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Introduction To Arithmetic
Nicomachus of Gerasa (; ) was an Ancient Greek Neopythagoreanism, Neopythagorean philosopher from Gerasa, in the Syria (Roman province), 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 Pythagoreanism, Pythagorean who came from Gerasa. His ''Manual of Harmonics'' was addressed to a lady of noble birth, at whose request Nicomachus wrote the ... [...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] |
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] |
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] |
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] |
Number
A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called ''numerals''; for example, "5" is a numeral that represents the number five. As only a relatively small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system, which allows for the representation of any Integer, non-negative integer using a combination of ten fundamental numeric symbols, called numerical digit, digits. In addition to their use in counting and measuring, numerals are often used for labels (as with telephone numbers), for ordering (as with serial numbers), and for codes (as with ISBNs). In common usage, a ''numeral'' is not clearly dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Androcydes (Pythagorean)
Androcydes () was a Pythagorean whose work ''On Pythagorean Symbols'' survives only in scattered fragments. The dating of his life is uncertain; he lived before the 1st century BC but possibly as early as the 4th. The frequency with which Androcydes is mentioned in other works indicates that he was a major source for the later Pythagorean tradition, and he is also of interest in studying the historical development of the literary and philosophical symbol. The Pythagorean symbols Walter Burkert featured Androcydes in his stemma of Pythagorean ''symbola'', consisting of gnomic utterances or maxims. Androcydes was regarded as one of the most important sources on the '' akousmata''. According to Grant (2002), he has said, ''wine and meat do harm the mind''. Paraphrases of his work in later writers demonstrate his method of interpreting these behavioral strictures. For instance, “Do not step over a yoke” should be understood as meaning “Do not transgress justice.” These int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archytas
Archytas (; ; 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 half-century earlier. ... [...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] |
Mystical
Mysticism is popularly known as becoming one with God or the Absolute, but may refer to any kind of ecstasy or altered state of consciousness which is given a religious or spiritual meaning. It may also refer to the attainment of insight in ultimate or hidden truths, and to human transformation supported by various practices and experiences. The term "mysticism" has Ancient Greek origins with various historically determined meanings. Derived from the Greek word μύω ''múō'', meaning "to close" or "to conceal", mysticism came to refer to the biblical, liturgical (and sacramental), spiritual, and contemplative dimensions of early and medieval Christianity. During the early modern period, the definition of mysticism grew to include a broad range of beliefs and ideologies related to "extraordinary experiences and states of mind". In modern times, "mysticism" has acquired a limited definition, with broad applications, as meaning the aim at the "union with the Absolute, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ptolemy
Claudius Ptolemy (; , ; ; – 160s/170s AD) was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine science, Byzantine, Islamic science, Islamic, and Science in the Renaissance, Western European science. The first was his astronomical treatise now known as the ''Almagest'', originally entitled ' (, ', ). The second is the ''Geography (Ptolemy), Geography'', which is a thorough discussion on maps and the geographic knowledge of the Greco-Roman world. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian physics, Aristotelian natural philosophy of his day. This is sometimes known as the ' (, 'On the Effects') but more commonly known as the ' (from the Koine Greek meaning 'four books'; ). The Catholic Church promoted his work, which included the only mathematically sound geocentric model of the Sola ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theon Of Smyrna
Theon of Smyrna ( ''Theon ho Smyrnaios'', ''gen.'' Θέωνος ''Theonos''; fl. 100 CE) was a Greek philosopher and mathematician, whose works were strongly influenced by the Pythagorean school of thought. His surviving ''On Mathematics Useful for the Understanding of Plato'' is an introductory survey of Greek mathematics. Life Little is known about the life of Theon of Smyrna. A bust created at his death, and dedicated by his son, was discovered at Smyrna, and art historians date it to around 135 CE. Ptolemy refers several times in his ''Almagest'' to a Theon who made observations at Alexandria, but it is uncertain whether he is referring to Theon of Smyrna.James Evans, (1998), ''The History and Practice of Ancient Astronomy'', New York, Oxford University Press, 1998, p. 49 The lunar impact crater Theon Senior is named for him. Works Theon wrote several commentaries on the works of mathematicians and philosophers of the time, including works on the philosophy of Plato. Most of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apuleius
Apuleius ( ), also called Lucius Apuleius Madaurensis (c. 124 – after 170), was a Numidians, Numidian Latin-language prose writer, Platonist philosopher and rhetorician. He was born in the Roman Empire, Roman Numidia (Roman province), province of Numidia, in the Berbers, Berber city of Madauros, modern-day M'Daourouch, Algeria. He studied Platonism in Athens, travelled to Roman Italy, Italy, Asia (Roman province), Asia Minor, and Egypt (Roman province), Egypt, and was an initiate in several cults or Greco-Roman mysteries, mysteries. The most famous incident in his life was when he was accused of using magic to gain the attentions (and fortune) of a wealthy widow. He declaimed and then distributed his own defense before the proconsul and a court of magistrates convened in Sabratha, near Oea (modern Tripoli, Libya, Tripoli, Libya). This is known as the ''Apologia''. His most famous work is his bawdy picaresque novel the ''Metamorphoses'', otherwise known as ''The Golden Ass''. It ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
