41. Online time A view like theirs was also expressed by hippocrates of chiosand his pupil Aeschylus Only they say that the tail does . For http://clothes.shopping-for-you.com/bottega_veneta_store.asp

42. History Of Geometry hippocrates of chios (470410 BC) wrote the first Elements of Geometry which Euclid may have used as a model for Books I and II. http://geometryalgorithms.com/history.htm

A Short History of Geometry Ancient This page gives a short outline of geometry's history, exemplified by major geometers responsible for it's evolution. Click on a person's picture or name for an expanded biography at the excellent: History of Mathematics Archive (Univ of St Andrews, Scotland). Also, Click these links for our recommended: Greek Medieval Modern History Books ... History Web Sites Ancient Geometry (2000 BC - 500 BC) Babylon Egypt The geometry of Babylon (in Mesopotamia) and Egypt was mostly experimentally derived rules used by the engineers of those civilizations. They knew how to compute areas, and even knew the "Pythagorian Theorem" 1000 years before the Greeks (see: Pythagoras's theorem in Babylonian mathematics ). But there is no evidence that they logically deduced geometric facts from basic principles. Nevertheless, they established the framework that inspired Greek geometry. A detailed analysis of Egyptian mathematics is given in the book: Mathematics in the Time of the Pharaohs India (1500 BC - 200 BC) The Sulbasutras Baudhayana (800-740 BC) Apastamba (600-540 BC) Greek Geometry (600 BC - 400 AD) Time Line of Greek Mathematicians Major Greek Geometers (listed cronologically) [click on a name or picture for an expanded biography].

43. The Five Squarable Lunes hippocrates of chios was the first to demonstrate such quadratures (around 440BC) for lunes. It turns out that only five particular lunes can be squared . http://www.mathpages.com/home/kmath171.htm

The Five Squarable Lunes Return to MathPages Main Menu

44. Mathematicians Zeno of Elea, Greek, 490425 BC, Zeno paradoxes, G. hippocrates of chios,Greek, 470-410 BC, Quadrature of Lunes (G). Hippias of Elias, Greek, 460-400BC,G. http://members.fortunecity.com/kokhuitan/mathematicians.html

Great Mathematicians and Their Achievements Mathematics exist before 1900 BC, in great civilizations everywhere, including China, India, Babylon etc. However, the first record of Mathematical manuscripts is found in Egypt, namely, the Moscow Papyrus and the Rhind Papyrus. In the 'Achievement' column below, the notations are as follows: AG = Analytic Geometry Al = Algebra Ar = Arithmetic As = Astronomy C = Calculus DE = Differential Equation FM = Foundation of Mathematics G = Geometry GT = Group Theory L = Logic M = Mechanics N = Number Theory P = Probability RM = Recreational Mathematics S = Statistic ST = Set Theory T = Topology The list here is not exhaustive. The mathematicians listed here are either pioneers in various fields of Mathematics, or those who have contributed to almost all fields, or those who have settled unsolved problems. For a more complete list of mathematicians, click on index of mathematicians Name Nationality Year Achievements Egyptian 1900 BC Moscow Papyrus (25 problems on G Ahmes Egyptian 1700 BC Rhind Papyrus (84 problems on Ar, Al, G

45. 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.

46. Euclid axiomatic method. It includes the work of hippocrates of chios; BooksI IV, XI. The Pythagoreans; the arithemtic of Books VII - IX. http://www.math.ubc.ca/~robles/hyperbolic/eucl/prll/euclid.html

Euclid 365 BC - ca 300 BC Alexandria,Egypt. Euclid complied the sum of known geometric theory in The Elements ; a text remarkable for its longevity (the predominate geometric text for 2000 yrs) and as the earliest extensive example of the axiomatic method. It includes the work of: Hippocrates of Chios ; Books I - IV, XI. The Pythagoreans ; the arithemtic of Books VII - IX. Eudoxus ' theory of similarity and ratios; Books V - VI Eudoxus ' method of exhaustion; Book XII Theaeteus The Elements rest on five "common notions" or postulates P-1. A straight line may be drawn from any one point to any other point. P-2. A finite straight line may be produced to any length in a straight line. P-3. A circle may be described with any centre at any distance from that centre. P-4. All right angles are equal. P-5. If a straight line meets two other straight lines, so as to make the two interior angles on one side of it together less than two right angles, the other straight lines will meet if produced on that side on which the angles are less than two right angles. The Fifth Postulate, also known as the Parallel Postulate, is considerably more elaborate than the previous four.

47. HISTORY OF MATHEMATICS IN THE LAST 25 YEARS: NEW DEPARTURES, NEW QUESTIONS, NEW mathematics . Vassilis Karasmanis, National Technological University,Athens (vasmar@hol.gr) The method of hippocrates of chios . http://www.tau.ac.il/humanities/cohn/workshop2001/speakers.htm

Annual International Workshop History of Mathematics in the Last 25 Years New Departures, New Questions, New Ideas May 14-17, 2001 Tel-Aviv and Jerusalem Invited Speakers David Rowe " " Ivo Schneider "A question of style: The background of Descartes'claim to the creation of a new mathematics." Ian Mueller , University of Chicago (i-mueller@uchicago.edu): " A minimalist Interpretation of Plato's Account of Arithmetic and Geometry in the Republic. " Marinus Taisback , Denmark (marinus@private.dk): "If Euclid ever wrote the Data, he neither invented it nor finished it. Must we?" Eric Brian , EHESS - Paris (brian@ehess.fr): "Mathematics and all that. Integrals, Series, Approximations around 1780" Orna Harari-Eshel , Tel Aviv University (oharari-eshel@dibinst.mit.edu): "Syllogistic logic and greek mathematical reasoning: a reassessment of the relationship between Aristotle's posterior analytics and Euclid's Elements" , Universidad de Sevilla (jmferre@cica.es ): "The emergence of the set-theoretical approach in mathematics"

48. M182f2002.html The squaring of the lune by hippocrates of chios is presented in Section3.4, and the argument is very elegant. Hippocrates tried http://www.math.montana.edu/~gillette/m330s2003/

Last modified Monday 17 March 2003 11:21 mst MATH 330 - SPRING SEMESTER, 2003 - History of Mathematics Instructor: Richard Gillette Office: Wilson 2-230 (SE corner of Wilson Hall; 2nd floor) Phone: 994-5363 e-mail : gillette@math.montana.edu Read This: First draft of final paper due Wed., April 16th. Final draft of final paper due Wed., April 30th. Final version of the mid-term paper is due Wednesday, March 19th. Brief Course Description A survey of the history of mathematics: from tally records notched in bone and preserved in paleolithic artifacts, to the nineteenth and twentieth centuries; a timeline that extends from 30,000 BCE to 2000 CE. The survey touches a large number of topics: early arithmetic; plane geometry; number theory; Diophantine equations; algebra and the theory of equations; calculus; Newtonian dynamics; probability theory; non-Euclidean geometry; group theory; set theory; differential geometry and topology. Grades are based on classroom participation, weekly assignments and two reports on topics chosen individually by students. Organizing Themes for this course A few themes, posed as questions, will help to organize our discussions in this course.

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51. The Inscribed Circle The Lune. of Hippocrates. hippocrates of chios lives in the second halfof the fifth century BCE and is believed to have died in Athens. http://web.pdx.edu/~marky/Assignment5/hippocrates.htm

The Lune of Hippocrates Hippocrates of Chios lives in the second half of the fifth century B.C.E. and is believed to have died in Athens. Although his original work was lost, it was referred to in detail by subsequent mathematicians such as Eudemus and Simplicius. Perhaps Hippocrates's greatest contribution to geometry dealt with the figure at the right. In a failed attempt to square a circle, he proved that certain regions between circles could be squared. Such regions resemble crescent moons and are called lunes. His result compares the areas of the red lune FBG and the area of triangle GOF. Hippocrates of Chios is sometimes confused with the Father of Medicine, Hippocrates of Cos pictured above. The Lune of Hippocrates Examining the Lune This is the same as the area of triangle FGO. It is amazing that the area of an object that is the intersection of two circles, can produce a triangle of exactly the same area. Hippocrates' discovery most likely came out of a failed attempt at one of the three great problems of antiquity. That given a circle, produce a square of exactly the same area. Sometimes this is referred to as "squaring the circle." Many people worked on this problem, until it was proven to impossible.

52. Crockett Johnson Homepage: Bibliography Of Crockett Johnson nd. Homethic Triangles (hippocrates of chios, 5th c BC). c. 1967. Law of Motion. SquaredLunes (hippocrates of chios). nd. Squared Lunex (hippocrates of chios). http://www.ksu.edu/english/nelp/purple/bibliography.html

Crockett Johnson: A Bibliography by Philip Nel In addition to my own research, major resources for this bibliography include the catalog of writings in Major Authors and Illustrators for Children and Young Adults (1993), pp. 1436-37, and the Thomas J. Dodd Research Center of the University of Connecticut Libraries Another source that provides more relating to Johnson's career as a comic-strip artist including items not listed here is the Reading Room Index of the Michigan State University Libraries Comic Art Collection (see the listing for " Johnson, Crockett " on the " Johns to Johnstown " index page). As a supplement to the " Cartoons " section of this page, please see " Crockett Johnson's Early Work: A Bibliography ." Cartoons Magazines Pamphlet Books ... About Crockett Johnson Cartoons Editorial cartoons The New Masses , April 1934 - May 1940. For a more complete bibliographic listing, please click here . Two of these cartoons appear in Robert Forsythe's Redder Than the Rose (listed under " Illustrated By ," below) and one in Joseph North's New Masses: An Anthology of the Rebel Thirties (listed under " About...

53. 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

54. Ancient Greek Philosophy: Additional Search Terms DAMON DEMOCRITUS DIODORUS CRONUS DIOGENES LAERTIUS ECHECRATES EMPEDOCLES EPICURUSEPIMENIDES GORGIAS HERACLITUS HESIOD HIPPIAS hippocrates of chios HYPATIA ION http://karn.ohiolink.edu/philosophy/keywords/ast31001.html

OhioLINK History of Philosophy Website Ancient Greek Philosophy: Additional Search Terms Contents Figures Titles Terms Search Tools ... About Additional Search Terms Figures Click here to begin an OhioLINK search Click here to begin a KentLINK search Use your "back button" to return to these pages. ANAXGORAS ANAXIMANDER ANAXIMENES ANTIPHON THE SOPHIST ANTITHENES ARCHYTAS ARISTIPPUS OF CYRENE ARISTOTLE CHRYSIPPUS CLEANTHES CRATYLUS CRITIAS DAMON DEMOCRITUS DIODORUS CRONUS DIOGENES LAERTIUS ECHECRATES EMPEDOCLES EPICURUS EPIMENIDES GORGIAS HERACLITUS HESIOD HIPPIAS HIPPOCRATES OF CHIOS HYPATIA ION OF CHIOS LEUCIPPUS LYCOPHRON LYSIS MELISSUS PANAETIUS PARMENIDES PHAEDO PHILOLANS OF ALEXANDRIA PLATO PLOTINUS PORPHYRY PRODICUS PYRRHO PYTHAGORAS SEXTUS EMPIRICUS SOCRATES SPEUSIPPUS THALES THEAGENES THEODORUS THEOPHRASTUS TIMEAUS XENOPHANES XENOPHONE ZENO Back to the Table of Contents Titles Click here to begin an OhioLINK search Click here to begin a KentLINK search Use your "back button" to return to these pages. APOLOGY CATEGORIES CHARMIDES CRATYLUS CRITO DE ANIMA EUTHYPHRO GORGIAS ION LACHES LYSIS MENO METAPHYSICS NICOMACHEAN ETHICS ON INTERPRETAITON PARMENIDES PHAEDO PHAEDRUS PHILEBUS POETICS POLITICS POSTERIOR ANALYTICS PRIOR ANALYTICS PROTAGORAS REPUBLIC RHETORIC SOPHIST SOPHISTICAL REFUTATIONS STATESMAN SYMPOSIUM THEATETUS TIMEAUS TOPICS Back to the Table of Contents Terms Click here to begin an OhioLINK search Click here to begin a KentLINK search Use your "back button" to return to these pages.

55. Compiled List Of Search Terms HILBERT David TwentiethCentury Philosophy HINTIKKA Jaakko Twentieth-Century PhilosophyHIPPIAS Ancient Greek Philosophy hippocrates of chios Ancient Greek http://karn.ohiolink.edu/philosophy/keywords/astglobal.html

OhioLINK History of Philosophy Website Compiled List of Search Terms Contents: Index of Figures A B C D ... Z Index of Titles A B C D ... W Index of Terms A B C D ... To the Search Tools Compiled List of Search Terms: Figures A ABBOT Francis E. American Philosophy ADORNO Theodor Twentieth-Century Philosophy ALLEN Ethan American Philosophy AMBROSE Alice American Philosophy ANAXGORAS Ancient Greek Philosophy ANAXIMANDER Ancient Greek Philosophy ANAXIMENES Ancient Greek Philosophy ANSCOMB Elizabeth Twentieth-Century Philosophy ANSELM Continental Rationalism ANTIPHON THE SOPHIST Ancient Greek Philosophy ANTITHENES Ancient Greek Philosophy APEL Karl Otto Twentieth-Century Philosophy APPIAH Kwame Anthony Twentieth-Century Philosophy ARCHYTAS Ancient Greek Philosophy ARENDT Hannah Twentieth-Century Philosophy ARISTIPPUS OF CYRENE Ancient Greek Philosophy ARISTOTLE Ancient Greek Philosophy German Critical Philosophy ARNAULD Antoine Continental Rationalism AST Friedrich Nineteenth-Century Philosophy AUSTIN J.L. Twentieth-Century Philosophy AYER Alred Jules Twentieth-Century Philosophy To the Search Tools Back to the Table of Contents Compiled List of Search Terms: Figures B BACON Francis British Empiricism German Critical Philosophy BAIN Alexander Nineteenth-Century Philosophy BARTHES Roland Twentieth-Century Philosophy BASEDOW Alexander Joseph German Critical Philosophy BATAILLE Georges Twentieth-Century Philosophy BAUMGARTEN Alexander German Critical Philosophy BENJAMIN Walter Twentieth-Century Philosophy BERGMANN Gustav Twentieth-Century Philosophy BERGSON Henri

56. Section 5-3 Theon. Alexandria. Napoleon. Vatican library. Adelard of Bath. Johannes Campanus.Venice. hippocrates of chios. Plato. Eudoxus. Previous. Previous Page. Next Page.Next. http://www.geocities.com/Athens/Parthenon/3947/sect5-3.html

5-3 Euclid’s "Elements" Euclid Euclid’s Elements Theon Alexandria ... Eudoxus Previous Next

57. 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."

58. The Beginnings Of Early Greek Sciene c = (p 2 + q 2 )/2 = (3 2 + 1 2 )/2 = 5. EARLY GREEK GEOMETRY. The quadratureof the lune was accomplished by hippocrates of chios (c. 440 BC). http://physics.weber.edu/carroll/Greeks/Greeks.htm

THE BEGINNINGS OF SCIENCE IN EARLY GREECE (c. 600 - 400 BC) "Atlas Brings Heracles the Apples of the Hesperides in the Presence of Athena," from the Temple of Zeus at Olympia, c. 460 BC. During this time, when gods embodied nature and interfered in human lives, the journey from mythos to logos began. WHAT DO WE KNOW OF THE PRESOCRATIC PHILOSOPHERS? Not much ... not a single original work has survived intact for us to study! The only sources are 1. Fragments - a few quotations from Presocratic works that have survived in works written later. 2. Testimonia - comments in the writings of Plato and Aristotle on Presocratic ideas. 3. Doxography - summaries and (summaries) of Presocratic works. Milesians Pythagoreans Eleatics Independent Atomists Physiologists Thales of Miletus Pythagoras of Samos Parmenides of Elea Heraclitus of Ephesus Democritus 624 - 546 BC 570 - 500 BC 540 - 480 BC c.500 BC c.460 - 370 BC Water Number Eon (Being) Pyr and Logos (Fire and Rule) Atom Anaximander of Miletus Philolaus Zeno of Elea Empedocles Leucippus 610 - 540 BC c.470 - 390 BC

59. Ancient Coins Are What I Collect Athens was a mecca for hippocrates of chios and Hippocrates of Cos, Anaximander,Aristotle, et. al, and home to Socrates, Meton, et al. http://www.limunltd.com/numismatica/articles/ancients-what-i-collect.html

Ancient Coins Are What I Collect by Michael E. Marotta , 4 Jun 1994 Like most libertarians, I have always held on to some silver and gold in preference to other forms of saving. After a while, one Kennedy half looks pretty much like the next. Just two years ago, my daughter worked as a page at a state coin show. Dropping her off and picking her up, I walked around the bourse room. It was all very nice and all, with American 19th Century Liberties being far lovelier than most others . . . until I sat down to a tray of ancients. Today, I have a Whitman for Mercuries that lacks only the 1916-D to be complete. Many of the entries have been upgraded to Fine and above. I have some Hard Times Tokens, 19th century world bronzes featuring Liberty, political silver bars, phone cards, Barber Dimes, and a lot more of this and that. However, my formal answer to what I collect is: Ancients. Greeks. Archaic to Hellenistic, from 650 to 38 BC: From the rise of Croesus to the fall of Cleopatra. Here is what I have and why: Miletus; 1/12 stater; 6thC; SGCV 3532(var); SNG vonA 2080

60. Schiller Institute -Pedagogy - Hyberbolic Functions- A Fugue Across 25 Centuries 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.schillerinstitute.org/educ/pedagogy/hyperbolic_bmd3.html

Home Search About Fidelio ... Dialogue of Cultures SCHILLER INSTITUTE Hyperbolic Functions: A Fugue Across 25 Centuries by Bruce Director May, 2002 This pedagogical exercise is part of an ongoing series on ``Riemann for Anti-Dummies.'' For more articles like this, visit the Schiller Institute Pedagogy List, which is updated frequently. To contact the authors, or Mr. LaRouche, who commissioned and directs these these pedagogical exercises, send an email to schiller@schillerinstitute.org . Each Figure is linked to a separate page. Use your back button to return to this article and this site. 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, in which Riemann speaks of a darkness that had shrouded human thought from Euclid to Legendre. After more than 2,000 thousand years of concentration on the matter, Riemann, standing on the shoulders of his teacher, Carl F. Gauss, lifted that darkness, by developing what he called, ``a general concept of multiply-extended magnitude.''

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