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	Cissoid of Diocles - Wikipedia, the free encyclopedia
		The cissoid of Diocles is an unbounded plane curve with a single cusp, which is symmetric about the line of tangency of the cusp, and whose pair of symmetrical branches both approach the same asymptote (but in opposite directions) as a point moving along the cissoid moves farther away from the cusp.
		Diocles' solution is correct, except that the solution involves an intersection of a line with a construction of a cissoid of Diocles, which cannot be accomplished by means of the simple but strict Greek rules of compass and straightedge construction.
		The reason is that the cissoid of Diocles cannot be constructed perfectly, at least not with compass and straightedge.
	en.wikipedia.org /wiki/Cissoid_of_Diocles (2012 words)

	Wikipedia: Diocletian
		Diocletian (born Diocles) Gaius Aurelius Valerius Diocletian (245-313) was Roman Emperor from November 20, 284 to May 1, 305.
		An Illyrian of low birth, Diocles rose through the ranks to the consulship.
		He was chosen by the Army in 284 to replace Numerian and after the assassination of Carinus became sole ruler of the Roman Empire.
	www.factbook.org /wikipedia/en/d/di/diocletian.html (383 words)

	No. 837: Diocles
		Most of what we knew of Diocles came from reference to his work by a noted 6th-century mathematician.
		Diocles began with work Archimedes did a century before him.
		Although Diocles makes no such claim, you and I have heard the legend that Archimedes used burning mirrors to set the Roman fleet afire as it invaded Syracuse.
	www.uh.edu /engines/epi837.htm (478 words)

	The Charioteer Diocles
		It is recorded in the Record that Aurelius Teres was the first of his faction to win 1011 victories, of which he won in one year [....but Diocles in that] year in which he won 100 races, won 103 times, and in races involving one chariot from each faction, he won 83 times.
		It was noted with admiration by everyone that in one year, with a lead-horse who was not a regular part of his team, with Cotynus and Pompeianus as the two horses on the yoke, he won 99 races, in one race for 60,000 HS, in four for 50,000, one for 40,000, two for 30,000.
		Diocles was a victor with Pompeianus 152 times, and won 50,000 HS 10 times, 60,000 HS once.
	www.umich.edu /~classics/programs/class/cc/372/sibyl/db/C304.html (879 words)

	Diocles (Site not responding. Last check: 2007-10-08)
		Although Diocles' text was largely ignored by later Greeks, it had considerable influence on the Arab mathematicians, in particular on al-Haytham.
		No writing of Diocles was known to Heath in 1921 when he wrote [3], but Toomer translated and published the newly found Arabic translation of the lost treatise On burning mirrors by Diocles in 1976.
		In On burning mirrors Diocles also studies the problem of finding a mirror such that the envelope of reflected rays is a given caustic curve or of finding a mirror such that the focus traces a given curve as the Sun moves across the sky.
	www-history.mcs.st-andrews.ac.uk /history/Mathematicians/Diocles.html (1020 words)

	Dictionary of Greek and Roman Biography and Mythology, page 1010 (v. 1) (Site not responding. Last check: 2007-10-08)
		We know nothing of its details, but it is praised by Diodorus for its conciseness of style, and the care with which it distinguished different offences and assigned to each its peculiar penalty.
		The next year he commanded the forces sent by Syracuse and the other cities of Sicily to the relief of Himera, besieged by Hannibal, the son of Gisco.
		The latter Diocles was still alive in the time of Aristoxenus (Diog.
	ancientlibrary.com /smith-bio/1016.html (948 words)

	Maybe this Explains the Economic Cycle... best Cissoid of Diocles (Site not responding. Last check: 2007-10-08)
		The cissoid of Diocles is the cissoid of a circle and a tangent line, with respect...
		Cissoid of Diocles Catacaustic -- from MathWorld Cissoid of Diocles Catacaustic -- from MathWorld For the parametric representation x = {2t^2\over 1+t^2} y = {2t^3\over 1+t^2}, the catacaustic of this curve from the radiant point (8a,0) is...
		The cissoid of Diocles is a special case of the generalized cissoid, where line...
	ascot.pl /th/Fourier3/Cissoid-of-Diocles.htm (610 words)

	Cissoid (Site not responding. Last check: 2007-10-08)
		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 Cissoid of Diocles is the roulette of the vertex of a parabola rolling on an equal parabola.
		It is in commentaries on Archimedes' On the sphere and the cylinder that the cissoid appears and is attributed to Diocles.
	www-groups.dcs.st-and.ac.uk /~history/Curves/Cissoid.html (369 words)

	Eingang zum Volltext
		The aim of this study was (1) to describe diversity, density, distribution and host range of the phasmid community (Phasmatodea) of a moist neotropical forest in Panamá, and (2) to experimentally assess bottom-up and top-down factors that may regulate populations of the phasmid Metriophasma diocles.
		In M. diocles, oviposition may not be linked to nymph performance, because the evolutionary prediction of a relation between female adult preference and nymph performance was missing.
		In conclusion, I suggest that predation pressure with its direct effects on nymph survival may be a stronger factor regulating M. diocles populations, compared to direct and indirect effects of host plant quality, particularly because slow growth and off-host migration both may feed back into an increase of predation related mortality.
	kluedo.ub.uni-kl.de /frontdoor.php?source_opus=1753 (471 words)

	Cissoid of Diocles (Site not responding. Last check: 2007-10-08)
		Diocles is one of many mathematicians who have attempted to construct a cube whose volume is exactly twice that of a given cube.
		The curve invented by Diocles in about 180 BC later appears in the works of Fermat, Roberval, Huygens, Wallis, Newton, and others.
		Diocles investigated the properties of the focal point of a parabola in On Burning Mirrors.
	curvebank.calstatela.edu /diocles/diocles.htm (442 words)

	[No title]
		After that unfortunate scene in Diocles' room (friggen bards indeed), Xena slapped her famous 'pinch' on the old man to make him go back to sleep (poor soul didn't even know what hit him), and then herded her posse out of his room and into hers.
		She was Diocles' neighbor of eighty years, and something that she said made Xena stop and remember...
		Time to straighten things out with Diocles, and then she'll be able to focus completely on Marlon — not that she was worried; she'd seen Joxer's radish stew take down entire armies.
	thebookcase.org /xwp/text/lprecious.txt (10172 words)

	cissoid
		The name "cissoid," which means "ivy-shaped," first appears in the work of Geminus in the first century B.C. A special case of this curve, now known as the cissoid of Diocles, was first explored by Diocles in his attempt to the solve the classical problem of duplicating the cube.
		The cissoid of Diocles is traced out by the vertex of a parabola as it rolls, without slipping, on a second parabola of the same size.
		Interestingly, Diocles investigated the properties of the focal point of a parabola in On Burning Mirrors (a similar title appears in the works of Archimedes).
	www.daviddarling.info /encyclopedia/C/cissoid.html (284 words)

	Roman Emperors - DIR Numerian
		The premature discovery of the body led to a military assembly in which the commander of the imperial bodyguard, Valerius Diocles accused Aper of having encompassed Numerian's death.
		Diocles then vindicated his claim by running Aper through with his sword.
		The assembled troops took the hint and proclaimed Diocles emperor.
	www.roman-emperors.org /numerian.htm (696 words)

	[No title]
		It looked that he might have had a chance to catch him but not anymore.” In the meanwhile, Diocles and the two remaining quadrigae were still going at it.
		Despite the death of one of the competitors and the serious injury of two others, Diocles was able to keep his cool and win the race.
		However, when Diocles wasn’t participating in one of his three races that day, they were busy watching other things, like pulchrae feminae and some of the crazy drunks.
	www.bitsofhistory.com /ace/Spring_03_essays/School_15_John.doc (1227 words)

	Cissoid of Diocles
		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
		Around 180 B.C., Diocles used this curve to solve the problem of the duplication of the cube, i.e.
		Diocles showed that if in addition you allow the use of the cissoid, then one can construct
	www.geocities.com /CapeCanaveral/Hall/3131/cissoid_diocles.html (237 words)

	Light
		Most of what we know of Diocles comes from reference to this very work by a noted sixth-century mathematician.
		Diocles began by talking about Archimedes's work a century earlier -- with the legend of burning mirrors and the Roman fleet.
		Before he gets down to geometrical analysis, Diocles takes a moment to talk about the practical use of his theory.
	www.uh.edu /engines/astron2.htm (2968 words)

	Greek sources II (Site not responding. Last check: 2007-10-08)
		In the paper La cissoid et Diocles written by Paul Tannery, which was certainly known to Heath, it was noted that the reference to Apollonius in Eutocius's commentary on Archimedes' On the Sphere and Cylinder II must be an addition by Eutocius, but Heath clearly must have felt that Paul Tannery was wrong.
		If indeed Diocles lived a century or more after Apollonius, as Heath "proves", then he would be very familiar with Apollonius's Conics and so his own work on conic sections would have to be evaluated in that light.
		When we asked how the dates of Apollonius and Diocles fitted we were thinking of those of Apollonius as being known while those of Diocles being less well known.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Greek_sources_2.html (2423 words)

	"Precious" by Lexxie
		It took a little while, but finally she got Diocles to calm down and soon, his eyes were once more closed and he was snoring.
		Behind Xena and Ares, Diocles had sat bolt upright when he heard the outburst, and his jaw hung open when he saw his 'wife' in the arms of that walking advertisement for sinfulness (down girl).
		With strong, sure strides, Xena made her way to Diocles' door followed by the two men and reached for the knob and pushed the door open.
	thebookcase.org /xwp/fxwplprecious.html (10202 words)

	Diocles of Carystus. Volume 1, Text and Translation (Site not responding. Last check: 2007-10-08)
		Diocles of Carystus (4th century BCE), also known as "the younger Hippocrates", was one of the most prominent medical authorities in antiquity.
		He wrote extensively on a wide range of areas such as anatomy, physiology, pathology, therapeutics, embryology, gynaecology, dietetics, foods and poisons.
		The study of Diocles' ideas has long been hampered by the absence of a reliable collection of the remaining evidence.
	www.brill.nl /product.asp?ID=870 (255 words)

	lucian-eunuch.htm
		The close of the trial, however, took a new turn; Diocles, discontinuing the advertisement of his own merits, passed over to Bagoas and made a great effort to show up his private life, and Bagoas met this attack by exploring the history of Diocles in like manner.
		But if that person himself were alive and advanced similar claims, Diocles would (he said) have excluded him too, undismayed by his reputation among the common sort; and he repeated a number of humorous remarks made to the man by Stoics and Cynics regarding his physical imperfection.
		That was what the judges dwelt upon, and the point thenceforward at issue was whether the seal of approval should be set upon a eunuch who was proposing himself for a career in philosophy and requesting that the governance of boys be committed to him.
	www.well.com /user/aquarius/lucian-eunuch.htm (1495 words)

	Hemisphere Differences (Site not responding. Last check: 2007-10-08)
		This is how a 12th-century Latin codex describes the views of Diocles of Carystus, a famous Athenian physician from the 4th century B.C.:
		He says that phrenitis (madness, frenzy) arises from an inflammation of the heart and an obstruction of the blood or innate heat, from which the brain derives sentience and intellect.
		Before Diocles, Alcmaeon and Empedocles had already distinguished between sentience and intellect; moreover, it may already have been surmised in his time that the hemispheres are different in that each one only controls the opposite half of the body.
	www.tbm.tudelft.nl /webstaf/gertjanl/bbs1985.html (675 words)

	Cissoid de Diocles (Site not responding. Last check: 2007-10-08)
		La solución de Diocles está correcta, excepto que la solución implica una intersección de una línea con una construcción de un cissoid de Diocles, que no se puede lograr por medio de las reglas griegas simples sino terminantes de la construcción del compás y de la regla.
		Para construir el cissoid de Diocles, uno construiría un número finito de sus puntos individuales, entonces conecta todos estos puntos para formar una curva.
		Uno podría también construir un cissoid de Diocles por medio de una herramienta mecánica diseñada especialmente para ese propósito, pero éste viola la regla solamente de usar el compás y la regla.
	www.yotor.net /wiki/es/ci/Cissoid%20de%20Diocles.htm (2107 words)

	cissoid
		Given a circle C with diameter OA and a tangent l through A. Now, draw lines m through O, cutting circle C in point Q, line l in point R. Then the cissoid is the set of points P for which OP = QR.
		Because of Diocles' previous work on the curve his name has been added: cissoid of Diocles.
		The cissoid of Diocles is a special case of the generalized cissoid, where line l and circle C have been substituted by arbitrary curves C1 and C2.
	www.2dcurves.com /cubic/cubicc.html (281 words)

	Search Tuna Report for Diocletian (Site not responding. Last check: 2007-10-08)
		Diocletian Diocles rose through the ranks of the military and achieved high position....
		Emperor Diocletian Diocles rose through the ranks of the military and achieved high position....
		Roman Emperors - DIR Diocletian He was of very humble birth, and was originally named Diocles....
	searchtuna.com /ftlive/3397.html (2751 words)

	Amazon.de: English Books: Diocles of Carystus: A Collection of the Fragments With Translation and Commentary: 2 ... (Site not responding. Last check: 2007-10-08)
		Diocles of Carystus: A Collection of the Fragments With Translation and Commentary: 2 (Studies in Ancient Medicine)
		Diocles of Carystus (4th Century BC), also known as the "younger Hippocrates", was one of the most prominent medical authorities in antiquity.
		Zum Seitenanfang : Diocles of Carystus: A Collection of the Fragments With Translation and Commentary: 2 (Studies in Ancient Medicine)
	www.amazon.de /exec/obidos/ASIN/9004120122/geldverdie053-21 (318 words)

	Table of contents for Library of Congress control number 2004056141 (Site not responding. Last check: 2007-10-08)
		Diocles and the Hippocratic writings on the method of dietetics and the limits of causal explanation 3.
		Principles and practices of therapeutics in the Hippocratic corpus and in the work of Diocles of Carystus 4.
		The heart, the brain, the blood and the pneuma: Hippocrates, Diocles and Aristotle on the location of the cognitive processes Part II.
	www.loc.gov /catdir/toc/cam051/2004056141.html (229 words)

	.. \| ..\| the walls of astyanax
		Diocles, even in his older age, had hands of iron.
		Avicenna was dragged bodily from his mother's chambers, weeping and shouting at her to speak to him.
		Diocles hobbled a step back at his eruption of emotion.
	www.commonastherain.com /woa/chap02.html (2907 words)

	Encyclopedia: Diocles
		Greek mythology comprises the collected legends of Greek gods and goddesses and ancient heroes and heroines, originally created and spread within an oral-poetic tradition.
		The Eleusinian Mysteries were annual initiation ceremonies for the cult of Demeter and Persephone based at Eleusis in ancient Greece.
		See also : Diocletian, formerly named Diocles Gaius Aurelius Valerius Diocletianus (245- 313 AD/CE), born Diocles, was Roman Emperor from November 20, 284 to May 1, 305.
	www.nationmaster.com /encyclopedia/Diocles (189 words)

	Aratus by Plutarch (Site not responding. Last check: 2007-10-08)
		For Technon, one of Aratus's servants, was sent away to Diocles, that they might together view the wall.
		Now he had never seen Diocles, but made no question of knowing him by the marks Erginus had given him of him; namely, that he had curly hair, a swarthy complexion, and no beard.
		In the meantime, Dionysius, elder brother to Erginus and Diocles, who knew nothing at all of the matter, but much resembled Diocles, happened to pass by.
	www.4literature.net /Plutarch/Aratus/5.html (592 words)

	Joseph SHOEMAKER - Martha SIDEWAY (Site not responding. Last check: 2007-10-08)
		1 Diocles Of SICAMBRI =Sue Jane 2 Bassanus Magnus Of SICAMBRI =Of The Orcades NORWAY 3 Clodimir I Of SICAMBRI =Delores ELAINE 4 Nicanor I Of SICAMBRI =Glennis DEE 5 Marcomir II SICAMBRI =(Unknown)
		1 Helenus V Of SICAMBRI =Clare Emaline 2 Diocles Of SICAMBRI =Sue Jane 3 Bassanus Magnus Of SICAMBRI =Of The Orcades NORWAY 4 Clodimir I Of SICAMBRI =Delores ELAINE 5 Nicanor I Of SICAMBRI =Glennis DEE
		1 Priamus SICAMBRI =Hecuba 2 Helenus V Of SICAMBRI =Clare Emaline 3 Diocles Of SICAMBRI =Sue Jane 4 Bassanus Magnus Of SICAMBRI =Of The Orcades NORWAY 5 Clodimir I Of SICAMBRI =Delores ELAINE
	www.jhcarney.com /html/people/p00000df.htm (1170 words)

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