Euclid not only was the earliest major Greek mathematical work to come down to us, but also the most influential textbook of all times. The first printed versions of the Elements appeared at Venice in 1482, one of the very earliest of mathematical books to be set in type; it has been estimated that since then at least a thousand editions have been published. Perhaps no book other than the Bible can boast so many editions, and certainly no mathematical work has had an influence comparable with that of Euclid's Elements".
- Bunt, Jones & Bedient 1988, p. 142 harvnb error: no target: CITEREFBuntJonesBedient1988 (help) state, "the Elements became known to Western Europe via the Arabs and the Moors. There, the Elements became the foundation of mathematical education. More than 1000 editions of the Elements are known. In all probability, it is, next to the Bible, the most widely spread book in the civilization of the Western world."
- The epithet "the most tragic of poets" was mastered by Aristotle, probably in reference to a perceived preference for unhappy endings, but it has wider relevance: "For in his representation of human suffering Euripides pushes to the limits of what an audience can stand; some of his scenes are almost unbearable."—B. Knox,'Euripides' in The Cambridge History of Classical Literature I: Greek Literature, P. Easterling and B. Knox (ed.s), Cambridge University Press (1985), p. 339
References
- "Ancient Greek philosophy, Herodotus, famous ancient Greek philosophers. Ancient Greek philosophy at Hellenism.Net". www.hellenism.net. Retrieved 2019-01-28.
- Alfred North Whitehead (1929), Process and Reality, Part II, Chap. I, Sect. I.
- Kevin Scharp (Department of Philosophy, Ohio State University) – Diagrams Archived 2014-10-31 at the Wayback Machine.
- Griffin, Jasper; Boardman, John; Murray, Oswyn (2001). The Oxford history of Greece and the Hellenistic world. Oxford : Oxford University Press. p. 140. ISBN 978-0-19-280137-1.
- William Keith Chambers Guthrie, (1978), A history of Greek philosophy, Volume 1: The earlier Presocratics and the Pythagoreans, p. 173. Cambridge University Press
- Huffman, Carl A., ed. (2014). A History of Pythagoreanism. Cambridge: Cambridge University Press. doi:10.1017/CBO9781139028172. ISBN 978-1-107-01439-8.
- "Plato FAQ: Plato's real name". www.plato-dialogues.org.
- Kraut 2013 harvnb error: no target: CITEREFKraut2013 (help)
- "Plato and Aristotle: How Do They Differ?". Britannica. "Plato (c. 428–c. 348 BCE) and Aristotle (384–322 BCE) are generally regarded as the two greatest figures of Western philosophy".
- Cooper, John M.; Hutchinson, D.S., eds. (1997): "Introduction."
- Cooper 1997, p. vii. sfn error: no target: CITEREFCooper1997 (help)
- Whitehead 1978, p. 39. sfn error: no target: CITEREFWhitehead1978 (help)
- ^ " Philosophers who affirm the existence of abstract objects are sometimes called platonists; those who deny their existence are sometimes called nominalists. The terms "platonism" and "nominalism" have established senses in the history of philosophy, where they denote positions that have little to do with the modern notion of an abstract object. In this connection, it is essential to bear in mind that modern platonists (with a small 'p') need not accept any of the doctrines of Plato, just as modern nominalists need not accept the doctrines of medieval Nominalists." "Abstract Objects" Archived 2013-12-02 at the Wayback Machine, Gideon Rosen, The Stanford Encyclopedia of Philosophy (Spring 2012 Edition), Edward N. Zalta (ed.).
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{{cite book}}
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External links
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- The Canadian Museum of Civilization—Greece Secrets of the Past
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- Illustrated Greek History, Janice Siegel, Department of Classics, Hampden–Sydney College, Virginia
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