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Book Of Lemmas
The ''Book of Lemmas'' or ''Book of Assumptions'' (Arabic ''Maʾkhūdhāt Mansūba ilā Arshimīdis'') is a book attributed to Archimedes by Thābit ibn Qurra, though the authorship of the book is questionable. It consists of fifteen propositions ( lemmas) on circles. History Translations The ''Book of Lemmas'' was first introduced in Arabic by Thābit ibn Qurra; he attributed the work to Archimedes. A translation from Arabic into Latin by John Greaves and revised by Samuel Foster (c. 1650) was published in 1659 a''Lemmata Archimedis'' Another Latin translation by Abraham Ecchellensis and edited by Giovanni A. Borelli was published in 1661 under the name ''Liber Assumptorum''. T. L. Heath translated Heiburg's Latin work into English in his ''The Works of Archimedes''. A more recently discovered manuscript copy of Thābit ibn Qurra's Arabic translation was translated into English by Emre Coşkun in 2018. Authorship The original authorship of the ''Book of Lemmas'' has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Works Of Archimedes Lemmas
Works may refer to: People * Caddy Works (1896–1982), American college sports coach * John D. Works (1847–1928), California senator and judge * Samuel Works (c. 1781–1868), New York politician Albums * ''Works'' (Pink Floyd album), a Pink Floyd album from 1983 * ''Works'', a Gary Burton album from 1972 * ''Works'', a Status Quo album from 1983 * ''Works'', a John Abercrombie album from 1991 * ''Works'', a Pat Metheny album from 1994 * ''Works'', an Alan Parson Project album from 2002 * ''Works Volume 1'', a 1977 Emerson, Lake & Palmer album * ''Works Volume 2'', a 1977 Emerson, Lake & Palmer album * '' The Works'', a 1984 Queen album Other uses *Good works, a topic in Christian theology * Microsoft Works, a collection of office productivity programs created by Microsoft * IBM Works, an office suite for the IBM OS/2 operating system * Mount Works, Victoria Land, Antarctica See also * The Works (other) * Work (other) Work may refer to: * Work ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Routledge
Routledge ( ) is a British multinational corporation, multinational publisher. It was founded in 1836 by George Routledge, and specialises in providing academic books, academic journals, journals and online resources in the fields of the humanities, behavioral science, behavioural science, education, law, and social science. The company publishes approximately 1,800 journals and 5,000 new books each year and their backlist encompasses over 140,000 titles. Routledge is claimed to be the largest global academic publisher within humanities and social sciences. In 1998, Routledge became a subdivision and Imprint (trade name), imprint of its former rival, Taylor & Francis, Taylor & Francis Group (T&F), as a result of a £90-million acquisition deal from Cinven, a venture capital group which had purchased it two years previously for £25 million. Following the merger of Informa and T&F in 2004, Routledge became a publishing unit and major imprint within the Informa "academic publishing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greek Mathematical Works
Ancient history is a time period from the beginning of writing and recorded human history through late antiquity. The span of recorded history is roughly 5,000 years, beginning with the development of Sumerian cuneiform script. Ancient history covers all continents inhabited by humans in the period 3000 BCAD 500, ending with the expansion of Islam in late antiquity. The three-age system periodises ancient history into the Stone Age, the Bronze Age, and the Iron Age, with recorded history generally considered to begin with the Bronze Age. The start and end of the three ages vary between world regions. In many regions the Bronze Age is generally considered to begin a few centuries prior to 3000 BC, while the end of the Iron Age varies from the early first millennium BC in some regions to the late first millennium AD in others. During the time period of ancient history, the world population was exponentially increasing due to the Neolithic Revolution, which was in full prog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Salt Cellar
A salt cellar (also called a salt, salt-box) is an article of tableware for holding and dispensing salt. In British English, the term can be used for what in North American English are called salt shakers. Salt cellars can be either lidded or open, and are found in a wide range of sizes, from large shared vessels to small individual dishes. Styles range from simple to ornate or whimsical, using materials including glass and ceramic, metals, ivory and wood, and plastic. Use of salt cellars is documented as early as ancient Rome. They continued to be used through the first half of the 20th century; however, usage began to decline with the introduction of free-flowing salt in 1911, and they have been almost entirely replaced by salt shakers. Salt cellars were an early collectible as pieces of silver, pewter, glass, etc. Soon after their role at the table was replaced by the shaker, salt cellars became a popular collectible in their own right. Etymology The word salt cellar is att ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Salinon Shaded
The salinon (meaning 'salt-cellar' in Greek) is a geometrical figure that consists of four semicircles. It was first introduced in the ''Book of Lemmas'', a work attributed to Archimedes. Construction Let ''A'', ''D'', ''E'', and ''B'' be four points on a line in the plane, in that order, with ''AD'' = ''EB''. Let ''O'' be the bisector of segment ''AB'' (and of ''DE''). Draw semicircles above line ''AB'' with diameters ''AB'', ''AD'', and ''EB'', and another semicircle below with diameter ''DE''. A salinon is the figure bounded by these four semicircles. Properties Area Archimedes introduced the salinon in his ''Book of Lemmas'' by applying Book II, Proposition 10 of Euclid's ''Elements''. Archimedes noted that "the area of the figure bounded by the circumferences of all the semicircles sequal to the area of the circle on CF as diameter." Namely, if r_1 is the radius of large enclosing semicircle, and r_2 is the radius of the small central semicircle, then the area of the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pappus Of Alexandria
Pappus of Alexandria (; ; AD) was a Greek mathematics, Greek mathematician of late antiquity known for his ''Synagoge'' (Συναγωγή) or ''Collection'' (), and for Pappus's hexagon theorem in projective geometry. Almost nothing is known about his life except for what can be found in his own writings, many of which are lost. Pappus apparently lived in Alexandria, where he worked as a Mathematics education, mathematics teacher to higher level students, one of whom was named Hermodorus.Pierre Dedron, J. Itard (1959) ''Mathematics And Mathematicians'', Vol. 1, p. 149 (trans. Judith V. Field) (Transworld Student Library, 1974) The ''Collection'', his best-known work, is a compendium of mathematics in eight volumes, the bulk of which survives. It covers a wide range of topics that were part of the ancient mathematics curriculum, including geometry, astronomy, and mechanics. Pappus was active in a period generally considered one of stagnation in mathematical studies, where, to s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pappus Chain
In geometry, the Pappus chain is a ring of circles between two tangent circles investigated by Pappus of Alexandria in the 3rd century AD. Construction The arbelos is defined by two circles, and , which are tangent at the point and where is enclosed by . Let the radii of these two circles be denoted as , respectively, and let their respective centers be the points . The Pappus chain consists of the circles in the shaded grey region, which are externally tangent to (the inner circle) and internally tangent to (the outer circle). Let the radius, diameter and center point of the th circle of the Pappus chain be denoted as , respectively. Properties Centers of the circles Ellipse All the centers of the circles in the Pappus chain are located on a common ellipse, for the following reason. The sum of the distances from the th circle of the Pappus chain to the two centers of the arbelos circles equals a constant \overline + \overline = (r_U + r_n) + (r_V - r_n) = r_U + r_V ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedes's Twin Circles
In geometry, the twin circles are two special circles associated with an arbelos. An arbelos is determined by three collinear points , , and , and is the curvilinear triangular region between the three semicircles that have , , and as their diameters. If the arbelos is partitioned into two smaller regions by a line segment through the middle point of , , and , perpendicular to line , then each of the two twin circles lies within one of these two regions, tangent to its two semicircular sides and to the splitting segment. These circles first appeared in the ''Book of Lemmas'', which showed (Proposition V) that the two circles are congruent. Thābit ibn Qurra, who translated this book into Arabic, attributed it to Greek mathematician Archimedes. Based on this claim the twin circles, and several other circles in the Arbelos congruent to them, have also been called Archimedes's circles. However, this attribution has been questioned by later scholarship. Construction Specifically, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semicircle
In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle. It is a circular arc that measures 180° (equivalently, radians, or a half-turn). It only has one line of symmetry (reflection symmetry). In non-technical usage, the term "semicircle" is sometimes used to refer to either a closed curve that also includes the diameter segment from one end of the arc to the other or to the half- disk, which is a two-dimensional geometric region that further includes all the interior points. By Thales' theorem, any triangle inscribed in a semicircle with a vertex at each of the endpoints of the semicircle and the third vertex elsewhere on the semicircle is a right triangle, with a right angle at the third vertex. All lines intersecting the semicircle perpendicularly are concurrent at the center of the circle containing the given semicircle. Arithmetic and geometric means A semicircle can be used to construct th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arbelos
In geometry, an arbelos is a plane region bounded by three semicircles with three apexes such that each corner of each semicircle is shared with one of the others (connected), all on the same side of a straight line (the ''baseline'') that contains their diameters. The earliest known reference to this figure is in Archimedes's ''Book of Lemmas'', where some of its mathematical properties are stated as Propositions 4 through 8. The word ''arbelos'' is Greek for 'shoemaker's knife'. The figure is closely related to the Pappus chain. Properties Two of the semicircles are necessarily concave, with arbitrary diameters and ; the third semicircle is Convex curve, convex, with diameter Let the diameters of the smaller semicircles be and ; then the diameter of the larger semircle is . Area Let be the intersection of the larger semicircle with the line perpendicular to at . Then the area (geometry), area of the arbelos is equal to the area of a circle with diameter . Proof: For ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometrical Figure
A shape is a graphical representation of an object's form or its external boundary, outline, or external surface. It is distinct from other object properties, such as color, texture, or material type. In geometry, ''shape'' excludes information about the object's position, size, orientation and chirality. A ''figure'' is a representation including both shape and size (as in, e.g., figure of the Earth). A plane shape or plane figure is constrained to lie on a ''plane'', in contrast to ''solid'' 3D shapes. A two-dimensional shape or two-dimensional figure (also: 2D shape or 2D figure) may lie on a more general curved ''surface'' (a two-dimensional space). Classification of simple shapes Some simple shapes can be put into broad categories. For instance, polygons are classified according to their number of edges as triangles, quadrilaterals, pentagons, etc. Each of these is divided into smaller categories; triangles can be equilateral, isosceles, obtuse, acute, scalene, etc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cut-the-Knot
Alexander Bogomolny (January 4, 1948 July 7, 2018) was a Soviet Union, Soviet-born Israeli Americans, Israeli-American mathematician. He was Professor Emeritus of Mathematics at the University of Iowa, and formerly research fellow at the Moscow Institute of Electronics and Mathematics, senior instructor at Hebrew University and software consultant at Ben Gurion University. He wrote extensively about arithmetic, probability, algebra, geometry, trigonometry and mathematical games. He was known for his contribution to heuristics and mathematics education, creating and maintaining the mathematically themed educational website ''Cut-the-Knot'' for the Mathematical Association of America (MAA) Online. He was a pioneer in mathematical education on the internet, having started ''Cut-the-Knot'' in October 1996. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
