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Bryson Of Heraclea
Bryson of Heraclea ( el, Βρύσων Ἡρακλεώτης, ''gen''.: Βρύσωνος; fl. late 5th-century BCE) was an ancient Greek mathematician and sophist who studied the solving the problems of squaring the circle and calculating pi. Life and work Little is known about the life of Bryson; he came from Heraclea Pontica, and he may have been a pupil of Socrates. He is mentioned in the '' 13th Platonic Epistle'', and Theopompus even claimed in his ''Attack upon Plato'' that Plato stole many ideas for his dialogues from Bryson of Heraclea. He is known principally from Aristotle, who criticizes his method of squaring the circle. He also upset Aristotle by asserting that obscene language does not exist. Diogenes Laërtius and the Suda refer several times to a Bryson as a teacher of various philosophers, but since some of the philosophers mentioned lived in the late 4th-century BCE, it is possible that Bryson became confused with Bryson of Achaea, who may have lived around that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic period (), and the Classical period (). Ancient Greek was the language of Homer and of fifth-century Athenian historians, playwrights, and philosophers. It has contributed many words to English vocabulary and has been a standard subject of study in educational institutions of the Western world since the Renaissance. This article primarily contains information about the Epic and Classical periods of the language. From the Hellenistic period (), Ancient Greek was followed by Koine Greek, which is regarded as a separate historical stage, although its earliest form closely resembles Attic Greek and its latest form approaches Medieval Greek. There were several regional dialects of Ancient Greek, of which Attic Greek developed into Koine. Dia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lower Bound
In mathematics, particularly in order theory, an upper bound or majorant of a subset of some preordered set is an element of that is greater than or equal to every element of . Dually, a lower bound or minorant of is defined to be an element of that is less than or equal to every element of . A set with an upper (respectively, lower) bound is said to be bounded from above or majorized (respectively bounded from below or minorized) by that bound. The terms bounded above (bounded below) are also used in the mathematical literature for sets that have upper (respectively lower) bounds. Examples For example, is a lower bound for the set (as a subset of the integers or of the real numbers, etc.), and so is . On the other hand, is not a lower bound for since it is not smaller than every element in . The set has as both an upper bound and a lower bound; all other numbers are either an upper bound or a lower bound for that . Every subset of the natural numbers has a lowe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
5th-century BC Births
The 5th century is the time period from 401 ( CDI) through 500 ( D) ''Anno Domini'' (AD) or Common Era (CE) in the Julian calendar. The 5th century is noted for being a period of migration and political instability throughout Eurasia. It saw the collapse of the Western Roman Empire, which came to an end in 476 AD. This empire had been ruled by a succession of weak emperors, with the real political might being increasingly concentrated among military leaders. Internal instability allowed a Visigoth army to reach and ransack Rome in 410. Some recovery took place during the following decades, but the Western Empire received another serious blow when a second foreign group, the Vandals, occupied Carthage, capital of an extremely important province in Africa. Attempts to retake the province were interrupted by the invasion of the Huns under Attila. After Attila's defeat, both Eastern and Western empires joined forces for a final assault on Vandal North Africa, but this campaign was a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
4th-century BC Greek People
The 4th century (per the Julian calendar and Anno Domini/Common era) was the time period which lasted from 301 ( CCCI) through 400 ( CD). In the West, the early part of the century was shaped by Constantine the Great, who became the first Roman emperor to adopt Christianity. Gaining sole reign of the empire, he is also noted for re-establishing a single imperial capital, choosing the site of ancient Byzantium in 330 (over the current capitals, which had effectively been changed by Diocletian's reforms to Milan in the West, and Nicomedeia in the East) to build the city soon called Nova Roma (New Rome); it was later renamed Constantinople in his honor. The last emperor to control both the eastern and western halves of the empire was Theodosius I. As the century progressed after his death, it became increasingly apparent that the empire had changed in many ways since the time of Augustus. The two emperor system originally established by Diocletian in the previous century fell in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
5th-century BC Greek People
The 5th century is the time period from 401 ( CDI) through 500 ( D) ''Anno Domini'' (AD) or Common Era (CE) in the Julian calendar. The 5th century is noted for being a period of migration and political instability throughout Eurasia. It saw the collapse of the Western Roman Empire, which came to an end in 476 AD. This empire had been ruled by a succession of weak emperors, with the real political might being increasingly concentrated among military leaders. Internal instability allowed a Visigoth army to reach and ransack Rome in 410. Some recovery took place during the following decades, but the Western Empire received another serious blow when a second foreign group, the Vandals, occupied Carthage, capital of an extremely important province in Africa. Attempts to retake the province were interrupted by the invasion of the Huns under Attila. After Attila's defeat, both Eastern and Western empires joined forces for a final assault on Vandal North Africa, but this campaign was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greek Mathematicians
Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly extant from the 7th century BC to the 4th century AD, around the shores of the Eastern Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean from Italy to North Africa but were united by Greek culture and the Greek language. The word "mathematics" itself derives from the grc, , máthēma , meaning "subject of instruction". The study of mathematics for its own sake and the use of generalized mathematical theories and proofs is an important difference between Greek mathematics and those of preceding civilizations. Origins of Greek mathematics The origin of Greek mathematics is not well documented. The earliest advanced civilizations in Greece and in Europe were the Minoan and later Mycenaean civilizations, both of which flourished during the 2nd millennium BCE. While these civilizations possessed writing an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prior Analytics
The ''Prior Analytics'' ( grc-gre, Ἀναλυτικὰ Πρότερα; la, Analytica Priora) is a work by Aristotle on reasoning, known as his syllogistic, composed around 350 BCE. Being one of the six extant Aristotelian writings on logic and scientific method, it is part of what later Peripatetics called the ''Organon''. Modern work on Aristotle's logic builds on the tradition started in 1951 with the establishment by Jan Łukasiewicz of a revolutionary paradigm. His approach was replaced in the early 1970s in a series of papers by John Corcoran and Timothy Smiley—which inform modern translations of ''Prior Analytics'' by Robin Smith in 1989 and Gisela Striker in 2009. The term ''analytics'' comes from the Greek words ''analytos'' (ἀναλυτός, 'solvable') and ''analyo'' (ἀναλύω, 'to solve', literally 'to loose'). However, in Aristotle's corpus, there are distinguishable differences in the meaning of ἀναλύω and its cognates. There is also the possi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sophism
A sophist ( el, σοφιστής, sophistes) was a teacher in ancient Greece in the fifth and fourth centuries BC. Sophists specialized in one or more subject areas, such as philosophy, rhetoric, music, athletics, and mathematics. They taught ''arete'' – "virtue" or "excellence" – predominantly to young statesmen and nobility. In the present day, however, a sophist refers to someone who deliberately argues using fallacious arguments or reasoning, in order to mislead; see the section below. Etymology The Greek word el, σοφός, sophos, a wise man, label=none is related to the noun el, σοφία, sophia, wisdom, label=none. Since the times of Homer it commonly referred to an expert in his profession or craft. Charioteers, sculptors, or military experts could be referred to as in their occupations. The word has gradually come to connote general wisdom and especially wisdom in human affairs such as politics, ethics, and household management. This was the meaning ascr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Kilwardby
Robert Kilwardby ( c. 1215 – 11 September 1279) was an Archbishop of Canterbury in England and a cardinal. Kilwardby was the first member of a mendicant order to attain a high ecclesiastical office in the English Church. Life Kilwardby studied at the University of Paris, then was a teacher of grammar and logic there. He then joined the Dominican Order and studied theology,Lawrence "Thirteenth Century" ''English Church and the Papacy'' p. 146 and became regent at Oxford University before 1261,Knowles ''Evolution of Medieval Thought'' p. 288 probably by 1245.Leff ''Paris and Oxford Universities'' pp. 290–293 He was named provincial prior of the Dominicans for England in 1261,Greenway Fasti Ecclesiae Anglicanae 1066-1300: Volume 2: Monastic Cathedrals (Northern and Southern Provinces): Canterbury: Archbishops' and in October 1272 Pope Gregory X appointed him as Archbishop of Canterbury to end a dispute over the election. Kilwardby was provided to the archbishopric on 11 Oc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perimeter
A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden. The perimeter of a wheel/circle (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter; if the length of the string was exact, it would equal the perimeter. Formulas The perimeter is the distance around a shape. Perimeters for more general shapes can be calculated, as any path, with \int_0^L \mathrms, where L is the length of the path and ds is an infinitesimal line element. Both of these must be replaced by algebraic forms in order to be practically calculated. If the perimeter is given as a closed piecewise smooth plane curve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Method Of Exhaustion
The method of exhaustion (; ) is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. If the sequence is correctly constructed, the difference in area between the ''n''th polygon and the containing shape will become arbitrarily small as ''n'' becomes large. As this difference becomes arbitrarily small, the possible values for the area of the shape are systematically "exhausted" by the lower bound areas successively established by the sequence members. The method of exhaustion typically required a form of proof by contradiction, known as ''reductio ad absurdum''. This amounts to finding an area of a region by first comparing it to the area of a second region, which can be "exhausted" so that its area becomes arbitrarily close to the true area. The proof involves assuming that the true area is greater than the second area, proving that assertion false, assuming it is less than the second area ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedes
Archimedes of Syracuse (;; ) was a 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. Heath, Thomas L. 1897. ''Works of Archimedes''. Archimedes' other mathematical achievements include deriving an approximation of pi, defining and in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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