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Diocles: more books (21)

Essai Sur les Propriétés de la Nouvelle Cissoïde,: Et sur les rapports de cette courbe, tant avec la cissoïde de dioclès, qu'avec un grand nombre d'autres courbes (French Edition) by Rallier, 2009-04-27
Diocles of Carystus: A Collection of the Fragments With Translation and Commentary (Studies in Ancient Medicine) by Philip J. Van Der Eijk, 2001-08-01
The Number One A-Z Family Health Adviser by Diocles, 1996-04
Home Medical Encyclopaedia (Paperfronts) by Diocles, 1989-11-14
Lusitania: Viriathus, Lusitanian Language, Lusitanian War, Audax, Ditalcus and Minurus, Gaius Appuleius Diocles, Cornelius Bocchus
The home medical encyclopedia (Paperfront series) by Diocles, 1965
Cissoid of Diocles
Diocles of Carystus: An entry from Gale's <i>Science and Its Times</i> by Evelyn B. Kelly, 2001
Date de Naissance Inconnue (Ve Siècle Av. J.-C.): Hippocrate, Sophocle, Empédocle, Marcus Furius Camillus, Alcibiade, Dioclès, Mélissos (French Edition)
Ancient Euboeans: Isaeus, Lycophron, Callias of Chalcis, Euphraeus, Diocles of Carystus, Euphorion of Chalcis, Charidemus
Diocles: An entry from Gale's <i>Science and Its Times</i> by Judson Knight, 2001
Essai Sur Les Propriétés De La Nouvelle Cissoïde: Et Sur Les Rapports De Cette Courbe, Tant Avec La Cissoïde De Dioclès, Qu'Avec Un Grand Nombre D'Autres Courbes (French Edition) by Rallier, 2009-12-31
Date de Décès Inconnue (Ive Siècle Av. J.-C.): Hippocrate, Thucydide, Dioclès, Publius Cornelius Rufinus, Platon le Comique, Cléarque (French Edition)
Meneur: Aurige de Delphes, Cocher, Postillon, Ratuména, Crescens, Gaius Appuleius Diocles, Publius Aelius Gutta Calpurnianus (French Edition)

lists with details

Diocles -- Encyclopædia Britannica
MLA style " diocles." Encyclopædia Britannica. 2004. Encyclopædia Britannica Premium Service. APA style diocles. Encyclopædia Britannica. Retrieved April 25, 2004, from
http://www.britannica.com/eb/article?eu=31017
No. 837: Diocles
diocles' parabolic mirror in an old Arabic book make our civilization run, and the people whose ingenuity created them. Who was diocles? We don't really know to tell us that it was diocles
http://www.uh.edu/engines/epi837.htm

Extractions: by John H. Lienhard Click here for audio of Episode 837. Today, we focus the rays of the sun. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them. W ho was Diocles? We don't really know. All we have is a text he wrote over 2000 years ago. It's not even in his own tongue. It was written in AD 1462 by a careless scribe who left only spaces where figures should've gone. But it's enough to tell us that it was Diocles who invented the parabolic mirror. Who was Diocles? Historian G.J. Toomer picks through this skimpy legacy this ancient text, titled On Burning Mirrors . Most of what we knew of Diocles came from reference to his work by a noted 6th-century mathematician. Now we finally read this copy of his book, penned 1600 years after the fact. Toomer does his historical detective work. He decides that Diocles flourished in Greece just after 200 BC. He was a mathematician a geometer. Toomer takes us through the text, recreating the figures. We read Diocles' opening: The burning-mirror surface submitted to you is the surface bounding the figure produced by a section of a ... cone ... revolved about [its axis].
ComPilots.com - Aviation Portal
Last 10 Forum Topics by diocles Find all posts by diocles Last 10 News Submissions sent by diocles Last 10 Aerodrome Modifications sent by diocles
http://www.compilots.com/userinfo-diocles.html
Diocles
diocles. Born about 240 BC in Carystus (now Káristos), Euboea (now Evvoia),Greece Died about 180 BC. diocles was a contemporary of Apollonius.
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Diocles.html

Extractions: Diocles was a contemporary of Apollonius . Practically all that was knew about him until recently was through fragments of his work preserved by Eutocius in his commentary on the famous text by Archimedes On the sphere and the cylinder. In this work we are told that Diocles studied the cissoid as part of an attempt to duplicate the cube . It is also recorded that he studied the problem of Archimedes to cut a sphere by a plane in such a way that the volumes of the segments shall have a given ratio. The extracts quoted by Eutocius from Diocles' On burning mirrors showed that he was the first to prove the focal property of a parabolic mirror. Although Diocles' text was largely ignored by later Greeks, it had considerable influence on the Arab mathematicians, in particular on al-Haytham . Latin translations from about 1200 of the writings of al-Haytham brought the properties of parabolic mirrors discovered by Diocles to European mathematicians. Recently, however, some more information about Diocles' life has come to us from the Arabic translation of Diocles'
Diocles
Biography of diocles (240BC180BC) Next. Main index. diocles was a contemporary of Apollonius the cylinder. In this work we are told that diocles studied the cissoid as part of an attempt to
http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Diocles.html

Extractions: Diocles was a contemporary of Apollonius . Practically all that was knew about him until recently was through fragments of his work preserved by Eutocius in his commentary on the famous text by Archimedes On the sphere and the cylinder. In this work we are told that Diocles studied the cissoid as part of an attempt to duplicate the cube . It is also recorded that he studied the problem of Archimedes to cut a sphere by a plane in such a way that the volumes of the segments shall have a given ratio. The extracts quoted by Eutocius from Diocles' On burning mirrors showed that he was the first to prove the focal property of a parabolic mirror. Although Diocles' text was largely ignored by later Greeks, it had considerable influence on the Arab mathematicians, in particular on al-Haytham . Latin translations from about 1200 of the writings of al-Haytham brought the properties of parabolic mirrors discovered by Diocles to European mathematicians. Recently, however, some more information about Diocles' life has come to us from the Arabic translation of Diocles'
Cissoid
Cissoid of diocles. Cartesian equation y 2 = x 3 /(2a x). The Cissoid of dioclesis the roulette of the vertex of a parabola rolling on an equal parabola.
http://www-gap.dcs.st-and.ac.uk/~history/Curves/Cissoid.html

Extractions: If your browser can handle JAVA code, click HERE to experiment interactively with this curve and its associated curves. This curve (meaning 'ivy-shaped') was invented by Diocles in about 180 BC in connection with his attempt to duplicate the cube by geometrical methods. The name first appears in the work of Geminus about 100 years later. Fermat and Roberval constructed the tangent in 1634. Huygens and Wallis found, in 1658, that the area between the curve and its asymptote was 3 a . From a given point there are either one or three tangents to the cissoid. The Cissoid of Diocles is the roulette of the vertex of a parabola rolling on an equal parabola. Newton gave a method of drawing the Cissoid of Diocles using two line segments of equal length at right angles. If they are moved so that one line always passes through a fixed point and the end of the other line segment slides along a straight line then the mid-point of the sliding line segment traces out a Cissoid of Diocles Diocles was a contemporary of Nicomedes . He studied the cissoid in his attempt to solve the problem of finding the length of the side of a cube having volume twice that of a given cube. He also studied the problem of Archimedes to cut a sphere by a plane in such a way that the volumes of the segments shall have a given ratio.
Diocles Search
diocles search Book Search. diocles. Toys. Books. Audio by the name of diocles. Modified text originally written by Andrew Lang.
http://www.geocities.com/namebookstwo/diocles.html
Xah: Special Plane Curves: Cissoid Of Diocles
Table of Contents. Cissoid of diocles. Parallels of a cissoid of diocles. diocles(~250~100 BC) invented this curve to solve the doubling of the cube problem.
http://www.xahlee.org/SpecialPlaneCurves_dir/CissoidOfDiocles_dir/cissoidOfDiocl

Extractions: Table of Contents Parallels of a cissoid of Diocles Mathematica Notebook for This Page History Description Formulas ... Related Web Sites Diocles (~250-~100 BC) invented this curve to solve the doubling of the cube problem. (aka the Delian problem) The name cissoid (ivy-shaped) came from the shape of the curve. Later the method used to generate this curve is generalized, and we call curves generated this way as cissoids From Thomas L. Heath's Euclid's Elements translation (1925) (comments on definition 2, book one): This curve is assumed to be the same as that by means of which, according to Eutocius, Diocles in his book On burning-glasses solved the problem of doubling the cube. From Robert C. Yates' Curves and their properties (1952): As early as 1689, J. C. Sturm, in his Mathesis Enucleata, gave a mechanical device for the constructions of the cissoid of Diocles. From E.H.Lockwood A book of Curves (1961): The name cissoid ('Ivy-shaped') is mentioned by Geminus in the first century B.C., that is, about a century after the death of the inventor Diocles. In the commentaries on the work by Archimedes On the Sphere and the Cylinder , the curve is referred to as Diocles' contribution to the classic problem of doubling the cube. ... Fermat and Roberval constructed the tangent (1634); Huygens and Wallis found the area (1658); while Newton gives it as an example, in his
Cissoid Of Diocles
Cissoid of diocles. diocles showed that if in addition you allow the useof the cissoid, then one can construct . Here is how it works.
http://www.geocities.com/famancin/cissoid_diocles.html

Extractions: Cissoid of Diocles Here is the definition of cissoid of two curves. Cissoid[ Let O be a fixed point and let L be a line through O intersecting the curves C and C at Q and Q . The locus of points P and P on L such that OP = OQ - OQ = Q Q is the cissoid of C and C with respect to O. The cissoid of Diocles is the cissoid of a circle and a tangent line, with respect to a fixed point O on the circumference opposite the point of tangency A. The screenshot below shows the cissoid drawn using Jeometry Let O be the origin and x = a be the line tangent to the circle. Let Ô be the angle BÔA in the picture above. Considering the right triangles OBA and CAO, we have OP OC OB a secÔ - a cosÔ a sinÔ tanÔ Hence the polar equation of the cissoid is r = a sinÔ tanÔ Then the Cartesian equation follows immediately by substitution, y (a - x) = x This is the same equation we found when considering the pedal of a parabola with respect to its vertex (let a = - We would like to find a parametric rapresentation of the curve. To do that, we note that the cissoid of Diocles is a cubic curve with a cusp in the origin, so we can find a rational parametrization by intersecting the cissoid with the line
Cissoid
CISSOID OF diocles. include graphics.h include math.h main() {int gd=DETECT,gm,x,y,i,j; float a; initgraph( gd, gm, c\\tc\\bgi
http://www.geocities.com/ashwinkrec/cissoid.htm
Perseus Lookup Tool
Collections Classics ·. Papyri ·. Renaissance ·. London ·. California ·. Upper Midwest ·. Chesapeake ·. Boyle ·. Tufts History. Configure display ·. Help ·. Tools ·. Copyright ·. FAQ ·. Publications
http://www.perseus.tufts.edu/cgi-bin/vor?type=phrase&alts=0&group=typeca
Cissoid Of Diocles -- From MathWorld
Cissoid of diocles. A cubic curve invented by diocles in about 180 BC in connectionwith his attempt to duplicate the cube by geometrical methods.
http://mathworld.wolfram.com/CissoidofDiocles.html

Extractions: A cubic curve invented by Diocles in about 180 BC in connection with his attempt to duplicate the cube by geometrical methods. The name "cissoid" first appears in the work of Geminus about 100 years later. Fermat and Roberval constructed the tangent in 1634. Huygens and Wallis found, in 1658, that the area between the curve and its asymptote was (MacTutor Archive). From a given point there are either one or three tangents to the cissoid. Given an origin O and a point P on the curve, let S be the point where the extension of the line OP intersects the line and R be the intersection of the circle of radius a and center with the extension of OP . Then the cissoid of Diocles is the curve which satisfies OP = RS The cissoid of Diocles is the roulette of a parabola vertex of a parabola rolling on an equal parabola Newton gave a method of drawing the cissoid of Diocles using two line segments of equal length at right angles . If they are moved so that one line always passes through a fixed point and the end of the other line segment slides along a straight line, then the
Cissoid Of Diocles From MathWorld
Cissoid of diocles from MathWorld A cubic curve invented by diocles in about 180 BC in connection with his attempt to duplicate the cube by geometrical methods. The name "cissoid" first appears
http://rdre1.inktomi.com/click?u=http://mathworld.wolfram.com/CissoidofDiocles.h
Cissoid Of Diocles Catacaustic -- From MathWorld
Cissoid of diocles Catacaustic. (6). is the equation of a cardioid, the catacausticof the cissoid of diocles for radiant point at is a cardioid with a = 2.
http://mathworld.wolfram.com/CissoidofDioclesCatacaustic.html
Cissoid Of Diocles
Cissoid of diocles. Here is the definition of cissoid of two curves. The cissoid of diocles is the cissoid of a circle and a tangent line, with respect to
http://www.geocities.com/CapeCanaveral/Hall/3131/cissoid_diocles.html

Extractions: Cissoid of Diocles Here is the definition of cissoid of two curves. Cissoid[ Let O be a fixed point and let L be a line through O intersecting the curves C and C at Q and Q . The locus of points P and P on L such that OP = OQ - OQ = Q Q is the cissoid of C and C with respect to O. The cissoid of Diocles is the cissoid of a circle and a tangent line, with respect to a fixed point O on the circumference opposite the point of tangency A. The screenshot below shows the cissoid drawn using Jeometry Let O be the origin and x = a be the line tangent to the circle. Let Ô be the angle BÔA in the picture above. Considering the right triangles OBA and CAO, we have OP OC OB a secÔ - a cosÔ a sinÔ tanÔ Hence the polar equation of the cissoid is r = a sinÔ tanÔ Then the Cartesian equation follows immediately by substitution, y (a - x) = x This is the same equation we found when considering the pedal of a parabola with respect to its vertex (let a = - We would like to find a parametric rapresentation of the curve. To do that, we note that the cissoid of Diocles is a cubic curve with a cusp in the origin, so we can find a rational parametrization by intersecting the cissoid with the line
Cissoid Of Diocles
The Cissoid of diocles. diocles is one of many mathematicians who have attemptedto construct a cube whose volume is exactly twice that of a given cube.
http://curvebank.calstatela.edu/diocles/diocles.htm

Extractions: A number of legends surround this construction challenge. The good citizens of Athens were being devastated by a plague. History records that in 430 BC they sought advice from the oracle at Delos on how to rid their community of this pestilence. The oracle replied that the altar of Apollo, which was in the form of a cube, should be doubled. Thoughtless builders merely doubled the edges of the cube. Unfortunately the volume of the altar increased by a factor of 8. The oracle insisted the gods had been angered. As if to confirm this reprimand, the plague grew worse. Other delegations consulted Plato. When informed of the oracle's admonition, Plato told the citizens "the god has given this oracle, not because he wanted an altar of double the size, but because he wished in setting this task before them, to reproach the Greeks for their neglect of mathematics and their contempt of geometry."
Xah: Special Plane Curves: Cissoid Of Diocles
diocles (~250~100 BC) invented this curve to solve the doubling of the cube problem a century after the death of the inventor diocles. In the commentaries on the work
http://xahlee.org/SpecialPlaneCurves_dir/CissoidOfDiocles_dir/cissoidOfDiocles.h

Extractions: Table of Contents Parallels of a cissoid of Diocles Mathematica Notebook for This Page History Description Formulas ... Related Web Sites Diocles (~250-~100 BC) invented this curve to solve the doubling of the cube problem. (aka the Delian problem) The name cissoid (ivy-shaped) came from the shape of the curve. Later the method used to generate this curve is generalized, and we call curves generated this way as cissoids From Thomas L. Heath's Euclid's Elements translation (1925) (comments on definition 2, book one): This curve is assumed to be the same as that by means of which, according to Eutocius, Diocles in his book On burning-glasses solved the problem of doubling the cube. From Robert C. Yates' Curves and their properties (1952): As early as 1689, J. C. Sturm, in his Mathesis Enucleata, gave a mechanical device for the constructions of the cissoid of Diocles. From E.H.Lockwood A book of Curves (1961): The name cissoid ('Ivy-shaped') is mentioned by Geminus in the first century B.C., that is, about a century after the death of the inventor Diocles. In the commentaries on the work by Archimedes On the Sphere and the Cylinder , the curve is referred to as Diocles' contribution to the classic problem of doubling the cube. ... Fermat and Roberval constructed the tangent (1634); Huygens and Wallis found the area (1658); while Newton gives it as an example, in his
Cissoid Of Diocles Inverse Curve From MathWorld
Cissoid of diocles Inverse Curve from MathWorld If the cusp of the cissoid of diocles is taken as the inversion center, then the cissoid inverts to a parabola. http//mathworld.wolfram.com/
http://rdre1.inktomi.com/click?u=http://mathworld.wolfram.com/CissoidofDioclesIn
Diocles
diocles. In Greek mythology, diocles was one of the first priests of Demeterand one of the first to learn the secrets of the Eleusinian mysteries.
http://www.fact-index.com/d/di/diocles.html
Cisoide De Diocles
Translate this page Cisoide de diocles. (ver dibujo). La ecuación genérica de la cisoidede diocles en coordenadas cartesianas es y 2 = x 3 /(a -x).
http://www.terra.es/personal/jftjft/Geometria/Diferencial/Curvas/Enelplano/Cisoi

Extractions: Fecha de última actualización: 04-12-00 La cisoide es el lugar geométrico de los puntos M, tal que OM = PQ. (ver dibujo) La ecuación genérica de la cisoide de Diocles en coordenadas cartesianas es: y = x /(a -x) La ecuación en coordenadas polares es: r = a sen q /cos q La ecuación genérica de la cisoide de Diocles en ecuaciones paramétricas es: x = a sen q y = a sen q /cos q La asíntota es: x = a El área entre la curva y la asíntota es: A = 3/4 p a Dibuja la curva. En la página http://www-groups.dcs.st-and.ac.uk/~history/Curves/Curves.html encontrarás todo sobre las curvas. Principal

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