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On Risings And Settings
Autolycus of Pitane (; c. 360 – c. 290 BC) was a Greek astronomer, mathematician, and geographer. He is known today for his two surviving works ''On the Moving Sphere'' and ''On Risings and Settings'', both about spherical geometry. Life Autolycus was born in Pitane, a town of Aeolis within Ionia, Asia Minor. Of his personal life nothing is known, although he was a contemporary of Aristotle and his works seem to have been completed in Athens between 335–300 BC. Euclid references some of Autolycus' work, and Autolycus is known to have taught Arcesilaus. The lunar crater Autolycus was named in his honour. Work Autolycus' two surviving works are about spherical geometry with application to astronomy: ''On the Moving Sphere'' and ''On Risings and Settings'' (of stars). In late antiquity, both were part of the "Little Astronomy", a collection of miscellaneous short works about geometry and astronomy which were commonly transmitted together. They were translated into Arabic i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Autolycus - De Sphaera Quae Movetur Liber, 1587 - 51671
In Greek mythology, Autolycus (; ) was a robber who had the power to metamorphose or make invisible the things he stole. He had his residence on Mount Parnassus and was renowned among men for his cunning and oaths. Family There are a number of different accounts of the birth of Autolycus. According to most, he was the son of Hermes and ChioneHyginus, ''Fabulae'201/ref> or Philonis. In Ovid's version, Autolycus was conceived after Hermes had intercourse with the virgin Chione. Pausanias instead states that Autolycus' real father was Daedalion. Pausanias8.4.6/ref> In some accounts, his mother was also called Telauge. Depending on the source, Autolycus was the husband of Mestra (who could change her shape at will and was a daughter of Erysichthon), or of Neaera, or of Amphithea. He became the father of Anticlea (who married Laertes of Ithaca and was the mother of OdysseusHomer, ''Odyssey'24.334/ref>) and several sons, of whom only Aesimus, father of Sinon was named. Autoly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arabic
Arabic (, , or , ) is a Central Semitic languages, Central Semitic language of the Afroasiatic languages, Afroasiatic language family spoken primarily in the Arab world. The International Organization for Standardization (ISO) assigns language codes to 32 varieties of Arabic, including its standard form of Literary Arabic, known as Modern Standard Arabic, which is derived from Classical Arabic. This distinction exists primarily among Western linguists; Arabic speakers themselves generally do not distinguish between Modern Standard Arabic and Classical Arabic, but rather refer to both as ( "the eloquent Arabic") or simply ' (). Arabic is the List of languages by the number of countries in which they are recognized as an official language, third most widespread official language after English and French, one of six official languages of the United Nations, and the Sacred language, liturgical language of Islam. Arabic is widely taught in schools and universities around the wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Wiley & Sons, Inc
John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company that focuses on academic publishing and instructional materials. The company was founded in 1807 and produces books, journals, and encyclopedias, in print and electronically, as well as online products and services, training materials, and educational materials for undergraduate, graduate, and continuing education students. History The company was established in 1807 when Charles Wiley opened a print shop in Manhattan. The company was the publisher of 19th century American literary figures like James Fenimore Cooper, Washington Irving, Herman Melville, and Edgar Allan Poe, as well as of legal, religious, and other non-fiction titles. The firm took its current name in 1865. Wiley later shifted its focus to scientific, technical, and engineering subject areas, abandoning its literary interests. Wiley's son John (born in Flatbush, New York, October 4, 1808; died in East O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homocentric Spheres
The cosmological model of concentric (or homocentric) spheres, developed by Eudoxus, Callippus, and Aristotle, employed celestial spheres all centered on the Earth. In this respect, it differed from the epicyclic and eccentric models with multiple centers, which were used by Ptolemy and other mathematical astronomers until the time of Copernicus. Origins of the concept of concentric spheres Eudoxus of Cnidus was the first astronomer to develop the concept of concentric spheres. He was originally a student at Plato's academy and is believed to have been influenced by the cosmological speculations of Plato and Pythagoras."Eudoxus of Cnidus." Complete Dictionary of Scientific Biography. Vol. 4. Detroit: Charles Scribner's Sons, 2008. 465–467. Gale Virtual Reference Library. Web. 2 June 2014. He came up with the idea of homocentric spheres in order to explain the perceived inconsistent motions of the planets and to develop a uniform model for accurately calculating the movement of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hipparchus
Hipparchus (; , ; BC) was a Ancient Greek astronomy, Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equinoxes. Hipparchus was born in Nicaea, Bithynia, and probably died on the island of Rhodes, Greece. He is known to have been a working astronomer between 162 and 127 BC. Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of classical antiquity, antiquity. He was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. For this he certainly made use of the observations and perhaps the mathematical techniques accumulated over centuries by the Babylonians and by Meton of Athens (fifth century BC), Timocharis, Aristyllus, Aristarchus of Samos, and Eratosthenes, among others. He developed trigonometry and constructed trigonometric tables, and he solved se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eudoxus Of Cnidus
Eudoxus of Cnidus (; , ''Eúdoxos ho Knídios''; ) was an Ancient Greece, ancient Greek Ancient Greek astronomy, astronomer, Greek mathematics, mathematician, doctor, and lawmaker. He was a student of Archytas and Plato. All of his original works are lost, though some fragments are preserved in Hipparchus' ''Commentaries on the Phenomena of Aratus and Eudoxus''. ''Theodosius' Spherics, Spherics'' by Theodosius of Bithynia may be based on a work by Eudoxus. Life Eudoxus, son of Aeschines, was born and died in Cnidus (also transliterated Knidos), a city on the southwest coast of Anatolia. The years of Eudoxus' birth and death are not fully known but Diogenes Laertius, Diogenes Laërtius gave several biographical details, mentioned that Apollodorus of Athens, Apollodorus said he reached his wikt:acme#English, acme in the 103rd Olympiad (368–), and claimed he died in his 53rd year. From this 19th century mathematical historians reconstructed dates of 408–, but 20th century schola ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theodosius' Spherics
The ''Spherics'' (Ancient Greek, Greek: , ) is a three-volume treatise on spherical geometry written by the Greek mathematics, Hellenistic mathematician Theodosius of Bithynia in the 2nd or 1st century BC. Book I and the first half of Book II establish basic geometric constructions needed for spherical geometry using the tools of Euclidean geometry, Euclidean solid geometry, while the second half of Book II and Book III contain propositions relevant to astronomy as modeled by the celestial sphere. Primarily consisting of theorems which were known at least informally a couple centuries earlier, the ''Spherics'' was a foundational treatise for geometers and astronomers from its origin until the 19th century. It was continuously studied and copied in Greek manuscript for more than a millennium. It was translated into Arabic in the 9th century during the Islamic Golden Age, and thence translated into Neo Latin, Latin Latin translations of the 12th century, in 12th century Iberia, tho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theodosius Of Bithynia
Theodosius of Bithynia ( ; 2nd–1st century BC) was a Hellenistic astronomer and mathematician from Bithynia who wrote the '' Spherics'', a treatise about spherical geometry, as well as several other books on mathematics and astronomy, of which two survive, ''On Habitations'' and ''On Days and Nights''. Life Little is known about Theodosius' life. The ''Suda'' (10th-century Byzantine encyclopedia) mentioned him writing a commentary on Archimedes' ''Method'' (late 3rd century BC), and Strabo's ''Geographica'' mentioned mathematicians Hipparchus ( – ) and "Theodosius and his sons" as among the residents of Bithynia distinguished for their learning. Vitruvius (1st century BC) mentioned a sundial invented by Theodosius. Thus Theodosius lived sometime after Archimedes and before Vitruvius, likely contemporaneously with or after Hipparchus, probably sometime between 200 and 50 BC. Historically he was called Theodosius of Tripolis due to a confusing paragraph in the ''Suda'' which prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Small Circle
In spherical geometry, a spherical circle (often shortened to circle) is the locus of points on a sphere at constant spherical distance (the ''spherical radius'') from a given point on the sphere (the ''pole'' or ''spherical center''). It is a curve of constant geodesic curvature relative to the sphere, analogous to a line or circle in the Euclidean plane; the curves analogous to straight lines are called ''great circles'', and the curves analogous to planar circles are called small circles or lesser circles. If the sphere is embedded in three-dimensional Euclidean space, its circles are the intersections of the sphere with planes, and the great circles are intersections with planes passing through the center of the sphere. Fundamental concepts Intrinsic characterization A spherical circle with zero geodesic curvature is called a ''great circle'', and is a geodesic analogous to a straight line in the plane. A great circle separates the sphere into two equal '' hem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Great Circle
In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point. Discussion Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geometry are the natural analog of straight lines in Euclidean space. For any pair of distinct non- antipodal points on the sphere, there is a unique great circle passing through both. (Every great circle through any point also passes through its antipodal point, so there are infinitely many great circles through two antipodal points.) The shorter of the two great-circle arcs between two distinct points on the sphere is called the ''minor arc'', and is the shortest surface-path between them. Its arc length is the great-circle distance between the points (the intrinsic distance on a sphere), and is proportional to the measure of the central angle formed by the two points and the center of the sphere. A great circle is the largest ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Celestial Sphere
In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, which may be centered on Earth or the observer. If centered on the observer, half of the sphere would resemble a hemispherical screen over the observing location. The celestial sphere is a conceptual tool used in spherical astronomy to specify the position of an object in the sky without consideration of its linear distance from the observer. The celestial equator divides the celestial sphere into northern and southern hemispheres. Description Because astronomical objects are at such remote distances, casual observation of the sky offers no information on their actual distances. All celestial objects seem equally far away, as if fixed onto the inside of a sphere with a large but unknown radius, which appears to rotate westwa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
