41. Euclid Among these are hippocrates of chios (5th century BC), not to be confusedwith the physician Hippocrates of Cos (flourished 400 BC). http://zebu.uoregon.edu/~js/glossary/euclid.html

Euclid Euclid (fl. c. 300 BC, Alexandria), the most prominent mathematician of Greco-Roman antiquity, best known for his treatise on geometry, the Elements. Life and work. Of Euclid's life it is known only that he taught at and founded a school at Alexandria in the time of Ptolemy I Soter, who reigned from 323 to 285/283 BC. Medieval translators and editors often confused him with the philosopher Eucleides of Megara, a contemporary of Plato about a century before, and therefore called him Megarensis. Writing in the 5th century AD, the Greek philosopher Proclus told the story of Euclid's reply to Ptolemy, who asked whether there was any shorter way in geometry than that of the Elements"There is no royal road to geometry." Another anecdote relates that a student, probably in Alexandria, after learning the very first proposition in geometry, wanted to know what he would get by learning these things, whereupon Euclid called his slave and said, "Give him threepence since he must needs make gain by what he learns."

42. Hippias construction. The lunules of hippocrates of chios belong to it, andHippias, the universal genius, could not be left behind here. He http://ragz-international.com/hippias.htm

Hippias (5th cn. BCE.) A Greek sophist of Elis and a contemporary of Socrates. He taught in the towns of Greece, especially at Athens. He had the advantage of a prodigious memory, and was deeply versed in all the learning of his day. He attempted literature in every form which was then extant. He also made the first attempt in the composition of dialogues. In the two Platonic dialogues named after him ( Hippias Major and Hippias Minor ), he is represented as excessively vain and arrogant.

43. Assignment 4 The one on the right is a right lune. hippocrates of chios (ca. 460 380 BC) , who worked on the problems of squaring the circle http://mtl.math.uiuc.edu/modules/module13/Unit 1.4/assgn-4.html

Assignment 1.4 Assignment Completion and Submission Directions s: Prepare a single Geometer's Sketchpad document (or a MSWord document with GSP figures inserted) that presents the problems and their solutions in Assignment 1.4 in a manner that is technically correct and clearly described, and attractively displayed and organized. Your grade on this assignment will be based on the extent to which the GSP file you submit meets both of these criteria. If you are using Version 4.0 or later, use a separate page for each problem. When you complete Assignment 1.4, submit your GSP file through the Module Working Environment . Select Module 13 and enter your log-in and password. Then follow the directions there for submitting your assignment. Problem 1: Express cos(3 m) as a combinantion of positive integer powers of cos(m). Use this expression to obtain a cubic polynomial p(x) with rational number coefficients such that x = cos(m) is a root. Graph the resulting polynomial for m = 20 degrees on a window that displays all three of the roots. Problem 2: Trisecting Angles with a Marked Ruler.

44. Math Forum - Geometry Problem Of The Week of the original semicircle. What did hippocrates of chios prove aboutthese two regions? Hippocrates Lunes January 13-17, 1997. http://mathforum.org/geopow/archive/011797.geopow.html

A Math Forum Project Hippocrates' Lunes - January 13-17, 1997 Problems from Spring 1997 All Problems Search POWs 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? Solutions 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.

45. Math Forum: Geometry Problem Of The Week Archive, January - May 1997 What did hippocrates of chios prove about these two regions? Dividing upa Triangle January 20-24, 1997 Take any triangle. Label it ABC. http://mathforum.org/geopow/tocs/1997T1.toc.html

A Math Forum Project Geometry Problem of the Week Archive January - May 1997 Current Problem All Problems Cross Section of a Cube - January 1-10 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

46. Aristotle And Greek Mathematics: A Supplement To Aristotle And Mathematics by the intersection of two circular arcs (Prior Analytics ii 25, Sophistici Elenchi11, Physics i.2; this is a problem of hippocrates of chios, whom Aristotle http://plato.stanford.edu/entries/aristotle-mathematics/supplement4.html

Stanford Encyclopedia of Philosophy Supplement to Aristotle and Mathematics Citation Information Aristotle and Greek Mathematics This supplement provides some general indications of Aristotle's awareness and participation in mathematical activities of his time. Greek mathematics in Aristotle's Works Here are twenty-five of his favorite propositions (the list is not exhaustive). Where a proposition occurs in Euclid's Elements , the number is given, * indicates that we can reconstruct from what Aristotle says a proof different from that found in Euclid). Where the attribution is in doubt, I cite the scholar who endorses it. In many cases, the theorem is inferred from the context. In a given circle equal chords form equal angles with the circumference of the circle ( Prior Analytics i.24; not at all Euclidean in conception) The angles at the base of an isosceles triangle are equal ( Prior Analytics i.24; Eucl. i.5*). The angles about a point are two right angles ( Metaphysics ix 9; Eucl. follows from i def. 10). If two straight-lines are parallel and a straight-line intersects them, the interior angle is equal to the exterior angle (

47. 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

Greece Cities Abdera: Democritus Alexandria : Apollonius, Aristarchus, Diophantus, Eratosthenes, Euclid , Hypatia, Hypsicles, Heron, Menelaus, Pappus, Ptolemy, Theon Amisus: Dionysodorus Antinopolis: Serenus Apameia: Posidonius Athens: Aristotle, Plato, Ptolemy, Socrates, Theaetetus Byzantium (Constantinople): Philon, Proclus Chalcedon: Proclus, Xenocrates Chalcis: Iamblichus Chios: Hippocrates, Oenopides Clazomenae: Anaxagoras Cnidus: Eudoxus Croton: Philolaus, Pythagoras Cyrene: Eratosthenes, Nicoteles, Synesius, Theodorus Cyzicus: Callippus Elea: Parmenides, Zeno Elis: Hippias Gerasa: Nichmachus Larissa: Dominus Miletus: Anaximander, Anaximenes, Isidorus, Thales Nicaea: Hipparchus, Sporus, Theodosius Paros: Thymaridas Perga: Apollonius Pergamum: Apollonius Rhodes: Eudemus, Geminus, Posidonius Rome: Boethius Samos: Aristarchus, Conon, Pythagoras Smyrna: Theon Stagira: Aristotle Syene: Eratosthenes Syracuse: Archimedes Tarentum: Archytas, Pythagoras Thasos: Leodamas Tyre: Marinus, Porphyrius Mathematicians Thales of Miletus (c. 630-c 550)

48. Science Timeline Hipparchus of Rhodes, 134 bce. hippocrates of chios, 430 bce. Hippocratesof Cos, 400 bce, 1185. His, Wilhelm, 1887, early decades 20th century. http://www.sciencetimeline.net/siteindex_h.htm

use checkboxes to select items you wish to download Select Index Letter: a b c d ... w-x-y-z Haber, Edgar, 1962 Haber, Fritz,1909, 1915 Habermas, Jurgen, 1968 hackers, 1959 Haeckel, Ernst Heinrich, 1859, 1866, 1940 Hahn, Otto, 1938 Haken, Wolfgang, 1976 Haldane, John Burdon Sanderson, 1924, 1926, 1929, 1932, 1937, 1941 Hale, George Ellery, 1908, 1949 Hales, Stephen, 1727, 1733 Haley, Jay, 1952 Hall, Benjamin D., 1961 Hall, Chester More, 1733 Hall, Edwin Herbert, 1879, 1980 Hall, Howard, 1999 Hall, James, 1795 Hall, Jeffrey C., 1984, 1986, 1991 Hall, John L., 1989 Hall, Marshall, 1833 Halley, Edmund, 1678, 1693, 1705, 1718, 1758, 1759, 1835 hallucinagenic mushroom, 7000 bce Halm, Jacob, 1911 Hamburger, Viktor, 1975 Hamer, Dean H., 1993

49. Science Timeline About 430 bce, hippocrates of chios squared the lune, a major step toward squaringthe circle, probably using the theorem that circles are to one another as http://www.sciencetimeline.net/prehistory.htm

use checkboxes to select items you wish to download About 10,000 bce, wolves were probably domesticated. [added 02/01/03] By 9000 bce, sheep were probably domesticated in the Middle East. About 7000 bce, there was probably an hallucinagenic mushroom By 7000 bce, wheat was domesticated in Mesopotamia. The intoxicating effect of leaven on cereal dough and of warm places on sweet fruits and honey was noticed before men could write. By 6500 bce, goats [added 02/01/03] maces [added 02/01/03] walled communities [added 02/01/03] About 4800 bce, there is evidence of astronomical calendar stones on the Nabta plateau, near the Sudanese border in Egypt. A parade of six megaliths mark the position where Sirius About 4000 bce, horses were being ridden on the Eurasian steppe by the people of the Sredni Stog culture (Anthony et al. About 4000 bce, light wooden plows were used in Mesopotamia. Between 4000 and 3500 bce, copper smelting in minute quantities was introduced in Mesopotamia. [added 02/01/03] Between 4000 and 3500 bce, copper smelting in minute quantities was introduced in Mesopotamia.

50. Online time A view like theirs was also expressed by hippocrates of chios and his pupilAeschylus Only they say that the tail does We offer great quality compatible http://www.the-ink-shop.com/buy_minolta_ink_refill.asp

51. Time Hecataeus (550490 BC). Sun Tzu (544 - 496). 500BCE. Wars 524-500. History of fashion.Zeno (488 - 425). hippocrates of chios (470 - 410). Peloponnesian Wars , More. http://members.tripod.com/zephyr46/postmoderncogmap/id25.html

var cm_role = "live" var cm_host = "tripod.lycos.com" var cm_taxid = "/memberembedded" Check out the NEW Hotbot Tell me when this page is updated the Universal Declaration of Human Rights The Postmodern Cognitive Map ... Home POSTMODERN COGMAP Time Goto Scale Annalemma Martian Analemma Calachakra TIME Powers of 10 Time forum What is time? Time Travel? Lord Chronos Forum In gods time... The Revised Book of Genisis Galactic Time Cosmic Year ... 1.9 million years ago Yellow Horse Cave Art Buy this Art Print at AllPosters.com Pre-history Culinary History Timeline ... Tindale s Map of Tribal Boundaries Earliest evidence of occupation in Japan archipelago BCE The Stone Age Conservative Estimates for Colinisation of Australia ... Ancient Worlds Forum Huon Pines Holocene Calendar India History of Science 8500 BCE Oldest trees in the world BCE Links online Maps 6000 BCE CE Agricultural revolution ... Corn is domesticated potatoes squash pumpkins beans sweet potatoes tobacco History of Fabric ... Tomb History of Geography Lagesh City Map 2300 Urukagina's Code Earliest Legal decision 1850 Natya 1500 ... Shen Kua 1031-1095 BCE early form of Soccer first played in Japan Jerusalem Rome Athens ... Heraclitus ) the Logos The Atomists The Atomists: Leucippus of Miletus and Democritus of Abdera ... Thales of Miletus Timeline of Psychology Life of Buddha Daily words of Poetess Buy posters at AllPosters.com

52. World And Nation-State Nearly 80 years before Plato s rebuke of the Delians, hippocrates of chios offeredan insight based on the Pythagorean principle of the connection among music http://www.larouchepub.com/eiw/public/2002-33/bruce3/gauss3.html

Home Page A Fugue Across 25 Centuries - Doubling of the Line, Square, and Cube - Menaechmus' Discovery ... From Fermat to Gauss From the Vol.1 No.25 issue of Electronic Intelligence Weekly Hyperbolic Functions: A Fugue Across 25 Centuries by Bruce Director (This pedagogical exercise is part of an ongoing series on ``Riemann for Anti-Dummies.'' See for example EIR April 12, 2002 and May 3, 2002 When the Delians, circa 370 B.C., suffering the ravages of a plague, were directed by an oracle to increase the size of their temple's altar, Plato admonished them to disregard all magical interpretations of the oracle's demand and concentrate on solving the problem of doubling the cube. This is one of the earliest accounts of the significance of pedagogical, or spiritual, exercises for economics. Some crises, such as the one currently facing humanity, require a degree of concentration on paradoxes that outlasts one human lifetime. Fortunately, mankind is endowed with what LaRouche has called, ``super-genes,'' which provide the individual the capacity for higher powers of concentration, by bringing the efforts of generations past into the present. Exemplary is the case of Bernhard Riemann's 1854 habilitation lecture, On the Hypotheses that Underlie the Foundations of Geometry

53. PPE - Working Class Encyclopedia H2 and tuned in. hippocrates of chios (c430 BC) Greek mathematician.First to compile elements of geometry. PRS. HIPPOCRATES of Cos http://www.embassy.org.nz/encycl/h2encyc.htm

Herzen - HIV JUMP ELSEWHERE Jump Back to Hawke - Hero Jump Forward to Ho Chi Minh - Keri Hulme HERZEN, Alexander Ivanovich (1812-70) Russian writer. Known as a revolutionary writer yet commenting on the revolutionary year 1848 his 'Epilogue to 1849' opens " A curse upon thee, year of blood and madness, year of victorious stupidity, brutality and dullness. A curse upon thee! " He wished to replace the fanatical zeal of revolutionaries and Socialists with a carefully directed will, seeing history as a creative process, not preordained. He fled Russia in 1847 and lived chiefly in London. As known for his autobiography 'My Past and Thoughts', as well as 'From the Other Shore' (1850) which expresses his violent disillusion with revolution. [TBD] HESIOD Poet. HESS , Victor Physicist. HEYERDAHL, Thor (1914-) Norwegian explorer. Conducted a series of oceanic expeditions aimed at elucidating the spread of early civilizations. He has investigated the possibility of pre-Columbian contact between Egypt and South America, the settlement of Polynesia by voyagers from ancient Peru, and the spread of Sumerian culture through far-flung sea travel. [GRL] HEYWARD

54. Greek Mathematics hippocrates of chios (470410 BC) is famous for his quadrature of lunes (crescent-shapedfigures which are defined by two semi-circles of different radius). http://members.fortunecity.com/kokhuitan/greek.html

Era of Greek Mathematics The Greeks are responsible for initial explosion of Mathematical ideas. For several centuries, Greek mathematics reign the mathematical world, with great advances in Number Theory, the Theory of Equation, and in particular Geometry. The first great Greek mathematician is Thales of Miletus (624-547 BC). He brought the knowledge of Egyptian Geometry to the Greeks and discovered several theorems in elementary Geometry. He predicted a Solar Eclipse in 585 BC and could calculate the height of a pyramid, as well as how far a ship is from land. One of his pupils, the Greek philosopher, Anaximander of Miletus (610-546 BC), is considered the founder of Astronomy. Perhaps the most prominent Greek mathematicians is Pythagoras of Samos (569-475 BC). His ideas were greatly influenced by Thales and Anaximander. His school of thought practiced great secrecy and he (and his followers, called Pythagoreans) believe everything in the world can be reduced to numbers. This idea stemmed from Pythagoras' observations in Music, Mathematics and Astronomy. E.g. Pythagoras noticed that vibrating strings produce harmonics in which the lengths of the strings are in ratios of whole numbers. In fact, he contributed greatly to the mathematical theory of music. He had the notion of Odd and Even Numbers, Triangular Numbers, Perfect Numbers, etc. In particular, he is well known today for his Pythagoras Theorem. Although this theorem is known to the Babylonians and Chinese long before Pythagoras, he seemed to be the first person to provide a proof of it.

55. Dictionary Of The History Of Ideas hippocrates of chios (fifth century BC) had also written an Elements, a work unfortunatelylost; but we know that he had attempted in this work a systematic http://etext.lib.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv1-24

56. Euclid Among these are hippocrates of chios (fl. c. 460 BC), not to be confusedwith the physician Hippocrates of Cos (c. 460–377 BC). http://www.kat.gr/kat/history/Greek/Tc/Euclid.htm

Euclid flourished c. 300 BC , Alexandria, Egypt Greek Eukleides the most prominent mathematician of Greco-Roman antiquity, best known for his treatise on geometry, the Elements Life Of Euclid's life nothing is known except what the Greek philosopher Proclus (c. AD BC Elements BC Sources and contents of the Elements Euclid compiled his Elements from a number of works of earlier men. Among these are Hippocrates of Chios (fl. c. 460 BC BC BC ). The older elements were at once superseded by Euclid's and then forgotten. For his subject matter Euclid doubtless drew upon all his predecessors, but it is clear that the whole design of his work was his own, culminating in the construction of the five regular solids, now known as the Platonic solids. A brief survey of the Elements BC ). While Book V can be read independently of the rest of the Elements arithmos antanaresis (now known as the Euclidean algorithm), for finding the greatest common divisor of two or more numbers; Book VIII examines numbers in continued proportions, now known as geometric sequences (such as a x a x a x a x ); and Book IX proves that there are an infinite number of primes.

57. 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

PreSocratics (7th - 5th century B.C.) 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. The Pythagorean brotherhood is formed by Pythagoras of Samos . This society performed a great deal of progress in mathematics, but also had mystical beliefs. In addition to the Ionian and Pythagorian, other schools of this period include the Eleatic , the Atomists, and the Sophists All philosophers - scientists up to Democritus are considered to be PreSocratics. Philosophers-Scientists 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. Links: Thales of Miletus, Encyclopedia Britannica

58. Welcome To JMD COMPUTER TECH hippocrates of chios (ca. 450 BC) http//wwwgroups.dcs.st-and.ac.uk/~history/Mathematicians/Hippocrates.html.Hippocrates of Cos (460-ca. http://www.jmdcomp.com/wldhweb.htm

Home School Products! Home Contact Us Specials Our Family ... Buying A computer Quick Link Index Language Arts Foreign Language Math E-mail Science VIEW SHOPPING CART Software: Language Arts Software Foreign Language Software Math Software Science Software Software Bible Software Misc, Software Titles Specials HOME SCHOOL MATERIALS AND INFO: World History Web-Sites! Watch Here for my lists of past favorite web-sites. Eli Whitney Born December 8, 1765 - Died January 8, 1825 http://www.invent.org/book/book-text/108.html http://web.mit.edu/invent/www/inventorsR-Z/whitney.html Joseph John Thomson http://www.aip.org/history/electron/jjthomson.htm http://www.britannica.com/seo/s/sir-jj-thomson/ Mathematicians of the Seventeenth and Eighteenth Centuries http://www.maths.tcd.ie/pub/HistMath/People/RBallHist.htm Henry Ford http://www.hfmgv.org/histories/hf/montage-02-02.jpg http://www.hfmgv.org/smartfun/class/modelt/lessons.html The Model T Road Trip: Lesson Plans"Remembering the Model T"Conduct oral history interviews to collect, interpret and presentreminiscences about the impact of the automobile on American life. Grade Level: 4-8 http://www.aande.com/class/admin/study_guide/archives/aetv_guide.0072.html

59. Martin Tulic, Book Indexing - About Indexing - Qualifiers abstracts (pharmaceutical mixtures), Hippocrates ( Father of Medicine ),.. hippocrates of chios, Louis VIII, Louis IX, http://www.anindexer.com/about/qlifiers/qlifiersindex.html

About indexing Samples Rates Other indexers ... Site map Qualifiers Qualifiers are words or phrases added to a heading or subheading to clarify its meaning or to distinguish among homographs. They may or may not be enclosed in parentheses, as these examples demonstrate: By being added to the heading, they become part of it and are considered during alphabetization. Qualifiers are often used in relation to personal names , where homographs (including surnames and forenames) are common. For example: The date in the first qualifier above includes an question mark to indicate uncertainty about the date. Other abbreviations that are used include b. for "born" and d. for "died." For example: The order of entries for the Hamiltons is due to the fact that question marks and abbreviations signifying birth and death are ignored during alphabetization. Another use is to help identify things or people identified only by a forename or surname in the text. For example: In biographies , qualifiers are often used to specify the relationship between a person and the main subject or a person and others discussed in the text. For example: They may also be used to distinguish between corporate entities having the same name. For example:

60. Richard Delaware Talks hippocrates of chios Squares a Lune, But Can t Square a Circle! Apr. Hippocratesof Chios Squares a Lune, But Can t Square a Circle! Apr. http://d.faculty.umkc.edu/delawarer/RDtalks.htm

Richard Delaware Mathematics Talks Expository Mathematics Talks (Complete List) Conference Talks (not Math EXPO talks) Colloquium Talks Given Elsewhere Other Graduate/Research Mathematics Talks ... Other Mathematics Talks Locations Where Talks Given: Avila College Benedictine College Central Missouri State University Emporia State University Johnson County Community College Park University Penn Valley Community College Rockhurst University University of Iowa University of Louisville University of Missouri - Columbia University of Missouri - Kansas City Weber State University William Jewell College RETURN to Richard Delaware Curriculum Vitae RETURN to Richard Delaware Home Page Expository Mathematics Talks (Complete List) e and are Irrational. Jan. 20, 1988, UMKC Expository Talks Series. Two World Class Series: 1/n and 1/n Feb. 17, 1988, UMKC Expository Talks Series. Apr. 3, 1990, Kappa Mu Epsilon (Mathematics Honor Society) Banquet Speaker, Wm. Jewell College. Polya's Orchard Problem. Apr. 6, 1988, UMKC Expository Talks Series.

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