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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. In 1661, the Arabic manuscript was translated into Latin by Abraham Ecchellensis and edited by Giovanni A. Borelli. The Latin version was published 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 been in question because in proposition four, the book refers to Archimedes in third person; however ... [...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 * 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 * 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 (human activity), intentional activity people perform to support themselves, others, or the communit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cut-the-Knot
Alexander Bogomolny (January 4, 1948 July 7, 2018) was a Soviet-born 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.Interview with Alexander ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Works By Archimedes
Works may refer to: People * Caddy Works (1896–1982), American college sports coach * 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 * 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 (human activity), intentional activity people perform to support themselves, others, or the community * ... [...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 to as far as late antiquity. The span of recorded history is roughly 5,000 years, beginning with the Sumerian cuneiform script. Ancient history covers all continents inhabited by humans in the period 3000 BCAD 500. The three-age system periodizes 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 varies 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 already exponentially increasing due to the Neolithic Revolution, which was in full progress. While in 10,000 BC, the world population stood a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Salt Cellar
A salt cellar (also called a salt, salt-box and a salt pig) is an article of tableware for holding and dispensing salt. In British English, the term is normally 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 classical 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 at last 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. Etymo ... [...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 sa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pappus Of Alexandria
Pappus of Alexandria (; grc-gre, Πάππος ὁ Ἀλεξανδρεύς; AD) was one of the last great Greek mathematicians of antiquity known for his ''Synagoge'' (Συναγωγή) or ''Collection'' (), and for Pappus's hexagon theorem in projective geometry. Nothing is known of his life, other than what can be found in his own writings: that he had a son named Hermodorus, and was a teacher in Alexandria.Pierre Dedron, J. Itard (1959) ''Mathematics And Mathematicians'', Vol. 1, p. 149 (trans. Judith V. Field) (Transworld Student Library, 1974) ''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, including geometry, recreational mathematics, doubling the cube, polygons and polyhedra. Context Pappus was active in the 4th century AD. In a period of general stagnation in mathematical studies, he stands out as a remarkable exception. "How far he was above his contemporaries, how l ... [...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, ''C''U and ''C''V, which are tangent at the point A and where ''C''U is enclosed by ''C''V. Let the radii of these two circles be denoted as ''r''U and ''r''V, respectively, and let their respective centers be the points U and V. The Pappus chain consists of the circles in the shaded grey region, which are externally tangent to ''C''U (the inner circle) and internally tangent to ''C''V (the outer circle). Let the radius, diameter and center point of the ''n''th circle of the Pappus chain be denoted as ''r''''n'', ''d''''n'' and P''n'', 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 ''n''th circle of the Pappus chain to the two centers U ... [...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. The full arc of a semicircle always measures 180° (equivalently, radians, or a half-turn). It has only one line of symmetry ( reflection symmetry). In non-technical usage, the term "semicircle" is sometimes used to refer to a half- disk, which is a two-dimensional geometric shape that also includes the diameter segment from one end of the arc to the other as well as 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. Uses A semicircle can be used to construct the arithmetic and geometric means of two lengths using strai ... [...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 Area The area (geometry), area of the arbelos is equal to the area of a circle with diameter . Proof: For the proof, reflect the arbelos over the line through the points and , and observe that twice the area of the arbelos is what remains when the areas of the two smaller circles (with diameters , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometrical Figure
A shape or figure is a graphical representation of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture, or material type. 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 non-Euclidean 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. while quadrilaterals can be rectangles, rhombi, trapezoids, squares, etc. Other common shapes are points, lines, planes, and conic sections such as ellipses, circles, and parabolas. Among the mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
