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Archytas
Archytas (; el, Ἀρχύτας; 435/410–360/350 BC) was an Ancient Greek philosopher, mathematician, music theorist, astronomer, statesman, and strategist. He was a scientist of the Pythagorean school and famous for being the reputed founder of mathematical mechanics, as well as a good friend of Plato. Life and work Archytas was born in Tarentum, Magna Graecia and was the son of Mnesagoras or Hadees. For a while, he was taught by Philolaus, and was a teacher of mathematics to Eudoxus of Cnidus. Archytas and Eudoxus' student was Menaechmus. As a Pythagorean, Archytas believed that only arithmetic, not geometry, could provide a basis for satisfactory proofs. Archytas is believed to be the founder of mathematical mechanics.: ''Vitae philosophorum'' As only described in the writings of Aulus Gellius five centuries after him, he was reputed to have designed and built the first artificial, self-propelled flying device, a bird-shaped model propelled by a jet of what was probably st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagoreanism
Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the Ancient Greece, ancient Greek colony of Crotone, Kroton, in modern Calabria (Italy). Early Pythagorean communities spread throughout Magna Graecia. Pythagoras' death and disputes about his teachings led to the development of two philosophical traditions within Pythagoreanism. The ''akousmatikoi'' were superseded in the 4th century BC as a significant mendicant school of philosophy by the Cynicism (philosophy), Cynics. The ''mathēmatikoi'' philosophers were absorbed into the Platonic Academy, Platonic school in the 4th century BC. Following political instability in Magna Graecia, some Pythagorean philosophers fled to mainland Greece while others regrouped in Rhegium. By about 400 BC the majority of Pythagorean philosophers had left Italy. Pythagorean ideas exercised a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagoras
Pythagoras of Samos ( grc, Πυθαγόρας ὁ Σάμιος, Pythagóras ho Sámios, Pythagoras the Samos, Samian, or simply ; in Ionian Greek; ) was an ancient Ionians, Ionian Ancient Greek philosophy, Greek philosopher 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 Western philosophy, West in general. Knowledge of his life is clouded by legend, but he appears to have been the son of Mnesarchus, a gem-engraver on the island of Samos. Modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, around 530 BC, he travelled to Crotone, Croton in southern Italy, where he founded a school in which initiates were sworn to secrecy and lived a communal, asceticism, ascetic lifestyle. This lifestyle entailed a number of dietary prohibitions, traditionally said to have included vegetarianism, although m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eudoxus Of Cnidus
Eudoxus of Cnidus (; grc, Εὔδοξος ὁ Κνίδιος, ''Eúdoxos ho Knídios''; ) was an ancient Greek astronomer, mathematician, scholar, and student of Archytas and Plato. All of his original works are lost, though some fragments are preserved in Hipparchus' commentary on Aratus's poem on astronomy. ''Sphaerics'' by Theodosius of Bithynia may be based on a work by Eudoxus. Life Eudoxus was born and died in Cnidus (also spelled Knidos), which was a city on the southwest coast of Asia Minor. The years of Eudoxus' birth and death are not fully known but the range may have been , or . His name Eudoxus means "honored" or "of good repute" (, from ''eu'' "good" and ''doxa'' "opinion, belief, fame"). It is analogous to the Latin name Benedictus. Eudoxus's father, Aeschines of Cnidus, loved to watch stars at night. Eudoxus first traveled to Tarentum to study with Archytas, from whom he learned mathematics. While in Italy, Eudoxus visited Sicily, where he studied medicine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doubling The Cube
Doubling the cube, also known as the Delian problem, is an ancient geometric problem. Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume is double that of the first. As with the related problems of squaring the circle and trisecting the angle, doubling the cube is now known to be impossible to construct by using only a compass and straightedge, but even in ancient times solutions were known that employed other tools. The Egyptians, Indians, and particularly the Greeks were aware of the problem and made many futile attempts at solving what they saw as an obstinate but soluble problem. However, the nonexistence of a compass-and-straightedge solution was finally proven by Pierre Wantzel in 1837. In algebraic terms, doubling a unit cube requires the construction of a line segment of length , where ; in other words, , the cube root of two. This is because a cube of side length 1 has a volume of , and a cube of twice that volu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taranto
Taranto (, also ; ; nap, label= Tarantino, Tarde; Latin: Tarentum; Old Italian: ''Tarento''; Ancient Greek: Τάρᾱς) is a coastal city in Apulia, Southern Italy. It is the capital of the Province of Taranto, serving as an important commercial port as well as the main Italian naval base. Founded by Spartans in the 8th century BC during the period of Greek colonisation, Taranto was among the most important in Magna Graecia, becoming a cultural, economic and military power that gave birth to philosophers, strategists, writers and athletes such as Archytas, Aristoxenus, Livius Andronicus, Heracleides, Iccus, Cleinias, Leonidas, Lysis and Sosibius. By 500 BC, the city was among the largest in the world, with a population estimated up to 300,000 people. The seven-year rule of Archytas marked the apex of its development and recognition of its hegemony over other Greek colonies of southern Italy. During the Norman period, it became the capital of the Principality of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magna Graecia
Magna Graecia (, ; , , grc, Μεγάλη Ἑλλάς, ', it, Magna Grecia) was the name given by the Romans to the coastal areas of Southern Italy in the present-day Italian regions of Calabria, Apulia, Basilicata, Campania and Sicily; these regions were extensively populated by Greek settlers. These settlers, who began arriving in the 8th century BC, brought with them their Hellenic civilization, which left a lasting imprint on Italy (such as in the culture of ancient Rome). They also influenced the native peoples, such as the Sicels and the Oenotrians, who became hellenized after they adopted the Greek culture as their own. The Greek expression ''Megálē Hellás'', later translated into Latin as ''Magna Graecia,'' first appears in Polybius' '' Histories,'' where he ascribed the term to Pythagoras and his philosophical school. Strabo also used the term to refer to the size of the territory that had been conquered by the Greeks, and the Roman poet Ovid used the term in his p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plato
Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution of higher learning on the European continent. Along with his teacher, Socrates, and his student, Aristotle, Plato is a central figure in the history of Ancient Greek philosophy and the Western and Middle Eastern philosophies descended from it. He has also shaped religion and spirituality. The so-called neoplatonism of his interpreter Plotinus greatly influenced both Christianity (through Church Fathers such as Augustine) and Islamic philosophy (through e.g. Al-Farabi). In modern times, Friedrich Nietzsche diagnosed Western culture as growing in the shadow of Plato (famously calling Christianity "Platonism for the masses"), while Alfred North Whitehead famously said: "the safest general characterization of the European philosophical tra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doubling The Cube
Doubling the cube, also known as the Delian problem, is an ancient geometric problem. Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume is double that of the first. As with the related problems of squaring the circle and trisecting the angle, doubling the cube is now known to be impossible to construct by using only a compass and straightedge, but even in ancient times solutions were known that employed other tools. The Egyptians, Indians, and particularly the Greeks were aware of the problem and made many futile attempts at solving what they saw as an obstinate but soluble problem. However, the nonexistence of a compass-and-straightedge solution was finally proven by Pierre Wantzel in 1837. In algebraic terms, doubling a unit cube requires the construction of a line segment of length , where ; in other words, , the cube root of two. This is because a cube of side length 1 has a volume of , and a cube of twice that volu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Villa Of The Papyri
The Villa of the Papyri ( it, Villa dei Papiri, also known as ''Villa dei Pisoni'' and in early excavation records as the ''Villa Suburbana'') was an ancient Roman villa in Herculaneum, in what is now Ercolano, southern Italy. It is named after its unique library of ''papyri'' (or scrolls), discovered in 1750. The Villa was considered to be one of the most luxurious houses in all of Herculaneum and in the Roman world. Maiuri, Amedeo. ''Herculaneum and the Villa of the Papyri.'' Italy (1974): 35-39. Its luxury is shown by its exquisite architecture and by the very large number of outstanding works of art discovered, including frescoes, bronzes and marble sculpture which constitute the largest collection of Greek and Roman sculptures ever discovered in a single context. It was situated on the ancient coastline below the volcano Vesuvius with nothing to obstruct the view of the sea. It was perhaps owned by Julius Caesar's father-in-law, Lucius Calpurnius Piso Caesoninus.Hornblower ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Music Theorist
Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the "rudiments", that are needed to understand music notation (key signatures, time signatures, and rhythmic notation); the second is learning scholars' views on music from antiquity to the present; the third is a sub-topic of musicology that "seeks to define processes and general principles in music". The musicological approach to theory differs from music analysis "in that it takes as its starting-point not the individual work or performance but the fundamental materials from which it is built." Music theory is frequently concerned with describing how musicians and composers make music, including tuning systems and composition methods among other topics. Because of the ever-expanding conception of what constitutes music, a more inclusive definition could be the consideration of any sonic phenomena, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanics (Aristotle)
''Mechanics'' ( el, Μηχανικά; la, Mechanica), also called ''Mechanical Problems'' or ''Questions of Mechanics'', is a text traditionally attributed to Aristotle, but generally regarded as spurious. Thomas Winter has suggested that the author was Archytas. However, Michael Coxhead says that it is only possible to conclude that the author was one of the Peripatetics. During the Renaissance, an edition of this work was published by Francesco Maurolico. A Latin translation was made by Vettor Fausto, dedicated to Giovanni Badoer Giovanni Badoer or Zuan Badoer ( – January 1535) was a poet, politician and diplomat of the Republic of Venice. Badoer was the resident ambassador in Spain (1498–1499; 1512–1514), Naples (1500–1501), Hungary (1501–1503), the Holy See (15 ... in 1517. See also * Aristotle's wheel paradox Notes External links * Pseudo-Aristotle, ''Mechanica''- Greek text and English translation * Works by Aristotle Ancient Greek technology< ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vitruvius
Vitruvius (; c. 80–70 BC – after c. 15 BC) was a Roman architect and engineer during the 1st century BC, known for his multi-volume work entitled ''De architectura''. He originated the idea that all buildings should have three attributes: , , and ("strength", "utility", and "beauty"). These principles were later widely adopted in Roman architecture. His discussion of perfect proportion in architecture and the human body led to the famous Renaissance drawing of the ''Vitruvian Man'' by Leonardo da Vinci. Little is known about Vitruvius' life, but by his own descriptionDe Arch. Book 1, preface. section 2. he served as an artilleryman, the third class of arms in the Roman military offices. He probably served as a senior officer of artillery in charge of ''doctores ballistarum'' (artillery experts) and ''libratores'' who actually operated the machines. As an army engineer he specialized in the construction of ''ballista'' and '' scorpio'' artillery war machines for sieges. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
