61. Euclid's Elements Welcome to the Platonic Solids as Demonstrated in Book Thirteen of euclid's Elements. http://www.dform.com/projects/euclid/home.html

Welcome to the Platonic Solids as Demonstrated in Book Thirteen of Euclid's Elements This site demonstrates the construction of the five Platonic Solids from Book 13 of Euclid's Elements This project has brought forth much philosophizing on the nature of the internet, geometry, and the world, and how we orient ourselves in it. In order to orient yourself, we recommend taking a look at how to best view the site, and to take a look at the resources available on Euclid on the WWW. Enjoy. Prop 13 -the pyramid Prop 14 - the octahedron Prop 15 - the cube Prop 16 - the icosahedron Prop 17 - the dodecahedron A Glossary Of Terms This site is supported by Brendon F. Buckley of the Metropolitan School District of Pike Township, Indianapolis, Indiana.

62. Euclid Forum Frigate Discussion forum and live chat devoted to euclid's life and works. http://jollyroger.com/zz/yna3d/Euclidhall/shakespeare1.html

Euclid Forum Frigate Post Message The Jolly Roger One Page Version WRITER ... Online Education Euclid Forum Frigate THE GREAT BOOKS FLEET Carolinanavy.com Quarterdeck Classicals.com ... hatteraslight.com Welcome to the Euclid Forum Frigate. Post yer opinion, a link to some of yer work, or yer thoughts regarding the best books and criticisms concerning Euclid. We'd also like to invite ye to sail on by the Euclid Live Chat , and feel free to use the message board below to schedule a chat session. And the brave of heart shall certainly wish to sign their souls aboard The Jolly Roger Oak planks of reason, riveted with rhyme, designed to voyage across all of time. The Thirteen Books of Euclid's Elements Post Message The Jolly Roger One Page Version legitimate money krandell legitimate money krandell legitimate money krandell Exkursionen Sprachreisen Spanisch Lernen Sprachschule Spanisch www.123TeachMe.com Sprachkurse Sprachschule Spanisch Schule Südamerika www.123TeachMe.com Exkursionen Sprachreisen Spanisch Lernen Sprachschule Spanisch www.123TeachMe.com Sprachkurse Sprachschule Spanisch Schule Südamerika www.123TeachMe.com Exkursionen Sprachreisen Spanisch Lernen Sprachschule Spanisch www.123TeachMe.com

63. Euclid High School athletics athletics awards calendar courses faculty guidance menu newsletternewspaper profile euclid Schools Principal Ron Seymour Associate Principal http://www.euclid.k12.oh.us/EHS/

Principal Ron Seymour Associate Principal: Claudia Spencer Unit Principals Tina Elliot - 12 Elie Thomas - 11 Alline Tyler-Sweeney - 9 Patrick Vuyancih - 10 711 East 222nd Street Euclid, Ohio 44123 Student of the Month Susan Adamic Art John Kulbis AV Holly Yanacek English Leslie Penko Foreign Language Lauren Hill Health Layota Davis Social Studies Jennifer Vandegrift Instrumental Music Anel Altmetavcic Math Nate Miller Modified Resources Archie Smith Orchestra Terrence Bolden Physical Education Melissa Paoloni Science Stephanie Maxwell Vocal Music Jethro Guilamo Naval Science Michael Crane Industrial Technology

64. Euclid Chamber Of Commerce Contains information about the chamber, city resources, Leadership euclid, events and member businesses. http://www.euclidchamberofcommerce.com/

Chamber of Commerce Home Our Mission About Us Newsletter ... Contact Information Members Member Directory Member Spotlight Member Application Resources The City of Euclid Euclid Public Library Euclid City Schools Additional Resources Search For a Member All results 5 results 10 results 20 results 30 results 50 results Welcome! Thank you for visiting the Euclid Chamber of Commerce. We invite you to explore our Website to learn more about the Chamber, membership benefits, special customer discounts, Leadership Euclid, Chamber events and our Euclid member businesses (listed by category). The Chamber is committed to serving area businesses and residents to advance the economic welfare of the City of Euclid, Ohio. Euclid is located on the shores of Lake Erie and boasts of incredible sunsets. Euclid is a residential community with a good industrial base. It is a friendly community where people walk the parks, business areas and neighborhoods. Euclid is a great place to live, work and do business. The Chamber will continually update our Web Site, so please visit us often. Look for member business offers of discounts and specials via this Website. If you should need additional information or have any questions, please call the Chamber office at (216) 731-9322

65. Euclid's Algorithm euclid's Algorithm. euclid's algorithm appears as the solution to theProposition VII.2 in the Element's Given two numbers not prime http://www.cut-the-knot.com/blue/Euclid.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Euclid's Algorithm Euclid's algorithm appears as the solution to the Proposition VII.2 in the Element's: Given two numbers not prime to one another, to find their greatest common measure. The algorithm is based on the following two observations: gcd (a, b) = b. This is indeed so because no number (b, in particular) may have a divisor greater than the number itself (I am talking here of non-negative integers.) If a = bt + r, for integers t and r, then gcd(a, b) = gcd(b, r). Indeed, every common divisor of a and b also divides r. Thus gcd(a, b) divides r. But, of course, . Therefore, gcd(a, b) is a common divisor of b and r and hence gcd(a, b) gcd(b, r). The reverse is also true because every divisor of b and r also divides a. Example Let a = 2322, b = 654. gcd(2322, 654) = gcd(654, 360) gcd(654, 360) = gcd(360, 294) gcd(360, 294) = gcd(294, 66) gcd(294, 66) = gcd(66, 30) gcd(66, 30) = gcd(30, 6) gcd(30, 6) = 6 Therefore, gcd(2322,654) = 6. For any pair a and b, the algorithm is bound to terminate since every new step generates a similar problem (that of finding gcd) for a pair of smaller integers. Let Eulen(a,b) denote the length of the Euclidean algorithm for a pair a,b.

66. Euclid Provides a detailed biography and related links. http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Euclid.html

Euclid of Alexandria Born: about 325 BC Died: about 265 BC in Alexandria, Egypt Click the picture above to see six larger pictures Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Euclid of Alexandria is the most prominent mathematician of antiquity best known for his treatise on mathematics The Elements . The long lasting nature of The Elements must make Euclid the leading mathematics teacher of all time. However little is known of Euclid's life except that he taught at Alexandria in Egypt. Proclus , the last major Greek philosopher, who lived around 450 AD wrote (see [1] or [9] or many other sources):- Not much younger than these pupils of Plato is Euclid, who put together the "Elements", arranging in order many of Eudoxus 's theorems, perfecting many of Theaetetus 's, and also bringing to irrefutable demonstration the things which had been only loosely proved by his predecessors. This man lived in the time of the first Ptolemy; for Archimedes , who followed closely upon the first Ptolemy makes mention of Euclid, and further they say that Ptolemy once asked him if there were a shorted way to study geometry than the Elements, to which he replied that there was no royal road to geometry. He is therefore younger than Plato 's circle, but older than

67. Euclid's Algorithm euclid's Game. The game is really very simple. It helps clarify the euclid'salgorithm and the notion of the Greatest Common Divisor of two integers. http://www.cut-the-knot.com/blue/EuclidAlg.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Euclid's Game At the beginning of this simple game, the applet below displays a board with two numbers. At any time you can use the edit control to input a positive difference of any two numbers already present on the board. The loser is the player unable to make a move. If you wish the computer to move first, check the box "Please start". The game is really very simple. It helps clarify the Euclid's algorithm and the notion of the Greatest Common Divisor why? ). Therefore, the total number of integers that will be written on the board equals N/gcd(N,M). From here you may calculate whether it's preferable to start or let the computer make the first move. Modular Arithmetic Differences and Similarities Solutions to some problems Chinese Remainder Theorem ... Euclid's Algorithm Euclid's Game Binary Euclid's Algorithm gcd and the Fundamental Theorem of Arithmetic Extension of Euclid's Algorithm Stern-Brocot Tree ... Alexander Bogomolny Assume the game is over - it's impossible to add a new difference. Let a be the smallest number present. Then the collection of the numbers on the board coincides with the set A of all multiples of a not exceeding the largest of M and N. The proof is very similar to the way we established a fundamental property of gcd.

68. Biography Of Euclid Biography of euclid. Sv euclid Life and Works by Ivor BulmerThomas.Heath, Thomas L. The Thirteen Books of euclid's Elements, 2 vols. http://www.lib.virginia.edu/science/parshall/euclid.html

Biography of Euclid Euclid ( PORTRAIT - 58K ) lived in Alexandria, Egypt, around 300 B.C. After receiving his education, probably at Plato's Academy in Athens, or from some of Plato's students, Euclid became a teacher and scholar at the school in Alexandria known as the Museum. While there, he wrote his most influential work, the Elements Sample page - 322K ) In this treatise, consisting of thirteen books, Euclid compiled and systematically arranged many of the major mathematical results known in his day. Beginning with a list of definitions, postulates and axioms, he proved one proposition after another, basing each proof only on those results that had preceded it. This axiomatic method, as it is known today, served as the standard for scientific argumentation for later generations. Likewise, the content of the Elements , consisting of geometry and number theory, makes up part of the core of basic mathematics even today. TOP MAIN DOCUMENT CONTENTS FIRST MENTION To return to place in document from which you came, click on your browser's BACK BUTTON. Selected Biographical References Gillispie, Charles C. ed.

69. South Euclid-Lyndhurst Public Library Provides overview of services, history, and hours of operation. http://www.southeuclidlyndhurst.locality.com

Your Browser Does Not Support Javascript The Locality website makes use of JavaScript for superior performance. Either your browser does not support JavaScript, or you have it turned off. For your convenience we have provided a list of supported browsers , links to the latest browsers , and an explanation of how to enable JavaScript in your browser. If you think that you were incorrectly taken to this page, please email us at: support@locality.com Supported browsers The following browsers are supported by the Locality website: Internet Explorer 4.0 or higher Download the Latest Browser Click on one of the links below to get the latest browser versions: Microsoft Internet Explorer Enabling JavaScript Following are the directions to enable Javascript: In Microsoft Internet Explorer 4.0 or higher, select either 'Low", "Medium", or "High" from the Options/Security screen under the View menu.

70. Sample Page From Euclid's Elements Sample Page from euclid's Elements. The scholium in the margin is one of thescholia Vaticana. Top of this Document Return to Biography of euclid. http://www.lib.virginia.edu/science/parshall/elementsamp.html

Sample Page from Euclid's Elements This is a page taken from the Bodleian Library manuscript of the Elements , D'Orville 301, written in the year 888. The scholium in the margin is one of the scholia Vaticana. Top of this Document Return to Biography of Euclid. Return to Main Document. Return to Portrait Index.

71. Thabit Gives information on background and contributions to noneuclidean geometry, spherical trigonometry, number theory and the field of statics. Was an important translator of Greek materials, including euclid's Elements, during the Middle Ages. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Thabit.html

Al-Sabi Thabit ibn Qurra al-Harrani Born: 826 in Harran, Mesopotamia (now Turkey) Died: 18 Feb 901 in Baghdad, (now in Iraq) Click the picture above to see a larger version Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Thabit ibn Qurra was a native of Harran and a member of the Sabian sect. The Sabian religious sect were star worshippers from Harran often confused with the Mandaeans (as they are in [1]). Of course being worshipers of the stars meant that there was strong motivation for the study of astronomy and the sect produced many quality astronomers and mathematicians. The sect, with strong Greek connections, had in earlier times adopted Greek culture, and it was common for members to speak Greek although after the conquest of the Sabians by Islam, they became Arabic speakers. There was another language spoken in southeastern Turkey, namely Syriac, which was based on the East Aramaic dialect of Edessa. This language was Thabit ibn Qurra's native language, but he was fluent in both Greek and Arabic. Some accounts say that Thabit was a money changer as a young man. This is quite possible but some historians do not agree. Certainly he inherited a large family fortune and must have come from a family of high standing in the community.

72. The Internet Classics Archive | Works By Euclid Buy Books and CDROMs, Get help Help. Works by euclid The ElementsFrom the Perseus Project Read discussion 6 comments © 1994-2000 http://classics.mit.edu/Browse/browse-Euclid.html

Home Search Buy Books and CD-ROMs ... Help Works by Euclid The Elements From the Perseus Project Read discussion : 6 comments

73. Acacia Lodge #651 Meeting second and forth Friday, September thru June, at 730 P.M. Officers, events. http://www.4masons.org/acacia651.html

Acacia Lodge #651 2003 Officers of Acacia Lodge Worshipful Master -W.B. Charles Wright Senior Warden- W.B. Errol Savage Junior Warden - W.B. Tom Daly Jr. Senior Deacon - Bro. Gregory Guy Junior Deacon - Bro. Ted Daly Secretary - W.B. William Dornback III Treasurer - R.W.Bro Terry MacDonald Meeting second and forth Friday, September thru June, at 7:30 P.M. At the Euclid Masonic Temple 27271 Tungstan Road Euclid, Ohio 44132 All Master Masons, who are members of lodges recognized by the Grand Lodge of Ohio, are welcome to attend meetings of Acacia Lodge. For information on the International Guild of Masonic Webmasters Click Here.

74. Euclid Corporate Site Copyright © 20012003 euclid. All Rights Reserved. http://www.euclid.ru/

c 12-ãî îêòÿáðÿ CREATIVE PC-CAM 300 1.3 MP Ïîÿâèëèñü îïèñàíèÿ barebone: MSI Hermes 845GV SHUTTLE Ïîÿâèëîñü îïèñàíèå 16-ñêîðîñòíîãî DVD-ROM ïðèâîäà: LG GDR-8161B Ïîÿâèëîñü îïèñàíèå WEB-êàìåðû: CREATIVE WebCam Pro LG MICRONET : Hub - ; Switch - ; Print Server - LG SONY SONY BENQ BENQ BENQ SONY BTC HP Ïîÿâèëîñü îïèñàíèå barebone: MSI Hermes 845GV-LE SONY S51R B S71R B ïðåçåíòàöèÿ íîâîé ëèíåéêè ìîíèòîðîâ LG (íà àíãë. ÿçûêå, îáú¸ì 1,5 ÌÁ)

75. Great Books Index - Euclid GREAT BOOKS INDEX. euclid (about 365about 300 BC). An Index to OnlineGreat Books in English Translation. Editions of euclid's Elements. http://books.mirror.org/gb.euclid.html

GREAT BOOKS INDEX Euclid (about 365about 300 BC) An Index to Online Great Books in English Translation AUTHORS/HOME TITLES GB CAFE ABOUT GB INDEX ... BOOK LINKS Editions of Euclid's Elements Elements Articles The Thirteen Books of Euclid's Elements HTML edition (Perseus, Tufts) Translated and with Commentary by T.L. Heath. Heath's commentary is excellent background information. HTML pages Interesting use of Java in diagrams. [Back to Top of Page] Links to Information About Euclid Biography of Euclid (History of Math Archive) [Back to Top of Page] Requests for Additional Material Please advise of other online editions you may discover. Have you written an online publication about Euclid? Please send the URL so it may be considered for a link. Comments and Corrections If you have comments or questions about the works listed on this page, you may enjoy discussing them at the Great Books Cafe If you find an error in this web page or wish to contact the editor, you can send e-mail to Ken Roberts at ken@mirror.org The editor cannot assist with school assignments. [Back to Top of Page] GREAT BOOKS INDEX MENU Great Books Index Home Page and Author List List of All Works by Author and Title [90KB] Great Books Cafe - A Discussion Area for the Great Books About the Great Books Index ... Mortimer J. Adler on Selecting the Great Books

76. WELCOME TO EUCLID Meets 1st and 3rd Friday, except July, August, legal holidays. http://community.webtv.net/ljs-ahs/WELCOMETOEUCLID

THE SCOTTISH TUNE PLAYING IS TITLED "THE MASONS APRON" BRO.GEORGE WASHINGTONS MASONIC APRON OUR TEMPLE IS LOCATED AT 200 DIVISION AVENUE HASBROUCK HEIGHTS NEW JERSEY GRAND MASTER OF NEW JERSEY M.W. Larry S. Plasket 17 Carlisle Court Mt. Laurel, N.J. 08054-2349 DISTRICT DEPUTY GRAND MASTER R.W. Joseph J. Kubik 62 Roehrs Drive Wallington N.J. 07057-2114 DISTRICT RITUAL INSTRUCTOR R.W. Eric E. Johansson 15 Elema Place Clifton, N.J. 07011 Euclid Lodge meets on the first and third Friday of every month except July and August,legal holidays and the second Friday in December. LODGE OFFICERS FOR 2003 Worshipful MasterWB. Paul M. Ferreira Senior Warden John R. Schulze Junior Warden- Robert J. Searle Treasurer..................................W.B. Michael J. DeMan,P.M. Secretary...................................R.W. Gilbert A. Hunt, PDDGM Chaplain.....................................M.W. Otto Gerhig Jr. ,P.G.M. Chaplain.....................................R.W. John R. Wright, P.G.C. Senior Deacon.............................Bruce W Werner, Sr. Junior Deacon..............................Michael F. Giuffre

77. AccuWeather.com - EUCLID, OH Local Weather Forecast Current, hourly, and extended forecasts, UV index, and radar maps. http://www.accuweather.com/adcbin/local_index?zipcode=44132

78. Euclid Timber Frames Designs, manufactures, and builds timber frame homes, commercial buildings, barns, great rooms, porches, and other structures. Online timber frame primer and photo gallery. http://www.euclidtf.com

79. Epworth-Euclid UMC Provides schedule of services, fellowship opportunities, and mission projects.Category Regional North America Religion Methodist......EPWORTHeuclid UNITED METHODIST CHURCH. Gathering to Worship This SundayMusic Ministry Locator Map Nurturing Our Faith Sunday School http://www.epworth-euclid.org/

EPWORTH-EUCLID UNITED METHODIST CHURCH Gathering to Worship This Sunday Music Ministry Locator Map Nurturing Our Faith Sunday School Study Groups Membership Development and Nurture Living Our Faith Neighborhood Lunch Mission Projects United Methodist Women Realization of a Dream Fellowship Opportunities UM Youth Fellowship Explorers Contact Us staff@epworth-euclid.org Pray for Peace during Lent more Prayer Room is open in Meditation Chapel for prayer and meditation any time the church is open. Join us in worship, Sundays 11 AM "Jesus Predicts His Death, Resurrection; Cleanses the Temple" subject of Sunday services more Tuesday Lenten Program more Chancel Choir Presents Requiem in Memoriam by Eileen Marie Moore Sunday, April 6, 11 AM more Meal in Upper Room Maundy Thursday, April 17 more Lent: Retreat

80. Welcome To Euclid Hospital http://www.euclidhospital.org/

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