Aegean Links - Greek Islands Tourist Guide sites. www.chiosnet.gr/tourism/default.htm. hippocrates of chios Allabout the philosopher and medic who was born on Chios. wwwgroups http://www.greekisland.co.uk/links/linksaegean.htm
Lecture 3 Hippocrates Quadrature Of Lunes hippocrates of chios, c. 410 ( Plato -400, Euclid -360, Archimedes -250)was a failed merchant of Athens who took to mathematics as consolation. http://www.maths.uwa.edu.au/~schultz/3M3/L3Hippocrates.html
Extractions: The distinguishing feature of Greek mathematics is that it is concerned with logical development, not problem solving. We use the term Greek Mathematics to denote mathematics written in the Greek language between about -600 (Thales) and about 250 (Diophantos). The mathematicians were not necessarily ethnically Greek nor living in the region we now call Greece. In fact the major developments occurred in the Greek colonies now known as Turkey, Egypt and Italy. The Greeks did not have a sophisticated number system. The integers were expressed by concatenating the letters a-k for 19, and l-u for1090 etc. Special letters were invented for larger numbers. Later, Archimedes in the "Sand Reckoner", (in which he calculated the number of grains of sand needed to fill the Universe) developed an exponential system for arbitrarily large numbers. The Greeks used a decimal system for common purposes and a sexigesimal system for scientific purposes, for example astronomy. Concatenations of unit fractions were used for rationals, although later Diophantos developed special symbols for rationals. In Greek mathematics the numbers were 2,3,4,.. The unity 1 was not a number, but the unit in which the numbers were measured. There were no negative numbers or zero. Geometrical quantities such as line segments, angles, areas and volumes were called
The Cosmologic Timeline c. 475 bce Pythagoras of Samos dies. c. 470 bce - hippocrates of chiosis born. c. 440 bce - hippocrates of chios writes his Elements. http://www.panikon.com/cosmo/timeline.html
Extractions: This timeline is distilled down from a more general timeline originally created for Phurba. It is meant to give a better idea of the linear history of the topics discussed in Cosmologic. Some dates given are simply there to give a better grasp of the timeperiods, comparatively. This document will be expanded and fleshed out heavily in time.
Malaspina.com - Hippocrates (ca. 460-377 BC) Internet Classics Archive; On Ulcers HTML, Internet Classics Archive.MacTutor Entry on hippocrates of chios. Click Here! Top of Page. http://www.mala.bc.ca/~mcneil/hippo1.htm
Extractions: Hippocrates (ca. 460-377 B.C.) [Biography, SFU] Etexts by this Author [Athena] Great Books Biography [Malaspina] Amazon Search Form] Library of Canada Online Citations [NLC] Library of Congress Online Citations [LC] Library of Congress Offline Citations [MGB] COPAC UK Online Citations [COPAC] Free Online Practice Exams [Grad Links] Canadian Book Orders! Chapters-Indigo Save on Textbooks! [Study Abroad] Used Books Search Form Alibris Dummies Books Amazon Books from Amazon Amazon EBay! Ebay Books from Amazon UK Amazon UK Books from Chapters Canada Chapters Amazon's 100 Hot Books Amazon Hippocrates Amazon Greek Medicine Amazon Hippocrates in a World of Pagans and Christians Amazon Works by Hippocrates [HTML, Internet Classics Archive] Oath and Law of Hippocrates [Text, Wiretap] On Airs, Waters, and Places [HTML, Internet Classics Archive] On Ancient Medicine [HTML, Internet Classics Archive] Aphorisms [HTML, Internet Classics Archive] On the Articulations [HTML, Internet Classics Archive] The Book of Prognostics [HTML, Internet Classics Archive] On Fistulae [HTML, Internet Classics Archive]
Malaspina.com - Hippocrates (ca. 460-377 BC) On the Surgery HTML, Internet Classics Archive; On Ulcers HTML, Internet ClassicsArchive. MacTutor Entry on hippocrates of chios. Click Here! Top of Page. http://www.mala.bc.ca/~mcneil/thippo1.htm
Extractions: Hippocrates (ca. 460-377 B.C.) [Biography] Etexts by this Author [Athena] Great Books Biography [Malaspina] Amazon Search Form] Library of Canada Online Citations [NLC] Library of Congress Online Citations [LC] Library of Congress Offline Citations [MGB] COPAC UK Online Citations [COPAC] Free Online Practice Exams [Grad Links] Canadian Book Orders! Chapters-Indigo Save on Textbooks! [Study Abroad] Used Books Search Form Alibris Dummies Books Amazon Books from Amazon Amazon EBay! Ebay Books from Amazon UK Amazon UK Books from Chapters Canada Chapters Amazon's 100 Hot Books Amazon Hippocrates Amazon Greek Medicine Amazon Hippocrates in a World of Pagans and Christians Amazon Works by Hippocrates [HTML, MIT] Oath and Law of Hippocrates [Text, Wiretap] On Airs, Waters, and Places [HTML, Internet Classics Archive] On Ancient Medicine [HTML, Internet Classics Archive] Aphorisms [HTML, Internet Classics Archive] On the Articulations [HTML, Internet Classics Archive] The Book of Prognostics [HTML, Internet Classics Archive] On Fistulae [HTML, Internet Classics Archive]
History Of Mathematics: Greece Chios (c. 450?); Leucippus (c. 450); hippocrates of chios (c. 450);Meton (c. 430) *SB; Hippias of Elis (c. 425); Theodorus of Cyrene http://aleph0.clarku.edu/~djoyce/mathhist/greece.html
Antiphon.html Simplicius identifies the squaring through segments with the construction oflunules by hippocrates of chios, as suggested by Aristotle, Sophistical http://www.calstatela.edu/faculty/hmendel/Ancient Mathematics/Philosophical Text
Math Forum - Geometry Problem Of The Week What did hippocrates of chios prove about these two regions? Hippocrates' Lunes January 13-17, 1997. Problems from Spring 1997 All Problems Search POWs http://mathforum.org/geopow/archive/011797.geopow.html
Extractions: 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. What's the story? Annie says: We had a good batting average this week - 34 right and only 3 wrong. One of the "wrong" ones was essentially right but I could not for the life of me understand the explanation. Another person did all the work but never stated what the answer was. And the other person didn't understand what I was looking for. All in all, a pretty decent week. Here are some comments from Dale Pearson, who teaches at Highland Park Senior High School: It was surprising to most of my students that the two yellow figures must be equal in area. Only one student suspected that this might be the case before any calculations were made. Most students thought that the triangle was larger. A couple of students thought that the moon-shaped figure was larger. This was not the end of the surprises, however. Many students has difficulty finding any relationships whatsoever among the elements of the figure until they found a orderly way to keep track of their results.
Extractions: A 'cross section' of a cube is a shape that you get when you cut the cube with a plane. Given a cube with a surface area of 96 cm^2, if you cut the cube with a plane that is parallel to one of its faces, you will get a square. What is the perimeter of that square? What is the perimeter of the largest rectangle you can get as a cross section? How can you get an equilateral triangle as a cross section? What are the areas of the square, rectangle, and the largest possible equilateral triangle? Hippocrates' Lunes - January 13-17, 1997 ABC is half a square inscribed in a semi-circle (A->B->C). Then a semi-circle is constructed on AB. 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. What did Hippocrates of Chios prove about these two regions? Dividing up a Triangle - January 20-24, 1997
Hippocrats' Quadrature Of The Lune hippocrates of chios. Indroduction. hippocrates of chios taught in Athens and workedon the classical problems of squaring the circle and duplicating the cube. http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Math 7200/Math 7200 projec
Extractions: Iamblichus [4] writes:- One of the Pythagorean [Hippocrates] lost his property, and when this misfortune befell him he was allowed to make money by teaching geometry. Heath [6] recounts two versions of this story:- One version of the story is that [Hippocrates] was a merchant, but lost all his property through being captured by a pirate vessel. He then came to Athens to persecute the offenders and, during a long stay, attended lectures, finally attaining such proficiency in geometry that he tried to square the circle. Heath also recounts a different version of the story as told by Aristotle:- ... he allowed himself to be defrauded of a large sum by custom-house officers at Byzantium, thereby proving, in Aristotle's opinion, that, though a good geometer, he was stupid and incompetent in the business of ordinary life. The suggestion is that this 'long stay' in Athens was between about 450 BC and 430 BC.
Untitled Document of the circle in pure geometric form, with the specific restriction that only compassand straightedge should be used, was hippocrates of chios (440 BC) He http://jwilson.coe.uga.edu/emt668/EMT668.Folders.F97/Patterson/EMT 669/Lunes/Lun
Extractions: Squaring the Circle " or " Quadrature of the Circle refers to a geometrical problem of antiquity. The problem was if you were given a circle of known area, could you create a square of the same area using only a compass and straightedge. "One of the earliest Greek mathematicians to attempt to treat the problem of the "quadrature of the circle" in pure geometric form, with the specific restriction that only compass and straightedge should be used, was Hippocrates of Chios (440 B.C.) He was able to show that the area of certain lunes (cresent-shaped figures formed by two intersecting arcs) could be represented exactly by trianglular (and hence rectangular) areas. For example, if AOB is a quadrant of a circle and AB is the diameter of a semicircle lying outside the quadrant, then the lune bounded by the semicircle and the quadrant has the same area as triangle AOB. His success with such special cases led him to suppose that he could eventually draw a polygon and hence a square whose area is exactly that of a circle." (P150 NCTM Yearbook #31) In 1882 Ferdinand Lindemann, modelling his proof after Hermite, proved that pi, also, is a transcendental number. No transcendental number is constructible, therefore Lindemann's result settled the famous problem concerning the possibility of "squaring the circle".
JMM HM DICIONÁRIO Translate this page Hípias de Eleia Hipócrates de Quios (c. 425?) Hipsicles Hórus Ísis, HerodotusHipparchus, Hero Herodotos Hypatia Hipparchos hippocrates of chios, hekat Heron http://phoenix.sce.fct.unl.pt/jmmatos/HISTMAT/HMHTM/HMDIC.HTM
Hippoarea.html hippocrates of chios. Introduction the Area Problem. The Babylonians,the Egyptians, and indeed every ancient civilization had knowledge http://cerebro.cs.xu.edu/math/math147/02f/hippocrates/hippoarea.html
Extractions: The Babylonians, the Egyptians, and indeed every ancient civilization had knowledge of basic geometric concepts like how to calculate the areas of simple plane figures (triangles, squares, rectangles, parallelograms, trapezoids, and the like) and the volumes of simple solid bodies (parallelopipeds and pyramids). The Greeks however turned geometry into a real science by applying to it the deductive methods they were systematizing through philosophy. For the first time, epistemological questions were being studied about mathematical ideas: how do we know that the results we have discovered are true? Are these ideas interrelated? Dialectical reasoning strove to find the first principles of mathematical knowledge as a foundation for understanding the real world. This created an architecture of logical structure for mathematical ideas based on cause and effect relationships: if a certain theorem was a consequence of another, then the second was given an a priori precedence over the first. It became standard for geometers to communicate in a very spare language, consisting of statements of theorems followed by their proofs followed the next theorem in the logical development, with little in the way of discussion or explanation. It may not have had the same emotive force as the epic poetry of Homer, but it was beautiful in its own abstract way, like music to the listener. Moreover it was seen as uncovering the secrets of the physical universe, since physical objects and phenomena like light and sound behaved according to geometric principles.
Hippotext.html hippocrates of chios the quadrature of a lune 1. hippocrates of chios wasa merchant who fell in with a pirate ship and lost all his possessions. http://cerebro.cs.xu.edu/math/math147/02f/hippocrates/hippotext.html
Extractions: From Philoponus Commentary on Aristotle's Physics Hippocrates of Chios was a merchant who fell in with a pirate ship and lost all his possessions. He came to Athens to prosecute the pirates and, staying a long time in Athens by reason of the indictment, consorted with philosophers, and reached such proficiency in geometry that he tried to affect the quadrature of the circle. He did not discover this, but having squared the lune he falsely thought from this that he could square the circle also. For he thought that from the quadrature of the lune the quadrature of the circle could also be calculated. From Simplicius Commentary on Aristotle's Physics Eudemus , however, in his History of Geometry says that Hippocrates did not demonstrate the quadrature of the lune on the side of a square but generally, as one might say. For every lune has an outer circumference equal to a semicircle or greater or less, and if Hippocrates squared the lune having an outer circumference equal to a semicircle and greater and less, the quadrature would appear to be proved generally. I shall set out what Eudemus wrote word for word, adding only for the sake of clearness a few things taken from Euclid's Elements on account of the summary style of Eudemus, who set out his proofs in abridged form in conformity with the ancient practice. He writes thus in the second book of the History of Geometry.
Grecia Heroica study. Anaxagoras of Clazomenae (Athens) hippocrates of chios (Athens).squaring the success. 3. hippocrates of chios (430 BC). He spent http://descartes.cnice.mecd.es/ingles/maths_workshop/A_history_of_Mathematics/Gr
Extractions: THE GREEK HEROIC AGE History THE HEROIC AGE (Vth century B.C.) One of the most important personalities of this century is Pericles Athens attracted intellectuals from all parts of the Greek world wanting to satisfy their thirst for knowledge. Rather than coming up with necessary solutions to practical problems at that time, the scholars were more interested in developing their own personal intellect. This desire for wisdom lead them to focus their learning on theoretical issues. During this period the three famous (or classical) problems were dealt with and two methods of reasoning were put into use The table below lists the mathematicians who lived during this period and the problems that formed the focus of their study. Anaxagoras of Clazomenae (Athens) Hippocrates of Chios (Athens) squaring the circle or how to draw a square whose area is the same as that of a circle using a ruler and compass. Hippias de Elis (Attic peninsular) the trisection of the angle or how to construct an angle equal to a third of another given angle Philolaus of Tarentum (Southern Italy) Archytas of Tarentum the duplication of the cube or how to construct another cube whose volume is double that of the given cube Hippasus of Metapontum (Southern Italy) Incommensurability or line segments which are not in rational proportion to one another (THE GOLDEN SECTION)
Acronyms H Page 2 Of 2 ScienceMathematicsMathematicians. hippocrates of chios, His InterPersonalProficiency's Often Considered Rusty Although The http://acronyms.co.nz/H2.html
Acronym ACRONYMS logo Abundant Crazy Ramblings, Openly Nice, Yippee! My Stars! ACRONYM. HIPPOCRATESOF CHIOS, His InterPersonal Proficiency's Often Considered Rusty http://acronyms.co.nz/cgi-bin/gonym?HIPPOCRATES OF CHIOS
Proof - Lloyd such as mathematics and philosophy and of specialists in them - before Plato (thoughthere are some partial exceptions hippocrates of chios was, so far as http://www.columbia.edu/cu/reidhall/5_events/activities/2002_spring_proof_lloyd.
Extractions: We should be wary of thinking of well-defined disciplines, such as mathematics and philosophy - and of specialists in them - before Plato (though there are some partial exceptions: Hippocrates of Chios was, so far as we know, mostly engaged in 'mathematike' broadly construed). Figures who cannot be defined exclusively as either 'mathematikos' or 'philosophos' include Philolaus, Archytas, Democritus, Eudoxus, not to speak of 'Thales' and 'Pythagoras' themselves (as tradition represents them). That throws some light on the old dispute between Knorr and Szabo on who 'invented' deductive argument ('philosophers' OR 'mathematicians'). Contributions to the discussion of the three 'traditional' mathematical problems (cf Knorr) come from different quarters and show evidence of attempts to police the borders . In squaring the circle, Aristotle and the commentators aim to discount the work of Antiphon and of Bryson, though they deem Hippocrates of Chios worthy of refutation. There is further input from 'sophists' (another indeterminate category) e.g. Protagoras' claim that the tangent does not touch the circle at a point. That may be classed as a metamathematical issue, but the boundaries between math.s and meta-math.s were/are hard to draw.
Index Of Ancient Greek Philosophers - Scientists Euctemon of Athens (430 BC). hippocrates of chios. Wrote his Elements almostone century before Euclid's. Hippocrates of Cos (460377 BC). http://www.ics.forth.gr/~vsiris/ancient_greeks/presocratics.html
Extractions: Period marking the begining of science, as well as the development of literature, arts, politics, and philosophy. During these years, the city-states (polis in Greek) flourish. These include the Sparta and Athens. Within this period the Ionian school of natural philosophy was founded by Thales of Miletus . This is considered the first school for speculating about nature in a scientific way, hence signifies the birth of science. All philosophers - scientists up to Democritus are considered to be PreSocratics. Thales of Miletus (624-560 B.C.). Astronomer, mathematician and philosopher. Learned astronomy from the Babylonians. Founder of the Ionian school of natural philosophy. Predicted the solar eclipse on May 28, 585. Proved general geometric propositions on angles and triangles. Considered water to be the basis of all matter. He believed that the Earth floated in water. Used the laws of prospectives to calculate the height of the pyramids.
Index Of Ancient Greek Scientists Links Hippocrates, Encyclopedia Britannica; hippocrates of chios. Wrotehis Elements almost one century before Euclid's. Hypsicles (180 BC). http://www.ics.forth.gr/~vsiris/ancient_greeks/whole_list.html
Extractions: not complete Agatharchos. Greek mathematician. Discovered the laws of perspectives. Anaxagoras of Clazomenae (480-430 B.C.). Greek philosopher. Believed that a large number of seeds make up the properties of materials, that heavenly bodies are made up of the same materials as Earth and that the sun is a large, hot, glowing rock. Discovered that the moon reflected light and formulated the correct theory for the eclipses. Erroneously believed that the Earth was flat. Links: Anaxagoras of Clazomenae, MIT Anaximander (610-545 B.C.). Greek astronomer and philosopher, pupil of Thales. Introduced the apeiron (infinity). Formulated a theory of origin and evolution of life, according to which life originated in the sea from the moist element which evaporated from the sun ( On Nature ). Was the first to model the Earth according to scientific principles. According to him, the Earth was a cylinder with a north-south curvature, suspended freely in space, and the stars where attached to a sphere that rotated around Earth.
