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Topic: Hippocrates of Chios

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	Hippocrates Biography and Summary
		Hippocrates was born on the Greek island of Cos around 460 b.c.
		Hippocrates was born on the Greek island of Cos to a family of physicians.
		Hippocrates and the Hippocratic Corpus(B. 460 Bce) Hippocrates, who came from the Aegean island of Cos, is said to have been born in 460 BCE.
	www.bookrags.com /Hippocrates (496 words)

	Hippocrates of Chios (Site not responding. Last check: 2007-10-26)
		One of Hippocrates achievements was that of the quadrature or squaring of the circle.
		Hippocrates also worked on the duplication of the cube and was the first to reduce the problem of doubling the cube of side a to the problem of discovering two mean proportionals b, c between a and 2a.
		Hippocrates is said to be the first to have written an Elements of Geometry, which some argue contained most of Book I of the Elements.
	www.math.sfu.ca /histmath/Europe/Euclid300BC/hippocrates.html (184 words)

	Hippocrates of Chios, Greek mathematician born in Chios
		Hippocrates was a brilliant mathematician and One of the greatest geometers of antient Greece.
		One of Hippocrates achievements is squaring of the circle or the quadrature.
		In Hippocrates attempt to square the circle, he was able to find the areas of lunes, certain crescent-shaped figures, using his theory that the ratio of the areas of two circles is the same as the ratio of the squares of their radii.
	www.fragrant-chios.com /info/people_hippocrates.php (226 words)

	Chios
		Chios claims to be the birthplace Hippocrates, not Hippocrates of Cos the "Father of Medicine" but, Hippocrates of Chios an ancient Greek mathematician (geometer) and astronomer who was born on the island of Chios.
		Chios claims to be the birthplace of Oenopion, a legendary king, is said to have brought winemaking to the island.
		Chios is also the birthplace of some well known poets of modern times as Giorgos Dilvois, Nikos Gialouris, Dimitris Varos and Matheos Moundes.
	hausfay.com /chios.php (669 words)

	Hippocrats' Quadrature of the Lune
		In his attempts to square the circle, Hippocrates was able to find the areas of lunes, certain crescent-shaped figures, using his theorem that the ratio of the areas of two circles is the same as the ratio of the squares of their radii.
		Hippocrates also showed that a cube can be doubled if two mean proportional can be determined between a number and its double.
		Hippocrates of Chios, the discoverer of the quadrature of the lune,...
	jwilson.coe.uga.edu /EMT668/EMAT6680.2000/Obara/Math%207200/Math%207200%20project/Lune.html (522 words)

	Quadrature of a Convex Polygon and the Lune of Hippocrates
		Hippocrates of Chios was able to show that the area of the “Lune” (a lune is a curved shape bounded by two circular arcs whose radii are different)AEC (The dark area number 5) is equal to the area of the triangle AOC (area 4).
		Some say that Hippocrates was actually not able to provide a proof since he had to know that the ratio of areas of two circles is proportional to the ratio of the square of their diameter.
		Hippocrates’ method is further developed by Plato who introduces a procedure from hypotheses “formally identical to the one used by Hippocrates of Chios in his solution to the problem of the quadrature of the lunes” (Cambiano 1967, p.
	www.mlahanas.de /Greeks/PolygonQuadrature.htm (1195 words)

	Dessert Recipes with Chios Mastiha from Greece
		The purported birthplace of Homer and Hippocrates, Chios is best known as the world's exclusive source of mastiha, or mastic, a crystalline resin produced from the bark of the mastic tree (Pistacia lentiscus) that has been cultivated there for millennia.
		Originally used as a type of chewing gum to clean the teeth and freshen the breath and in cosmetology as a skin cleanser, its medicinal properties were first documented by Dioscorides (1st Century, B.C.), who is generally considered the "father of pharmacology".
		The Greek physician and botanist praised Chios Mastiha for its therapeutic effects on digestion, blood reproduction, chronic coughing, and for its tranquilizing and aphrodisiac effects.
	www.culturekiosque.com /chef/recipe-tips/chios_mastiha.html (858 words)

	Hippocrates of Chios - Wikipedia, the free encyclopedia
		Hippocrates of Chios was an ancient Greek mathematician (geometer) and astronomer, who lived c.
		On Chios Hippocrates may have been a pupil of the mathematician and astronomer Oenopides of Chios.
		The fact that Hippocrates thought that light rays originated in our eyes instead of in the object that is seen, adds to the unfamiliar character of his ideas, which belong to the realm of speculative philosophy.
	en.wikipedia.org /wiki/Hippocrates_of_Chios (670 words)

	Hippocrates
		Hippocrates was a Greek physician born in 460 BC on the island of Cos, Greece.
		Hippocrates held the belief that the body must be treated as a whole and not...
		Hippocrates, the ancient Greek physician considered to be the founder of medicine.
	www.cordah.co.uk /hippocrates.html (343 words)

	Hippocrates
		Hippocrates was the first to square three of the four lunes; Quadrature of the circle, which was the prominent problem of Greek mathematics.
		Hippocrates of Chios was a merchant who turned to mathematics as a way to escape financial troubles.
		Hippocrates was born on the Greek island of Chios.
	www.csca.us /math/precalc/hippocrates.htm (670 words)

	Hippocrates biography
		Before continuing with the quote we should note that Hippocrates is trying to 'square a lune' by which he means to construct a square equal in area to the lune.
		Then Hippocrates argues that the semicircle ABC with the two segments 1 removed is the triangle ABC which can be squared (it was well known how to construct a square equal to a triangle).
		In Hippocrates' study of lunes, as described by Eudemus, he uses the theorem that circles are to one another as the squares on their diameters.
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Hippocrates.html (1317 words)

	Hippocrates free essays
		Hippocrates was a Greek physician who helped transform medicine from a field ruled by magic, religion, and superstition to a scientific discipline.
		Hippocrates based his medical practice on the study of the human body and on objective observations.
		It is believed Hippocrates was born around B.C. 460 on the Greek island of Cos, the son of Heraclides and Phenaretes.
	www.needfreeessays.com /viewpaper/6097.html (349 words)

	The Later years
		Chios was finally liberated and reunited with Greece on November 11, 1912, during the Balkan Wars.
		Chios faced occupation again on May 4, 1941 when it was taken over by the Germans in World War EE.
		Today, Chios is one of the most interesting and cultured islands of Greece with its wealth of physical beauties, its numerous monuments, its warm-hearted villagers, and the traditional nature and nobility of its residents.
	www.chiosonline.gr /lateryears.asp (303 words)

	Hippocrates biography
		Before continuing with the quote we should note that Hippocrates is trying to 'square a lune' by which he means to construct a square equal in area to the lune.
		In Hippocrates' study of lunes, as described by Eudemus, he uses the theorem that circles are to one another as the squares on their diameters.
		However, Eudoxus was born within a few years of the death of Hippocrates, and so there follows the intriguing question of how Hippocrates proved this theorem.
	www-history.mcs.st-andrews.ac.uk /Biographies/Hippocrates.html (1317 words)

	Ancient Chios
		By the 6th century BC Chios was a major city with estimated population of 60-80.000 residents, not including slaves.
		After Alexander’s death Chios became part of the Macedonian State and later passed under the influence of Ptolemy I, the Selefkides and the kings of Pergamon.
		But the Roman gradually stripped Chios of its work of art, and the destruction was completed by a series of catastrophic earthquakes.
	www.chiosonline.gr /ancienttimes.asp (685 words)

	UB&AC - Hippocrates, Part 1
		Hippocrates of Chios, the lune-squarer, was a contemporary of Plato.
		He should not be confused with the Hippocrates of Cos, known as the Father of Medicine.
		Hippocrates of Chios was the first known mathematician to begin to assemble the "elements" of geometry: those principles upon which most of the other theorems are based [3].
	www.unclebobpuzzles.com /Permasite/UB&AC/hippoc1.htm (1187 words)

	Hippocrates, Part 1
		Hippocrates of Chios, the lune-squarer, was a contemporary of Plato.
		Hippocrates of Chios was the first known mathematician to begin to assemble the "elements" of geometry: those principles upon which most of the other theorems are based [3].
		Later (210 A.D.), Alexander Aphrodisiensis objected to Hippocrates' claim that in squaring lunes, he established the squaring of the circle.
	doe.ncia.net /~bobmead/hippoc1.htm (1187 words)

	Famous people from Athens. Athens, Greece celebrities by europe-cities.com (Site not responding. Last check: 2007-10-26)
		Regarded by many as the most prominent mathematician of the fifth century B.C., Hippocrates of Chios worked towards solving the noticeable geometrical problems of his time, like duplicating the cube and squaring the circle.
		He was able to prove that the ratio of the areas of two circles was equal to the ratio of the squares of their radii.
		Hippocrates of Chios included much of his geometrical knowledge in the first math textbook titled "Elements of Geometry" (it is not in existence today).
	www.europe-cities.com /athens/famous-people.aspx (734 words)

	[No title]
		Hippocrates of Chios taught in Athens and worked on the classical problems of squaring the circle and duplicating the cube.
		Scientists in the 19th century realized it was the salicylic acid in the willow that made the painkiller work, but it was hard on stomachs and had to be buffered.
		Galen expressed the greatest respect for Hippocrates, published his most important works with explanatory notes, but never entered into the spirit of the school of Cos, although he adopted many of its doctrines.
	www.lycos.com /info/hippocrates--works.html (296 words)

	Angle Trisection by Hippocrates
		Hippocrates (470-410 B.C.) of Chios, famous for his work on quadrature of circular lunes and the arrangement of theorems in a logical manner, later used by Euclid in his Elements, also left the first known construction for the trisection of an angle.
		century construction which serves to show that some problems in mathematics never lose their appeal.) Hippocrates of Chios, a mathematician and astronomer, should not be confused with the physician Hippocrates of Cos (460-ca.
		Thus, assuming (1) that the solution is Hippocrates' and (2) that it was known to Archimedes, the characterization as "improvement" which suggests a reversed time sequence of events caught my attention.
	www.cut-the-knot.org /Curriculum/Geometry/Hippocrates.shtml (504 words)

	London Stock Exchange - Site Search
		To the later Plato and to Aristotle, Hippocrates from the island of Cos was known as a famous physician, and subsequent tradition sets Hippocrates into the...
		Hippocrates was a Greek mathematician who worked on the...
		Hippocrates, the famous classical Greek doctor, looked at the embryos of chick eggs 'for the nature of the bir...
	www.londonstockexchange.com /en-gb/global/H/Search?q=Hippocrates&rt=3&p=0 (371 words)

	Hippocrates of Chios
		HIPPOCRATES OF CHIOS by Rob Fisch It can be argued that if Euclid is the father of Geometry that Hippocrates of Chios could be considered the grandfather of geometry.
		Hippocrates was born about 410 BC in Chios, Greece and died about 410 BC.
		Hippocrates was the greatest geometer of antiquity (relating to ancient times) but was “stupid and incompetent in the business of everyday life” as quoted by Aristotle.
	www.radessays.com /viewpaper.php?nats=MTAxMToyOjE,0,0,0,0&request=99115 (254 words)

	The Five Squarable Lunes
		Hippocrates of Chios was the first to demonstrate such "quadratures" (around 440 BC) for lunes.
		Three of these were described by Hippocrates himself, and two more were discovered in the mid 1700's.
		Notice that the area of the lune equals the area of the major triangle to the left of the vertical line.
	www.mathpages.com /home/kmath171.htm (741 words)

	Hippocrates - Information from Reference.com
		Hippocrates is believed to have lived between 460 and 380 BCE.
		Hippocrates was a Greek mathematician who worked on the classical problems of
		HIPPOCRATES, the celebrated Greek physician, was a contemporary of the historian
	www.reference.com /search?db=web&q=Hippocrates&start=21 (216 words)

	Hippocrates
		Aristotle, wrote History of Geometry in which he described the contribution of Hippocrates on lunes.
		Eudoxus was born within a few years of the death of Hippocrates, and so there follows the intriguing question of how Hippocrates proved this theorem.
		Eudemus seems entirely satisfied that Hippocrates does indeed have a correct proof, it seems almost certain from this circumstantial evidence that we can deduce that Hippocrates himself developed at least a variant of the method of exhaustion.
	www.educ.fc.ul.pt /icm/icm2003/icm14/Hippocrates.htm (1192 words)

	Hippocrates
		Hippocrates was integrated with a group of medical treatises known as Hippocratic Corpus and over 60 medical treatises have conventionally been attributed to him.
		In fact, several of the existant treatises were written long after Hippocrates' demise.
		These treatises in question were written over about a two hundred year period and range in date from c.510-c.300 BCE, so he could not have authored all of them.
	www.essaysword.com /viewpaper/9478.html (155 words)

	Hippocrates - Information from Reference.com
		Hippocrates was the son of a man named Pantares (once a victor of the Olympic
		Hippocrates (470-410 B.C.) of Chios, famous for his work on quadrature of circular
		antiquity by Hippocrates, its principles are held sacred by doctors to...
	www.reference.com /search?db=web&q=Hippocrates&start=81 (192 words)

	Hippocrates of Chios
		For more information on the structure of entries and links available from them, read the notice at the beginning of the index of persons and locations.
		Hippocrates, born in the island of Chios, in Ionia, started, according to a tradition recorded in Philoponus' Commentary on Aristotle's Physics, as a merchant and came to Athens to prosecute pirates who had robbed him of all his goods.
		In trying to square the circle, Hippocrates adressed the problem of the surface of lunes, figures included between two intersecting arcs of circles.
	www.plato-dialogues.org /tools/char/hipchios.htm (297 words)

	UI438 Discussion Questions for Chapter 3, Section 4 (Site not responding. Last check: 2007-10-26)
		Although he had no formal teacher, Hippocrates learned from the Pythagoreans who had settled there.
		After he became a great geometer, he became one of the first mathematicians to sell his knowledge.
		4.) Hippocrates and Hippias calculated the square of a circle by using Pythagorean (right) triangles and isosceles trapezoids.
	cstl-csm.semo.edu /Roberts/ui438spring2006/dQChap34AS.htm (250 words)

	Theremin Vox - Archytas
		According to Eutocius Archytas solved the problem of duplicating the cube in his manner with a geometric construction.
		Hippocrates of Chios before reduced this problem to finding mean proportionals.
		Archytas' theory of proportions is treated in the book VIII.
	www.thereminvox.com /article/articleview/75/1/16 (154 words)

	Math Forum - Geometry Problem of the Week (Site not responding. Last check: 2007-10-26)
		BD is then constructed, the perpendicular bisector of AC, and triangle ABD is shaded, as is the part of the outer semi-circle that's not part of the original semicircle.
		Rumor has it that Hippocrates of Chios proved something about the two shaded regions, but the next page of my book is missing.
		As I understand it, it is just the absence of pi from the answer that was of interest to Hippocrates and his contemporaries.
	mathforum.org /geopow/archive/011797.geopow.html (1922 words)

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