Other uses Infobox scientist name Euclid image Scuola di atene 07.jpg caption Euclid in Raphael Sanzio ... ethnicity Greek people Greek field Mathematics known for Euclidean geometry br Euclid s Elements Euclid s Elements Euclid IPAc en icon ju k l d respell EWK lid lang grc Eukleid s , floruit fl. 300 BC, also known as Euclid of Alexandria , was a Greek mathematics Greek mathematician ... I 323 283 BC . His Euclid s Elements Elements is one of the most influential works in the history ... of History. New York Metro Books. g. 12. ref In the Elements , Euclid deduced the principles of what is now called Euclidean geometry from a small set of axiom s. Euclid also wrote works on Perspective ... . Euclid is the anglicized version of the Greek language Greek name polytonic &mdash Eukle d s , meaning Good Glory . Life Little is known about Euclid s life, as there are only a handful of references to him. The date and place of Euclid s birth and the date and circumstances of his death .... No likeness or description of Euclid s physical appearance made during his lifetime survived antiquity. Therefore, Euclid s depiction in works of art is the product of the artist s imagination. The few historical references to Euclid were written centuries after he lived, by Proclus and Pappus of Alexandria . ref Joyce, David. Euclid . Clark University Department of Mathematics and Computer Science. http aleph0.clarku.edu djoyce java elements Euclid.html ref Proclus introduces Euclid only briefly ... geometry than Euclid s Elements , Euclid replied there is no royal road to geometry. ref Proclus ... the purported citation of Euclid by Archimedes has been judged to be an interpolation by later editors of his works, it is still believed that Euclid wrote his works before those of Archimedes ... Euclid.html Euclid of Alexandria . The MacTutor History of Mathematics archive. ref In addition, the royal ... the Great . ref Boyer, p. 96. ref In the only other key reference to Euclid, Pappus briefly mentioned ... more details
Euclid was a Greek mathematician from Alexandria who authored Euclid s Elements Elements . The name has subsequently been used to refer to People Euclid of Alexandria, the ancient Greek mathematician and author of the Elements the euclid symbol Euc , a dimensionless unit of Proportionality mathematics proportion , named after the mathematician Euclid of Megara , an ancient Greek philosopher Eucleides ... Euclid Contest , a math competition held by the Centre for Education in Mathematics and Computing Euclid programming language Euclid computer program NOTABLE???? Euclid, the University College London computer system in the 1980s based on GEC 4000 series minicomputers Euclid, a computer system used by Euroclear Euclid spacecraft , a space telescope built by ESA, to be launched in 2017 Higher education EUCLIDEuclid University , an intergovernmental organization Euclid University Consortium , a group of universities Geographical Related to Cleveland, Ohio Euclid Avenue disambiguation Euclid Avenue Cleveland, Ohio , a main street in Cleveland and its eastern suburbs Euclid, Ohio , an eastern suburb of Cleveland, Ohio Euclid Trucks , a manufacturer of heavy construction equipment, which was based in Euclid, Ohio Village of Euclid, Ohio v. Ambler Realty Co. , a U.S. Supreme Court case South Euclid, Ohio , a south eastern suburb of Cleveland, Ohio Places in New York State Euclid Avenue IND Fulton Street Line , a station of the New York City Subway Euclid Road, the main road of Syracuse University s Off Campus housing area Fiction Euclid, a supercomputer built by the fictional character Maximillian Cohen in the 1998 film film TS MB1B Euclid, a List of Cosmic Era mobile units Mobile armors mobile armor in the anime Gundam Seed Destiny Euclid, a town in the game Tales of Phantasia disambig pl Euclid de Euklid Begriffskl rung fr Euclide homonymie la Euclides discretiva lt Euklidas reik m s hu Eukleid sz egy rtelm s t lap nl Euclides no Euklid pl Euclid ujednoznacznienie ... more details
Euclid Avenue is a street name used in multiple U.S. municipalities. Euclid Avenue or Euclid Avenue Historic District may refer to in the United States by state Euclid Avenue, in San Bernardino County, California, which is California State Route 83 Euclid Avenue Ontario and Upland, California , a historic district listed on the National Register of Historic Places NRHP , along California State Route 83 other Euclid Avenue sections in Los Angeles County, California and in Orange County, California Highland Park Historic Business District at Euclid and Sixth Avenues , Des Moines, Iowa, List of RHPs in IA listed on the NRHP in Iowa Euclid Avenue Montrose Street Historic District , Worcester, Massachusetts, listed on the NRHP in Massachusetts Euclid Avenue IND Fulton Street Line , subway station in New York City Euclid Avenue Cleveland, Ohio , a main boulevard of Cleveland, Ohio Euclid Avenue Historic District Cleveland, Ohio , listed on the NRHP in Ohio Euclid Avenue Historic District Bristol, Virginia , List of RHPs in VA listed on the NRHP in Virginia disambig ... more details
Infobox Geopolitical organization name EUCLIDEuclid University symbol type Logo image symbol Flag EUCLID.png symbol width 100px membership 5 initial Participating States, 15 maximum between 2008 2015 admin center type Office admin center Brussels , Belgium language English language English br French language French leader title1 Secretary General leader name1 span style white space nowrap flagicon Pakistan Syed Zahid Ali span leader title2 High Steward leader name2 span style white space nowrap flagicon Marshall Islands Banny de Brum span established event1 as Euclid University Consortium Extension established date1 2005 established event2 ICCI Qatar Conference, January 2008 EUCLID Phase 2 MOU established date2 2008 established event3 MOU entry into force established date3 April 11, 2008 official website http www.euclid.int EUCLID , also called Euclid University , is an intergovernmental non profit institution chartered as a university and umbrella organization dedicated to sustainable ... language French . Background and constitution The formation of EUCLID as an independently chartered ... and recognition for the programs offered by the Euclid Consortium . Prior to the constitution of EUCLID ... of N Djamena , this approach effectively prevented the Euclid Consortium from being recognized ... 2008, Syed Zahid Ali, the senior official of IOSD, the administrative organization for the Euclid Consortium, presented to various governments a new legal framework called EUCLID Phase 2 ref ... from various governments had taken advantage of the Euclid s program, the new framework would ensure ..., structure and organization According to the constitutive instruments, EUCLIDEuclid University is defined ... and operations of EUCLID was approved on behalf of the Participating Parties by the following ... of EUCLID was approved on behalf of the Participating Parties by the following Girlyn Miguel October ... of West African States Notes Reflist External links Official http www.euclid.int EUCLIDEuclid ... more details
Image Euclid s orchard 1.png thumb One corner of Euclid s orchard, in which trees are labelled with the x co ordinate of their projection on the plane x y 1. In mathematics Euclid s orchard is an array of one dimensional trees of unit height planted at the lattice points in one quadrant of a square lattice . ref MathWorld urlname EuclidsOrchard title Euclid s Orchard ref More formally, Euclid s orchard is the set of line segments from i , j , 0 to i , j , 1 where i and j are positive integers. Image Euclid s orchard 3.png thumb left Plan view of one corner of Euclid s orchard. Trees marked by a solid blue dot are visible from the origin. Image Euclid s orchard 2.PNG thumb Perspective view of Euclid s orchard from the origin. The trees visible from the origin are those at lattice points m , n , 0 where m and n are coprime , i.e., where the fraction sup m sup sub n sub is in Irreducible fraction reduced form . The name Euclid s orchard is derived from the Euclidean algorithm . If the orchard is 3D projection projected relative to the origin onto the plane x y 1 or, equivalently, drawn in perspective graphical perspective from a viewpoint at the origin the tops of the trees form a graph of Thomae s function . The point m , n , 1 projects to math left frac m m n , frac n m n , frac 1 m n right . math References reflist External links http education.ti.com educationportal activityexchange download file.jsp?cid US&fileurl Math 2FMathGeneral 2F7737 2FAct3 OrchardProblem Brutus final.pdf Euclid s Orchard Grades 9 11 activities and problem sheet , Texas Instruments Inc. Category Greek mathematics Category Lattice points ... more details
Data Ancient Greek Greek , Dedomena is a work by Euclid . It deals with the nature and implications of given information in geometrical problems. The subject matter is closely related to the first four books of Euclid s Euclid s Elements Elements . Editions and translations Greek text Data , ed. H. Menge, in Euclidis opera omnia , vol. 6, Leipzig Teubner , 1896 http books.google.com books?id vLM2AAAAMAAJ Google Books , http www.wilbourhall.org index.html euclid Wilbour Hall English versions Translated by Robert Simson http books.google.com books?id ZacAAAAAMAAJ&pg PA363 1821 edition , http books.google.com books?id 5lN1sy51SwYC&pg PA294 1838 edition The Data of Euclid , trans. from the text of Menge by George L. McDowell and Merle A. Sokolik, Baltimore Union Square Press, 1993 ISBN 0 9635924 1 6 The Medieval Latin Translation of the Data of Euclid , translated by Shuntaro Ito , Tokyo University Press, 1980 and Birkhauser, 1998. ISBN 3 7643 3005 8 Category Ancient Greek mathematical works Category Works by Euclid Mathpublication stub fr Donn es Euclide ... more details
morefootnotes date June 2009 refimprove date June 2009 Image Chuqui001.jpg thumb Euclid truck in use at Chuquicamata copper mine in 1984 The Euclid Company of Ohio was a company specialized in heavy equipment ... into a section of General Motors and later on by Hitachi, Ltd . Now Euclid is a section of Volvo . History Founding The Euclid Company of Ohio specialised in off road heavy haulers, specifically ... road earth hauling. The Euclid Crane and Hoist Co, owned by George A. Armington and his 5 sons, was a large, respected and profitable operation, when they introduced the Euclid Automatic Rotary Scraper in 1924 soon followed by the Euclid Wheeler wheeled scraper. These earthmoving products were conceived ... model, the Euclid Contractors Special, designed to cope with hard ground, was even more successful ... of the Road Machinery Division, of Euclid Crane and Hoist, in 1926. Big public works construction programs of 1927 and 1928, requiring large excavations, saw further success of the Euclid Road Machinery division. Euclid produced Tractor crawler crawler wagons on tracks similar to Athey Wagons known as Euclid Tu Way haulers. The crawler track speed restriction was seen as a problem, and the next ... the first hydraulic Euclid dumpers around 1930. Great Depression The Great Depression did not appear to affect Euclid greatly, and the expansion of the earthmoving portion of the Euclid business, led to the incorporation of the Euclid Road Machinery Co, on July 11, 1931. This company remained a subsidiary of Euclid Armington Corp, until January 1, 1933, when the companies were separated and Euclid Road Machinery, became a producer of fast, off road earthmoving haulers. The Euclid company ... designed, extremely heavy duty, Euclid rear axle , fitted with a new 17.5 x 24 tire, which had just ... a beefed up, road going, chain drive AC Bulldog Mack. The next Euclid design, was an articulated ... as the Model Z or ZW. Company expansion Euclid went on to produce thousands of off road haulers ... more details
In mathematics , Euclid numbers are integer s of the form E sub n sub p sub n sub 1 strong , where p sub n sub is the primorial of p sub n sub which is the n th prime. They are named after the ancient Greek mathematician Euclid . It is sometimes falsely stated ref Michael Hardy and Catherine Woodgold, Prime Simplicity , Mathematical Intelligencer , volume 31, number 4, fall 2009, pages 44&ndash 52. ref that Euclid s theorem Euclid s celebrated proof of the infinitude of prime number s relied on these numbers. In fact, Euclid did not begin with the assumption that the set of all primes is finite. Rather, he said consider any finite set of primes he did not assume it contained just the first n primes, e.g. it could have been 3, 41, 53 and reasoned from there to the conclusion that at least one prime exists that is not in that set. ref cite web last first authorlink coauthors title Proposition 20 work publisher date url http aleph0.clarku.edu djoyce java elements bookIX propIX20.html doi accessdate quote ref The first few Euclid numbers are 3 number 3 , 7 number 7 , 31 number 31 , 211 number 211 , 2311, 30031, 510511 OEIS id A006862 . unsolved mathematics Are there an infinite number of prime Euclid numbers? It is not known whether or not there are an infinite number of prime Euclid numbers. E sub 6 sub 13 1 30031 59 x 509 is the first composite Euclid number, demonstrating that not all Euclid numbers are prime. br A Euclid number can not be a Square number square . This is because Euclid numbers are always congruent to 3 mod 4. For all n 3 the last digit of E sub n sub is 1, since E sub n sub 1 is divisible by 2 and 5. References to cite a web resource, use this template ref cite web last first authorlink coauthors title work publisher date url format doi accessdate quote ref reflist See also Euclid Mullin sequence Prime number The number of prime numbers Proof of the infinitude of the primes Euclid s theorem Primorial prime Category Integer sequences ... more details
Infobox settlement See Template Infobox settlement for additional fields and descriptions name City of Euclid ... alt image shield shield alt nickname motto image map Euclid CuyahogaCoOH.png map alt map caption ... title Founded established date 1796 ref name City of Euclid Statistics http www.cityofeuclid.com about census City of Euclid Statistics Bot generated title ref established title2 Incorporated established date2 1903 Village United States village ref name City of Euclid Statistics http www.cityofeuclid.com about census City of Euclid Statistics Bot generated title ref established title3 established date3 1930 city ref name City of Euclid Statistics http www.cityofeuclid.com about census City of Euclid Statistics Bot generated title ref founder seat type seat government footnotes government ... footnotes Euclid is a city in Cuyahoga County, Ohio , United States . It is part of the Greater ... nav jsf pages index.xhtml title American FactFinder2 accessdate 2010 03 20 ref In 2006 Euclid s population ... 04 39.csv title 2006 US Census Estimates by city date 2007 06 28 ref In 2009, Euclid celebrated its Bicentennial. History The city was named after Euclid , the Greek mathematics Greek mathematician . ref cite web url http www.epodunk.com cgi bin genInfo.php?locIndex 16680 title Profile for Euclid, Ohio publisher ePodunk accessdate 2010 06 03 ref Geography Euclid is located at coord 41 35 44 N ... of beach front and beach front property along the North. Bordering Euclid are Cleveland, Ohio Cleveland on the west, South Euclid, Ohio South Euclid and Richmond Heights, Ohio Richmond Heights on the south ... Park Briardale Golf Course Sims Park Euclid Metropark Wiiard Park Hillandale Park Pools 1 outdoor ... of those age 65 or over. Notable attractions history Euclid is the site of the 1926 case Village of Euclid, Ohio v. Ambler Realty Co. Euclid v. Ambler . The case opened the doors for municipalities across the United States to establish zoning ordinances. Euclid is home to the National Cleveland Style ... more details
Infobox programming language name Concurrent Euclid ConEuc logo paradigm Multi paradigm programming language multi paradigm structured programming structured , Imperative programming imperative , Functional programming functional year 1980 designer James Cordy and Ric Holt developer James Cordy and Ric Holt latest release version X.Y.Z release date mf yes YYYY MM DD latest release date typing strong typing strong , static typing static implementations dialects influenced by Euclid programming language Euclid , Communicating Sequential Processes influenced Turing Plus operating system Cross platform PDP 11 , VAX 11 , Motorola 68000 , Motorola 6809 license website file ext Concurrent Euclid ConEuc is a concurrent descendant of the Euclid programming language designed by James Cordy and Ric Holt , then at the University of Toronto , in 1980. ConEuc was designed for concurrent, high performance, highly reliable system software , such as operating systems , compilers and embedded microprocessor systems. The TUNIS operating system, a Unix variant, was implemented entirely in Concurrent Euclid. ConEuc extends a core subset of Euclid with process computing processes and Monitor synchronization monitors as specified by C.A.R. Hoare as well as language constructs needed for systems programming including separate compilation, variables at absolute addresses, type converters, long integers ... comparable to the best C programming language C compilers. Concurrent Euclid programs that used concurrency ... is a direct descendant of Concurrent Euclid and its Turing Plus programming language Turing Plus variant ... of Concurrent Euclid. Technical reports CSRI 115 July 1980 and CSRI 133 August 1981 , Computer Systems Research Institute, University of Toronto. 54 pages. R.C. Holt 1982. Concurrent Euclid ... R.C. Holt 1982. A short introduction to Concurrent Euclid. SIGPLAN Not. 17, 5 May. 1982 , 60 79. http ... in Concurrent Euclid. SIGOPS Operating Systems Review 16, 1 January 1982 , 4 5. Category Concurrent ... more details
The P le d Extension Universitaire Euclide or Euclid Consortium is a distance learning or on line educational consortium created in 2005 by the University of Bangui Central African Republic , the Universit Libre Internationale Belgium , and the International Organization for Sustainable Development . The original name was Euclid University Consortium but the structure was renamed in December 2008 in order to avoid confusion with EUCLIDEuclid University which is an intergovernmental university framework established in 2008 and a member school of the consortium. ref http www.euclid.int legal.asp ref History, Membership and Programs The Euclid initiative began in June 2004 as a cooperative project ... alongside ULI. ref http www.euclidconsortium.eu euclid en essentials.asp ref The University of N ... of Business and Economics The Pavel Florensky School of Theology and Ministry The Euclid School of Education Development Effective January 2009, the programs will be directly managed by EUCLIDEuclid University and the academic units will be absorbed in EUCLID. The Euclid Consortium is headed by a High ... Touaboye and an Executive President, Mr. Syed Zahid Ali who is the Secretary General of EUCLID ... of the participating universities. Member Universities EUCLIDEuclid University , primary ... Euclid University was initially used as a short translation of the French name, hence giving ... world. In order to correct this situation, the official English name was amended to Euclid University Consortium to emphasize the fact that Euclid was originally designed as a consortium, not a free ... to Euclid Consortium. Because the international directory of UNESCO does not list inter institutional ... formalized the constitution of EUCLIDEuclid University as an intergovernmental university framework ... indicated that EUCLID would also become a member of the Euclid University Consortium which remains an active ... s official site , in French and English http www.euclid.int EUCLIDEuclid University , official site ... more details
Euclid Kiriakovich Kyurdzidis , a.k.a Euclid Gurdjieff Greek language Gr. , b.22 February 1968 in Yessentuki is a Russian actor, best known for his role as Ruslan Shamayev in War 2002 film Voyna . He was born to ethnic Greek parents in Yessentuki , Stavropol Krai . He has two brothers and an older sister. External links http www.evklid.ru Official Site http www.imdb.com name nm1126492 IMDB Profile Persondata Metadata see Wikipedia Persondata . NAME Kyurdzidis, Euclid ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Kyurdzidis, Euclid Category Living people Category Russian actors Category Pontic Greeks Category Russian people of Greek descent Russia actor stub ru , ... more details
Unreferenced date November 2009 Euclid Network is a European Network of civil society leaders, which was launched in Paris in March 2007 as a result of a joint initiative by three civil society umbrella bodies across Europe Acevo UK , Ideell Arena Sweden and CDJES France . Since the launch, Euclid Network connects around 300 members from 31 different countries. The network wishes to promote professionalism and innovation with charities and NGO s for a more cohesive European civil society . The Executive Director of Euclid Network is Filippo Addarii . Aims Euclid Network has 4 core aims. These are as follows Professional development Euclid Network s mission is to empower third sector leaders across Europe. They offer formal training courses, peer learning opportunities, and e learning . In addition they have introduced are a range of innovative new methodologies such as job shadowing. Good governance Euclid Network views good governance as an essential component to good leadership because it enables leaders to prove the transparency and accountability of their organisation, and build bridges ... with their boards. Welfare partnership Euclid Network believes that social welfare has to be developed as a partnership between all sectors, with the third sector playing a crucial role. Euclid Network ... The biggest concern for most members is funding. Euclid Network has two key goals in this field they wish .... The other main activity that Euclid Network focuses on in this field is to enable members to explore ... . A successful joint Euclid Network Foreign Commonwealth Office FCO civil society development project is underway in Albania , Kosovo , and Montenegro , and this year, Euclid is bidding to scale up ..., which focuses on developing leadership through cross border exchange. Funding Euclid Network receives ... . External links Euclid Network official website http www.euclidnetwork.eu ACEVO http www.acevo.org.uk Third Sector News http www.thirdsector.co.uk DEFAULTSORT Euclid Network Category Directorates ... more details
Other persons Euclid Infobox Philosopher region Western Philosophy era Ancient philosophy color B0C4DE image name Euclid of Megara.jpg image size 200px image caption Euclid of Megara name Euclid of Megara ... Ichthyas , Eubulides , Clinomachus , Thrasymachus of Corinth Thrasymachus , Stilpo signature Euclid ... scholars locate the life span of Euclid between 435 and 365 BCE. Giovanni Reale, John R. Catan, 1987 ... translators in the Middle Ages often confused him with EuclidEuclid of Alexandria when discussing the latter s Euclid s Elements Elements . Life Euclid was born in Megara , ref Diogenes La rtius, ii ... had a ban on any citizen of Megara entering the city, Euclid would sneak into Athens after nightfall ... is also supposed to have reproved Euclid for his fondness for eristic disputes. ref Diogenes La rtius ... Euclid returned to Megara, where he offered refuge to Plato and other frightened pupils of Socrates. ref Diogenes La rtius, ii. 106 iii. 6 ref In Megara, Euclid founded a school of philosophy which became known as the Megarian school , and which flourished for about a century. Euclid s pupils were .... Euclid himself wrote six dialogues though none survive. These diaglogues were named the Lamprias ... File Domenico Marol Euclid of Megara.jpg thumb right Euclid of Megara Dressing as a Woman to Hear Socrates Teach in Athens , by Domenico Marol , c. 1650 None of Euclid s works have survived. The main .... 106 8 ref Euclid s philosophy was a synthesis of Eleatic and Socratic ideas. Socrates claimed that the greatest ... universal Being of the world. Mixing these two ideas, Euclid claimed that good is the knowledge ..., ii. 42 ref The idea of a universal good also allowed Euclid to dismiss all that is not good because he claimed that good covered all things on Earth with its many names. Euclid adopted the Socratic ... the study of philosophy. Euclid taught that virtues themselves, however, were simply the knowledge ..., ii. 106 ref and he declared, the opposite of Good does not exist. ref name laertius106 Euclid was also ... more details
Unreferenced date March 2010 Infobox Space telescope name Euclid image caption organization ESA alt names Dark Universe Explorer, Spectroscopic All Sky Cosmic Explorer major contractors nssdc id location Lagrangian point Lagrangian point L2 orbit type height period velocity accel gravity launch date 2017 launch location launch vehicle mission length 5 years planned wavelength 550 920 nm visible light visible br 0.8 1.7 Micrometre m infrared mass style Korsch telescope Korsch diameter convert 1.2 m abbr on area focal length coolant instrument 1 name instrument 1 characteristics Visible CCD imager instrument 2 name instrument 2 characteristics Near IR photometer instrument 3 name instrument 3 characteristics Near IR spectrometer website http sci.esa.int science e www object index.cfm?fobjectid 42266 Euclid homepage Euclid after the ancient Greek mathematician Euclid of Alexandria , the Father of Geometry is a planned space telescope , an M class mission of the Cosmic Vision ESA Cosmic Vision 2020 2025 , planned to be launched in 2017. Its goal to map the large scale distribution of the dark matter and characterize properties of dark energy . Originally two, similar proposals were submitted for the call, the Dark Universe Explorer DUNE , intended to measure effects of weak gravitational lensing and Spectroscopic All Sky Cosmic Explorer SPACE , to measure the baryon acoustic oscillations . Both proposals were selected and considered as equally important, and a combined mission was planned enabling cross checking the results of both missions. The survey covers 20,000 square degree s and also has a 40 square degree deep survey , approximately half of the whole sky not covered ... Reflist External links http sci.esa.int science e www object index.cfm?fobjectid 42266 Euclid homepage European Space Agency Category Space telescopes Category European Space Agency fr Euclid hu Euclid rt vcs fi Euclid ... more details
river.htm ref . After retiring from the game, Nick Euclid went on to referee in two international ... Nick Euclid as being instrumental in diverting him from a life of trouble to that of a dedicated athlete. A hugely popular member of the Queensland Rugby League QRL office, Euclid was a father ... 20070401 ref and the recently deceased Barry Grasshopper Gomersall. Nick Euclid famously handed http ... ref . Nick Euclid was for many years charged with nominating and appointing Queensland based ... ARLRA ref . In many of the years that Nick Euclid occupied his Board positions with the ARL and QRL Referees, he did so in an honorary capacity, not receiving remuneration. In June 2002, Nick Euclid ... ref a read v1 15.pdf Nick Euclid Medal is given annually in his honor to the best Young Rugby League Referee in Australia. References reflist Persondata Metadata see Wikipedia Persondata . NAME Euclid ... OF DEATH 27 September 2007 PLACE OF DEATH DEFAULTSORT Euclid, Nicholas Category Recipients of the Medal ... more details
Euclid s Optics , is a work on the geometry of vision written by the Greek mathematician Euclid around 300 BC. The earliest surviving manuscript of Optics is in Greek and dates from the 10th century AD. The work deals almost entirely with the geometry of vision, with little reference to either the physical or psychological aspects of sight. No Western scientist had previously given such mathematical attention to vision. Euclid s Optics influenced the work of later Greek, Islamic, and Western European Renaissance scientists and artists. Historical significance See also History of optics Writers before Euclid had developed theories of vision. However, their works were mostly philosophical in nature and lacked the mathematics that Euclid introduced in his Optics . ref Lingberg, D. C. 1976 . Theories of Vision from Al Kindi to Kepler . Chicago University of Chicago Press. p. 12. ref Efforts by the Greeks prior to Euclid were concerned primarily with the physical dimension of vision. Whereas Plato and Empedocles thought of the visual ray as luminous and ethereal emanation , ref Zajonc, A. 1993 . Catching the Light The Entwined History of Light and Mind . Oxford Oxford University Press. p. 25. ref Euclid s treatment of vision in a mathematical way was part of the larger Hellenistic trend to quantify a whole range of scientific fields. Because Optics contributed a new dimension to the study of vision, it influenced later scientists. In particular, Ptolemy used Euclid s mathematical ... , Leon Battista Alberti Alberti , and Albrecht D rer D rer used Euclid s Optics in their own ... Similar to Euclid s much more famous work on geometry, Euclid s Elements Elements , Optics begins ... the same methodology as the Elements . Content According to Euclid, the eye sees objects that are within ... to the eye. For example, in proposition 8, Euclid shows that the perceived size of an object is not related ... Works by Euclid ... more details
DISPLAYTITLE Euclid s Elements Image Title page of Sir Henry Billingsley s first English version of Euclid ... Billingsley s first English version of Euclid s Elements , 1570 Euclid s Elements Greek language Greek ... of 13 books written by the Greek mathematics Greek mathematician Euclid in Alexandria circa 300 ... year 1991 chapter Euclid of Alexandria page 101 quote With the exception of the Sphere of Autolycus, surviving work by Euclid are the oldest Greek mathematical treatises extant yet of what Euclid wrote ... . It has proven instrumental in the development of logic and modern science . Euclid s Elements ... Guy Wilson, page 278. Published by Routledge Taylor and Francis Group. Quote Euclid s Elements subsequently ... Boyer title year 1991 chapter Euclid of Alexandria page 100 quote As teachers at the school he ... textbook ever written the Elements Stoichia of Euclid. ref and influential ref name Boyer Influence ... Euclid of Alexandria page 119 quote The Elements of Euclid not only was the earliest major Greek mathematical ... work has had an influence comparable with that of Euclid s Elements . ref textbook ever ... university students, knowledge of at least part of Euclid s Elements was required of all students ... of Euclid s Elements , c. 1309 1316 the oldest surviving Latin translation of the Elements is a 12th ... by some original work. Proclus , a Greek mathematician who lived several centuries after Euclid, wrote in his commentary of the Elements Euclid, who put together the Elements, collecting many of Eudoxus ... Account of the History of Mathematics, 4th ed., 1908, p. 54 ref Euclid often replaced fallacious ... Theon of Alexandria produced an edition of Euclid which was so widely used that it became the only ... to Euclid s Original Text Circa 850 an http www.ibiblio.org expo vatican.exhibit exhibit d mathematics ... received the Elements from the Byzantines in approximately 760 this version, by a pupil of Euclid ... of Euclid in the late ninth century. ref L.D. Reynolds and Nigel G. Wilson, Scribes and Scholars ... more details
Essay like date January 2011 File 105th and Euclid Today.jpg thumb letf 105th and Euclid Today East 105th Street and Euclid Avenue is the most famous intersection in the city of Cleveland, Ohio . The legendary ... heyday, substantiated 105th and Euclid s landmark status. Today, in spite of decades of resistance ... Cemetery http www.ectcf.org hezekiah ford and his descendent.htm ref , which was adjacent to the Euclid Avenue Congregational Church ref Euclid Avenue Congregational Church http www.universitycircle.org detail location.aspx?type location&id 142&cat §ion address 9606 Euclid Avenue Cleveland OH 44106 ... new location on the corner of Euclid Avenue and 96th Street. ref Euclid Avenue Congregational Church http blog.cleveland.com metro 2010 03 euclid avenue congregational c.html ref In later years, the most popular attraction on the site facing Euclid Avenue ref Post, Charles Asa 28 October 1848 2 May ... by another equally colorful era. File 105th and Euclid in 1981.jpg thumb 105th and Euclid in 1981 ... corner block and brought renewed prosperity to the black community. The new 105th and Euclid , sometimes ..., University Circle Properties Development, Inc. UCPD Inc. , businesses fronting on Euclid Avenue Cleveland, Ohio Euclid Avenue from East 107th Street to East 105th Street included UCPD, Inc. Headquarters ... Fly film Super Fly . With Curtis Mayfield s soundtrack wafting out onto Euclid Avenue Cleveland, Ohio Euclid Avenue , black Clevelanders by the thousands lined up for the inner city version of a Hollywood ... theater as the movie genre grew in popularity. Redevelopment The transformation of the 105th and Euclid ... of years of legal battles and courtroom confrontations ref Cleveland Press, Pg.19 A. 105th & Euclid ... on Euclid Avenue August 21, 1979 Rice, Joseph D. http www.plaindealer.com newsroom archives.php. ... of Euclid Avenue between E. 105th and E. 107th Streets. ref Verle R.Majied, Studio Majied, A Photographic ... driven out of the 105th and Euclid area and defeated under dubious land grab tactics, one man, Winston ... more details
Unreferenced date December 2009 In mathematics , Euclid s lemma Greek language Greek Polytonic is an important lemma mathematics lemma regarding divisor divisibility and prime number s. In its simplest form, the lemma states that a prime number that divides a multiplication product of two integer s must divide one of the two integers. This key fact requires a surprisingly sophisticated mathematical proof proof using B zout s identity , and is a necessary step in the standard proof of the fundamental theorem of arithmetic . Euclid s lemma also known as Euclid s first theorem appears as proposition 30 in Book VII of Euclid s Elements . In modern notation If math p math is prime and math p mid ab math then math p mid a math and or math p mid b math . Here math mid math means divides that is, math x mid y math if math x math is a divisor of math y math . In modern mathematics, Euclid s lemma is often used to refer to the following generalization of this statement If math n mid ab math and math n math and math a math are relatively prime , then math n mid b math . This statement reduces to Euclid s proposition 30 in the case where math n math is prime. Proof of Euclid s lemma The standard proof of Euclid s lemma uses B zout s identity . This states that, for any relatively prime integers x and y , there exist integers r and s such that math rx sy 1. math To prove Euclid s lemma, suppose that p is a prime factor of ab , but that p is not a factor of a . Then p and a must be relatively prime, so there exist integers r and s such that math rp sa 1. math Multiplying through by b gives math rb p s ab b. math Now, the first term on the left is clearly a multiple ... http books.google.com books?id r HuAAAAMAAJ&q Euclid Lemma&dq Euclid Lemma&hl en&ei au9aTaCMEo7EsAOa47WeCg ... the choice of p . In conclusion, the theorem must be true. Example Euclid s lemma in plain language ... 2 . See also Euclidean algorithm DEFAULTSORT Euclid s Lemma Category Number theory Category Lemmas Category ... more details
Infobox settlement official name Euclid, Minnesota settlement type Unincorporated community nickname motto Images image skyline imagesize image caption image flag image seal Maps image map mapsize map caption image map1 mapsize1 map caption1 pushpin map Minnesota Location coordinates region US MN subdivision type List of countries Country subdivision name United States subdivision type1 Political divisions of the United States State subdivision name1 Minnesota subdivision type2 List of counties in Minnesota County subdivision name2 Polk County, Minnesota Polk Government government footnotes government type leader title leader name leader title1 leader name1 established title established date Area unit pref area footnotes area magnitude area total km2 area land km2 area water km2 area total sq mi area land sq mi area water sq mi Population population as of population footnotes population total population density km2 population density sq mi General information timezone Central Time Zone Central CST utc offset 6 timezone DST CDT utc offset DST 5 elevation footnotes elevation m elevation ft 896 latd 47 latm 58 lats 19 latNS N longd 96 longm 38 longs 20 longEW W coordinates display Area postal codes & others postal code type ZIP code postal code 56722 area code Area code 218 218 blank name Geographic Names Information System GNIS feature ID blank info 643426 GR 3 blank1 name blank1 info website footnotes Euclid is an unincorporated community in Polk County, Minnesota Polk County , Minnesota , United States . Euclid is located on U.S. Route 75 mi to km 13.5 north of Crookston, Minnesota Crookston . Euclid has a post office with ZIP code 56722. ref http www.zipinfo.com cgi local zipsrch.exe?cnty cnty&zip 56722&Go Go ZIP Code Lookup ref References reflist Polk County, Minnesota Category Polk County, Minnesota Category Unincorporated communities in Minnesota polkCountyMN geo stub ... more details
Infobox Album See Wikipedia WikiProject Albums Name Euclid s Nightmare Type Album Artist John Zorn & Bobby Previte Cover Euclid s Nightmare.jpg Released March 2, 1997 Recorded 1997 Genre Avant garde Length 41 03 Label Depth of Field Producer Bobby Previte & John Zorn Reviews Allmusic class album id r313097 rating 3 5 Euclid s Nightmare is an album of improvised music by Bobby Previte and John Zorn . The album was released on the Depth of Field label in 1997. The album comprises 27 untitled tracks of which several are intentionally identical tracks 7 and 18 tracks 3 and 20 and tracks 5 , 14 , and 27 . ref Roussel, P. http home.arcor.de nyds exp discogs zorn.htm Discography of John Zorn accessed July 21, 2008. ref Track listing 1 07 1 05 1 09 1 06 2 02 1 06 1 03 2 00 1 01 1 41 1 05 0 59 1 07 2 02 2 06 2 04 1 01 1 03 3 43 1 13 2 06 2 38 1 13 1 07 1 02 1 19 4 01 All compositions by Previte Zorn Recorded at Avatar Recording Studios, New York City on March 2, 1997 Personnel Bobby Previte drums John Zorn alto References reflist Category John Zorn albums Category 1997 albums ... more details
File Pacioli.jpg thumb 300px Jacopo de Barbari ? . A Portrait of Luca Pacioli 1495 with scheme of Euclid s theorem left Euclid s theorem is a fundamental statement in number theory that asserts that there are Infinite set infinitely many prime number s. There are several well known proofs of the theorem. Euclid s proof Euclid offered the following proof published in his work Euclid s Elements Elements Book IX, Proposition 20 ref James Williamson translator and commentator , The Elements of Euclid, With Dissertations , Clarendon Press , Oxford, 1782, page 63. ref and paraphrased here. Take any finite list of prime numbers p sub 1 sub , p sub 2 sub , ..., p sub n sub . It will be shown that some additional prime numbers not in this list exist. Let P be the product of all the prime numbers in the list P p sub 1 sub ... p sub n sub . Let q P 1 1 more than this product. Then, q is either prime or not If q is prime then there is at least one more prime than is listed. If q is not prime then some prime factor p divides q . This factor p is not on our list if it were, then it would divide P since P is the product of every number on the list but as we know, p divides P 1 q . Then p would have to divide the difference of the two numbers, which is P 1 &minus P or just 1. But no prime number divides 1 so there would be a contradiction, and therefore p cannot be on the list. This means at least one more prime number exists beyond those in the list. This proves that for any finite ... many prime numbers. It is often erroneously reported that Euclid proved this result by proof by contradiction ... Pinasco Juan Pablo Pinasco has written the following proof. ref Juan Pablo Pinasco, New Proofs of Euclid ... External links MathWorld urlname EuclidsTheorems title Euclid s Theorem http aleph0.clarku.edu djoyce java elements bookIX propIX20.html Euclid s Elements, Book IX, Prop. 20 Euclid s proof, on David Joyce ... more details
Summary Euclid Avenue in Cleveland, under construction for the Euclid Corridor Project in late 2007. Licensing self GFDL cc by sa 3.0,2.5,2.0,1.0 Category Images of Cleveland, Ohio ... more details
Euclid is a CAD software which was developed since 1980 by the French company Matra Matra Datavision . Matra then developed EUCLID QUANTUM, a new generation in 1996, on the platform CAS.CADE Computer Aided Software for Computer Aided Design and Engineering . As in 1998 Matra Datavision specialized in software service provider, Dassault Syst mes acquired QUANTUM products Euclid Styler and Euclid Machinist. ref http archives.lesechos.fr archives 1998 LesEchos 17791 62 ECH.htm ref In 1999 Matra Datavision published CASCADE in open source on the Internet as Open CASCADE . ref http www.opencascade.org about profile history ref The BRL CAD CAD software imports and exports to the EUCLID file format . References references DEFAULTSORT Euclid Computer Program Category Computer aided design software CAD software stub pl Euclid system zh Euclid ... more details
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