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Nicomachus
Nicomachus of Gerasa (; ) was an Ancient Greek Neopythagorean philosopher from Gerasa, in the Roman province of Syria (now Jerash, Jordan). Like many Pythagoreans, Nicomachus wrote about the mystical properties of numbers, best known for his works ''Introduction to Arithmetic'' and ''Manual of Harmonics'', which are an important resource on Ancient Greek mathematics and Ancient Greek music in the Roman period. Nicomachus' work on arithmetic became a standard text for Neoplatonic education in Late antiquity, with philosophers such as Iamblichus and John Philoponus writing commentaries on it. A Latin paraphrase by Boethius of Nicomachus's works on arithmetic and music became standard textbooks in medieval education. Life Little is known about the life of Nicomachus except that he was a Pythagorean who came from Gerasa. His ''Manual of Harmonics'' was addressed to a lady of noble birth, at whose request Nicomachus wrote the book, which suggests that he was a respected schola ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagoreans
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) circa 530 BC. Early Pythagorean communities spread throughout Magna Graecia. Already during Pythagoras' life it is likely that the distinction between the ''akousmatikoi'' ("those who listen"), who is conventionally regarded as more concerned with religious, and ritual elements, and associated with the oral tradition, and the ''mathematikoi'' ("those who learn") existed. The ancient biographers of Pythagoras, Iamblichus () and his master Porphyry (philosopher), Porphyry ( ) seem to make the distinction of the two as that of 'beginner' and 'advanced'. As the Pythagorean cenobites practiced an esoteric path, like the Greco-Roman mysteries, mystery schools of antiquity, the adherents, ''akou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greek Mathematics
Ancient Greek mathematics refers to the history of mathematical ideas and texts in Ancient Greece during classical and late antiquity, mostly from the 5th century BC to the 6th century AD. Greek mathematicians lived in cities spread around the shores of the ancient Mediterranean, 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. The early history of Greek mathematics is obscure, and traditional narratives of mathematical theorems found before the fifth century BC are regarded as later inventions. It is now generally accepted that treatises of deductive mathematics written in Greek began circulating around the mid-fifth century BC, but the earliest complete work on the subject is the '' Elements'', written during the Hellenistic perio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Numbers
In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28. The first four perfect numbers are 6, 28, 496 and 8128. The sum of proper divisors of a number is called its aliquot sum, so a perfect number is one that is equal to its aliquot sum. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors; in symbols, \sigma_1(n)=2n where \sigma_1 is the sum-of-divisors function. This definition is ancient, appearing as early as Euclid's ''Elements'' (VII.22) where it is called (''perfect'', ''ideal'', or ''complete number''). Euclid also proved a formation rule (IX.36) whereby \frac is an even perfect number whenever q is a prime of the form 2^p-1 for positive integer p—what is now ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gerasa
Jerash (; , , ) is a city in northern Jordan. The city is the administrative center of the Jerash Governorate, and has a population of 50,745 as of 2015. It is located 30.0 miles north of the capital city Amman. The earliest evidence of settlement in Jerash is in a Neolithic site known as Tal Abu Sowan, where rare human remains dating to around 7500 BC were uncovered. Jerash flourished during the Greek, Hellenistic, Roman, and Byzantine periods, when it was known as Gerasa. It was one of the cities of the Hellenistic cities of the Decapolis.''The New Century Classical Handbook''; Catherine Avery, editor; Appleton-Century-Crofts, New York, 1962, p. 495: "Gerasa... (Modern name: Jerash.) In ancient geography, a city of the Decapolis, in Palestine, about 56 miles NE of Jerusalem... The forum, which is oval and 300 feet long, is surrounded by a range of Ionic columns... A theater has 28 tiers of seats still remaining above ground... A smaller theater on the same site is equally pe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jerash
Jerash (; , , ) is a city in northern Jordan. The city is the administrative center of the Jerash Governorate, and has a population of 50,745 as of 2015. It is located 30.0 miles north of the capital city Amman. The earliest evidence of settlement in Jerash is in a Neolithic site known as Tal Abu Sowan, where rare human remains dating to around 7500 BC were uncovered. Jerash flourished during the Greek, Hellenistic, Roman, and Byzantine periods, when it was known as Gerasa. It was one of the cities of the Hellenistic cities of the Decapolis.''The New Century Classical Handbook''; Catherine Avery, editor; Appleton-Century-Crofts, New York, 1962, p. 495: "Gerasa... (Modern name: Jerash.) In ancient geography, a city of the Decapolis, in Palestine, about 56 miles NE of Jerusalem... The forum, which is oval and 300 feet long, is surrounded by a range of Ionic columns... A theater has 28 tiers of seats still remaining above ground... A smaller theater on the same site is equally ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philolaus
Philolaus (; , ''Philólaos''; ) was a Greek Pythagorean and pre-Socratic philosopher. He was born in a Greek colony in Italy and migrated to Greece. Philolaus has been called one of three most prominent figures in the Pythagorean tradition and the most outstanding figure in the Pythagorean school. Pythagoras developed a school of philosophy that was dominated by both mathematics and mysticism. Most of what is known today about the Pythagorean astronomical system is derived from Philolaus's views. He may have been the first to write about Pythagorean doctrine. According to , who cites Nicomachus, Philolaus was the successor of Pythagoras. He argued that at the foundation of everything is the part played by the limiting and limitless, which combine in a harmony. With his assertions that the Earth was not the center of the universe (geocentrism), he is credited with the earliest known discussion of concepts in the development of heliocentrism, the theory that the Earth is not th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Numbers
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number , called trial division, tests whether is a multiple of any integer between 2 and . Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always produ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Philoponus
John Philoponus ( Greek: ; , ''Ioánnis o Philóponos''; c. 490 – c. 570), also known as John the Grammarian or John of Alexandria, was a Coptic Miaphysite philologist, Aristotelian commentator and Christian theologian from Alexandria, Byzantine Egypt, who authored a number of philosophical treatises and theological works. John Philoponus broke from the Aristotelian– Neoplatonic tradition, questioning methodology and eventually leading to empiricism in the natural sciences. He was one of the first to propose a "theory of impetus" similar to the modern concept of inertia over Aristotelian dynamics. He is also the historical founder of what is now called the Kalam cosmological argument. Later in life Philoponus turned to Christian apologetics, arguing against the eternity of the world in his '' De opificio mundi'', a theory which formed the basis of pagan attacks on the Christian doctrine of Creation. He also wrote on Christology and was posthumously condemned as a here ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iamblichus
Iamblichus ( ; ; ; ) was a Neoplatonist philosopher who determined a direction later taken by Neoplatonism. Iamblichus was also the biographer of the Greek mystic, philosopher, and mathematician Pythagoras. In addition to his philosophical contributions, his is important for the study of the sophists because it preserved about ten pages of an otherwise unknown sophist known as the Anonymus Iamblichi. Life According to the and Iamblichus' biographer, Eunapius, Iamblichus was born in Chalcis (later called Qinnašrīn) in Coele, now in northwest Syria. Iamblichus was descended from the Emesene dynasty. He initially studied under Anatolius of Laodicea and later studied under Porphyry, a pupil of Plotinus (the founder of Neoplatonism). Iamblichus disagreed with Porphyry about theurgy, reportedly responding to Porphyry's criticism of the practice in '' On the Mysteries of the Egyptians, Chaldeans, and Assyrians''. He returned to Coele Syria around 304 to found a school i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neopythagoreanism
Neopythagoreanism (or neo-Pythagoreanism) was a school of Hellenistic and Roman philosophy which revived Pythagorean doctrines. Neopythagoreanism was influenced by middle Platonism and in turn influenced Neoplatonism. It originated in the 1st century BC and flourished during the 1st and 2nd centuries AD. The ''Encyclopædia Britannica'' Eleventh Edition describes Neopythagoreanism as "a link in the chain between the old and the new" within Hellenistic philosophy. Central to Neopythagorean thought was the concept of a soul and its inherent desire for a ''unio mystica'' with the divine. The word ''Neopythagoreanism'' is a modern (19th century) term, coined as a parallel of "Neoplatonism". History In the 1st century BC Cicero's friend Nigidius Figulus made an attempt to revive Pythagorean doctrines, but the most important members of the school were Apollonius of Tyana and Moderatus of Gades in the 1st century AD. Other important Neopythagoreans include the mathematician Nicoma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jordan
Jordan, officially the Hashemite Kingdom of Jordan, is a country in the Southern Levant region of West Asia. Jordan is bordered by Syria to the north, Iraq to the east, Saudi Arabia to the south, and Israel and the occupied Palestinian territories to the west. The Jordan River, flowing into the Dead Sea, is located along the country's western border within the Jordan Rift Valley. Jordan has a small coastline along the Red Sea in its southwest, separated by the Gulf of Aqaba from Egypt. Amman is the country's capital and List of cities in Jordan, largest city, as well as the List of largest cities in the Levant region by population, most populous city in the Levant. Inhabited by humans since the Paleolithic period, three kingdoms developed in Transjordan (region), Transjordan during the Iron Age: Ammon, Moab and Edom. In the third century BC, the Arab Nabataeans established Nabataean Kingdom, their kingdom centered in Petra. The Greco-Roman world, Greco-Roman period saw the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
