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Encyclopedia > Euclid
Euclid

Born fl. 300 BC
Residence Alexandria, Egypt
Nationality Greek
Fields Mathematics
Known for Euclid's Elements

Euclid (Greek: Εὐκλείδης — Eukleidēs), fl. 300 BC, also known as Euclid of Alexandria, "The Father of Geometry" was a Greek mathematician of the Hellenistic period who almost certainly flourished during the reign of Ptolemy I (323 BC283 BC). His Elements is the most successful textbook in the history of mathematics. In it, the principles of Euclidean geometry are deduced from a small set of axioms. Euclid's method of proving mathematical theorems by logical deduction from accepted principles remains the backbone of all mathematics, imbuing that field with its characteristic rigor. He was thought of as a weird, solitary man. Euclid may refer to: Euclid of Alexandria, the ancient Greek mathematician and author of the Elements the euclid (symbol Euc), a dimensionless unit of proportion, named after the mathematician [1] [2] Euclid of Megara, an ancient Greek philosopher Eucleides, archon of Athens 403-2 NC. the Euclid programming language the... Image File history File links Euklid-von-Alexandria_1. ... Floruit (or fl. ... This article is about the city in Egypt. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems... Floruit (or fl. ... Centuries: 4th century BC - 3rd century BC - 2nd century BC Decades: 350s BC 340s BC 330s BC 320s BC 310s BC - 300s BC - 290s BC 280s BC 270s BC 260s BC 250s BC Years: 305 BC 304 BC 303 BC 302 BC 301 BC - 300 BC - 299 BC 298 BC... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... The term Hellenistic (derived from HéllÄ“n, the Greeks traditional self-described ethnic name) was established by the German historian Johann Gustav Droysen to refer to the spreading of Greek culture over the non-Greek people that were conquered by Alexander the Great. ... For the unrelated astronomer, see Ptolemy Ptolemy I Soter (367 BC–283 BC), ruler of Egypt (reigned 323 BC - 283 BC) and founder of the Ptolemaic dynasty. ... On his way from Ecbatana to Babylon, Alexander the Great fights and crushes the Cossaeans. ... Centuries: 4th century BC - 3rd century BC - 2nd century BC Decades: 330s BC 320s BC 310s BC 300s BC 290s BC - 280s BC - 270s BC 260s BC 250s BC 240s BC 230s BC 288 BC 287 BC 286 BC 285 BC 284 BC 283 BC 282 BC 281 BC 280... The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems... Three textbooks. ... For a timeline of events in mathematics, see timeline of mathematics. ... Euclid Euclidean geometry is a mathematical system attributed to the Greek mathematician [[Euclid]] of Alexandria. ... This article is about a logical statement. ... Look up theorem in Wiktionary, the free dictionary. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... For the medical term see rigor (medicine) Rigour (American English: rigor) has a number of meanings in relation to intellectual life and discourse. ...


Euclid also wrote works on perspective, conic sections, spherical geometry, and possibly quadric surfaces. Perspective when used in the context of vision and visual perception refers to the way in which objects appear to the eye based on their spatial attributes or dimension and the position of the eye relative to the objects. ... Wikibooks has more on the topic of Conic section Types of conic sections Table of conics, Cyclopaedia, 1728 In mathematics, a conic section (or just conic) is a curve that can be formed by intersecting a cone (more precisely, a right circular conical surface) with a plane. ... Spherical geometry is the geometry of the two-dimensional surface of a sphere. ... Ellipsoid Elliptic Paraboloid Hyperbolic Paraboloid Hyperboloid of One Sheet Hyperboloid of Two Sheets Cone Elliptic Cylinder Hyperbolic Cylinder Parabolic Cylinder In mathematics a quadric, or quadric surface, is any D-dimensional (hyper-)surface represented by a second-order equation in spatial variables (coordinates). ...

Contents

Biographical knowledge

Little is known about Euclid other than his writings. What little biographical information we do have comes largely from commentaries by Proclus and Pappus of Alexandria: Euclid was active at the great Library of Alexandria and may have studied at Plato's Academy in Greece. Euclid's exact lifespan and place of birth are unknown. It is believed that his father could have been named Naucrates. Also, he was born in 330 B.C. and died in 260 B.C., and lived to be about 70 years old. This article is about Proclus Diadochus, the Neoplatonist philosopher. ... Pappus of Alexandria is one of the most important mathematicians of ancient Greek time, known for his work Synagoge or Collection (c. ... Inscription regarding Tiberius Claudius Balbilus of Rome (d. ... For other uses, see Plato (disambiguation). ... For other uses, see Academy (disambiguation). ...


Some writers in the Middle Ages confused him with Euclid of Megara, a Greek Socratic philosopher who lived approximately one century earlier. The Middle Ages formed the middle period in a traditional schematic division of European history into three ages: the classical civilization of Antiquity, the Middle Ages, and modern times, beginning with the Renaissance. ... Euclid of Megara, a Greek Socratic philosopher who lived around 400 BC, was the follower of Socrates. ... This page is about the Classical Greek philosopher. ... A philosopher is a person who thinks deeply regarding people, society, the world, and/or the universe. ...


The Elements

Main article: Euclid's Elements
A fragment of Euclid's Elements found at Oxyrhynchus, which is dated to circa AD 100. The diagram accompanies Book II, Proposition 5.
A fragment of Euclid's Elements found at Oxyrhynchus, which is dated to circa AD 100. The diagram accompanies Book II, Proposition 5.

Although many of the results in Elements originated with earlier mathematicians, one of Euclid's accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 centuries later. The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems... Image File history File links Size of this preview: 800 × 487 pixelsFull resolution (1694 × 1032 pixel, file size: 320 KB, MIME type: image/jpeg) This is [o]ne of the oldest and most complete diagrams from Euclids Elements of Geometry. It is a fragment of papyrus found among the... Image File history File links Size of this preview: 800 × 487 pixelsFull resolution (1694 × 1032 pixel, file size: 320 KB, MIME type: image/jpeg) This is [o]ne of the oldest and most complete diagrams from Euclids Elements of Geometry. It is a fragment of papyrus found among the... Oxyrhynchus (Greek: Οξύρυγχος; sharp-nosed; ancient Egyptian Per-Medjed; modern Egyptian Arabic el-Bahnasa) is an archaeological site in Egypt, considered one of the most important ever discovered. ... Pliny the Younger advances to consulship. ...


Although best-known for its geometric results, the Elements also includes number theory. It considers the connection between perfect numbers and Mersenne primes, the infinitude of prime numbers, Euclid's lemma on factorization (which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations), and the Euclidean algorithm for finding the greatest common divisor of two numbers. Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ... In mathematics, a perfect number is an integer which is the sum of its proper positive divisors, excluding itself. ... In mathematics, a Mersenne prime is a prime number that is one less than a power of two. ... In mathematics, a prime number (or a prime) is a natural number which has exactly two distinct natural number divisors: 1 and itself. ... Euclids lemma is a generalisation of Proposition 30 of Book VII of Euclids Elements. ... In number theory, the fundamental theorem of arithmetic (or unique factorization theorem) states that every natural number either is itself a prime number, or can be written as a unique product of prime numbers. ... Prime decomposition redirects here. ... In number theory, the Euclidean algorithm (also called Euclids algorithm) is an algorithm to determine the greatest common divisor (GCD) of two elements of any Euclidean domain (for example, the integers). ... In mathematics, the greatest common divisor (gcd), sometimes known as the greatest common factor (gcf) or highest common factor (hcf), of two non-zero integers, is the largest positive integer that divides both numbers without remainder. ...


The geometrical system described in the Elements was long known simply as geometry, and was considered to be the only geometry possible. Today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called Non-Euclidean geometries that mathematicians discovered in the 19th century. For other uses, see Geometry (disambiguation). ... Euclid Euclidean geometry is a mathematical system attributed to the Greek mathematician [[Euclid]] of Alexandria. ... Behavior of lines with a common perpendicular in each of the three types of geometry In mathematics, non-Euclidean geometry describes hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. ... Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ...


Other works

Euclid, as imagined by Raphael in this detail from The School of Athens.
Euclid, as imagined by Raphael in this detail from The School of Athens.[1]

In addition to the Elements, at least five works of Euclid have survived to the present day. Image File history File links Euclid File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Euclid File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... This article is about the Renaissance artist. ... The School of Athens or in Italian is one of the most famous paintings by the Italian Renaissance artist Raphael. ...

  • Data deals with the nature and implications of "given" information in geometrical problems; the subject matter is closely related to the first four books of the Elements.
  • On Divisions of Figures, which survives only partially in Arabic translation, concerns the division of geometrical figures into two or more equal parts or into parts in given ratios. It is similar to a third century AD work by Heron of Alexandria.
  • Catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. This work is of doubtful authenticity, being perhaps by Theon of Alexandria.
  • Phaenomena, is a treatise on spherical Astronomy, it survives in Greek and is quite similar to "On the Moving Sphere", by Autolycus of Pitane, who flourished around 310 B.C.
  • Optics, is the earliest surviving Greek treatise on perspective. In its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye. One important definition is the fourth: ``Things seen under a greater angle appear greater, and those under a lesser angle less, while those under equal angles appear equal. In the 36 propositions which follow, Euclid relates the apparent size of an object to its distance from the eye and investigates the apparent shapes of cylinders and cones when viewed from different angles. Proposition 45 is interesting, proving that for any two unequal magnitudes, there is a point from which the two appear equal. Pappus believed such results to be important in astronomy and included Euclid's Optics, along with the previous work, Phaenomena, in the Little Astronomy, a compendium of smaller works to be studied before the Syntaxis (Almagest) of Claudius Ptolemy.

All of these works follow the basic logical structure of the Elements, containing definitions and proved propositions. Data is a work by Euclid. ... Arabic redirects here. ... This article is about the mathematical concept. ... (2nd century - 3rd century - 4th century - other centuries) Events The Sassanid dynasty of Persia launches a war to reconquer lost lands in the Roman east. ... Heros aeolipile Hero (or Heron) of Alexandria (c. ... This article belongs in one or more categories. ... Autolycus of Pitane (c. ... For the book by Sir Isaac Newton, see Opticks. ... The pappus of a Cirsium arvense This article is about a flower structure. ...


There are works credibly attributed to Euclid which have been lost.

  • Conics was a work on conic sections that was later extended by Apollonius of Perga into his famous work on the subject. It is likely that the first four books of Apollonius' work come directly from Euclid. Pappus states that ``Apollonius, having completed Euclid's four books of conics and added four others, handed down eight volumes of conics. The Conics of Apollonius quickly supplanted the former work, and by the time of Pappus, Euclid's work was already lost.
  • Porisms might have been an outgrowth of Euclid's work with conic sections, but the exact meaning of the title is controversial.
  • Pseudaria, or Book of Fallacies, was an elementary text about errors in reasoning.
  • Surface Loci concerned either loci (sets of points) on surfaces or loci which were themselves surfaces; under the latter interpretation, it has been hypothesized that the work might have dealt with quadric surfaces.
  • Several works on Mechanics are attributed to Euclid by Arabic sources. "On the Heavy and the Light" contains, in nine definitions and five propositions, Aristotelian notions of moving bodies and the concept of specific gravity. A book "On the Balance" treats the theory of the lever in a similarly Euclidean manner, containing one definition, two axioms, and four propositions. A third fragment, on the circles described by the ends of a moving lever, contains four propositions. These three works complement each other in such a way that it has been suggested that they are remnants of a single treatise on Mechanics written by Euclid.

Wikibooks has more on the topic of Conic section Types of conic sections Table of conics, Cyclopaedia, 1728 In mathematics, a conic section (or just conic) is a curve that can be formed by intersecting a cone (more precisely, a right circular conical surface) with a plane. ... Apollonius of Perga [Pergaeus] (ca. ... The pappus of a Cirsium arvense This article is about a flower structure. ... The subject of porisms is perplexed by the multitude of different views which have been held by geometers as to what a porism really was and is. ... Reasoning is the mental (cognitive) process of looking for reasons to support beliefs, conclusions, actions or feelings. ... In mathematics, a locus (Latin for place, plural loci) is a collection of points which share a common property. ... Ellipsoid Elliptic Paraboloid Hyperbolic Paraboloid Hyperboloid of One Sheet Hyperboloid of Two Sheets Cone Elliptic Cylinder Hyperbolic Cylinder Parabolic Cylinder In mathematics a quadric, or quadric surface, is any D-dimensional (hyper-)surface represented by a second-order equation in spatial variables (coordinates). ... For other uses, see Mechanic (disambiguation). ... For other uses, see Mechanic (disambiguation). ...

See also

Euclid Euclidean geometry is a mathematical system attributed to the Greek mathematician [[Euclid]] of Alexandria. ... In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. ... In number theory, the Euclidean algorithm (also called Euclids algorithm) is an algorithm to determine the greatest common divisor (GCD) of two elements of any Euclidean domain (for example, the integers). ...

Footnotes

  1. ^ No likeness or description of Euclid's physical appearance made during his lifetime survived antiquity. Therefore, Euclid's depiction in works of art depends on the artist's imagination.

References

  • Artmann, Benno (1999). Euclid: The Creation of Mathematics. New York: Springer. ISBN 0-387-98423-2.
  • Boyer, Carl B. (1991). A History of Mathematics, 2d ed., John Wiley & Sons, Inc.. ISBN 0-47154397-7. 
  • Bulmer-Thomas, Ivor (1971). "Euclid". Dictionary of Scientific Biography.
  • Heath, Thomas L. (1956). The Thirteen Books of Euclid's Elements, Vol. 1 (2nd ed.). New York: Dover Publications. ISBN 0-486-60088-2: includes extensive commentaries on Euclid and his work in the context of the history of mathematics that preceded him.
  • Heath, Thomas L. (1981). A History of Greek Mathematics, 2 Vols. New York: Dover Publications. ISBN 0-486-24073-8 / ISBN 0-486-24074-6.
  • Kline, Morris (1980). Mathematics: The Loss of Certainty. Oxford: Oxford University Press. ISBN 0-19-502754-X.
  • O'Connor, John J; Edmund F. Robertson "Euclid". MacTutor History of Mathematics archive.  

Carl Benjamin Boyer (November 3, 1906 - April 26, 1976) was a historian of mathematics. ... Ivor Bulmer-Thomas CBE FSA, originally Ivor Thomas (30 November 1905 – 7 October 1993) was a British journalist and author who served eight years as a Member of Parliament. ... The MacTutor history of mathematics archive is a website hosted by University of St Andrews in Scotland. ...

External links

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NAME Euclid
ALTERNATIVE NAMES Euclid of Alexandria; Εὐκλείδης (Greek)
SHORT DESCRIPTION Greek mathematician
DATE OF BIRTH 325 BCE
PLACE OF BIRTH
DATE OF DEATH 265 BCE
PLACE OF DEATH
Image File history File links This is a lossless scalable vector image. ... Wikiquote is one of a family of wiki-based projects run by the Wikimedia Foundation, running on MediaWiki software. ... Image File history File links Commons-logo. ... Statue at the center of campus of Sigmund Freud, commemorating his 1909 visit to the University Front Entrance to Clark Universitys Jonas Clark Hall, the main academic facility for undergraduate students For the university in Atlanta, see Clark Atlanta University. ... The University of Texas System comprises fifteen educational institutions in Texas, of which nine are general academic universities, and six are health institutions. ... Rare Book Room is an educational website for the repository of digitally scanned rare books made freely available to the public. ... Rare Book Room is an educational website for the repository of digitally scanned rare books made freely available to the public. ... Greek mathematics, as that term is used in this article, is the mathematics written in Greek, developed from the 6th century BC to the 5th century AD around the Eastern shores of the Mediterranean. ... Anaxagoras Anaxagoras (Greek: Αναξαγόρας, c. ... Anthemius of Tralles (c. ... Archytas Archytas (428 BC - 347 BC) was a Greek philosopher, mathematician, astronomer, statesman, strategist and commander-in-chief. ... Aristaeus the Elder (370 BCE-300 BCE) Aristaeus the Elder was a Greek mathematician who worked on conic sections. ... For other uses of this name, including the grammarian Aristarchus of Samothrace, see Aristarchus Statue of Aristarchus at Aristotle University in Thessalonica, Greece Aristarchus (Greek: Ἀρίσταρχος; 310 BC - ca. ... Apollonius of Perga [Pergaeus] (ca. ... For other uses, see Archimedes (disambiguation). ... Autolycus of Pitane (c. ... For other people of the same name, see Boethius (disambiguation). ... Bryson of Heraclea (ca. ... Calippus of Syracuse Callippus (or Calippus) (ca. ... Chrysippus of Soli (279-207 BC) was Cleanthess pupil and eventual successor to the head of the stoic philosophy (232-204 BC). ... Cleomedes was a Greek astronomer who is known chiefly for his book On the Circular Motions of the Celestial Bodies. ... Conon of Samos (circa 280 BC - circa: 220 BC) was a Greek mathematician and astronomer. ... Ctesibius or Ktesibios or Tesibius (Greek Κτησίβιος) (flourished 285–222 BC) was a Greek[1] inventor and mathematician in Alexandria. ... ‎ Democritus (Greek: ) was a pre-Socratic Greek materialist philosopher (born at Abdera in Thrace ca. ... Dicaearchus (also Dicearchos, Dicearchus or Dikæarchus, Greek Δικαιαρχος; circa 350 BC – circa 285 BC) was a Greek philosopher, cartographer, geographer, mathematician and author. ... Diocles was a Greek mathematician and geometer, who probably flourished sometime around the end of the second century and the beginning of the first century BC. He was probably the first to prove the focal property of a parabola. ... Title page of the 1621 edition of Diophantus Arithmetica, translated into Latin by Claude Gaspard Bachet de Méziriac. ... Dinostratus (b. ... Dionysodorus of Caunus (ca. ... Domninus of Larissa (ca. ... This article is about the Greek scholar of the third century BC. For the ancient Athenian statesman of the fifth century BC, see Eratosthenes (statesman). ... Eudemus (350-290 BC) was the second major companion of Aristotle besides Theophrastus. ... Another article concerns Eudoxus of Cyzicus. ... Geminus of Rhodes was a Greek astronomer and mathematician. ... Hero (or Heron) of Alexandria (Greek: Ήρων ο Αλεξανδρεύς) (c. ... For the Athenian tyrant, see Hipparchus (son of Pisistratus). ... Hippasus of Metapontum, born circa 500 B.C. in Magna Graecia, was a Greek philosopher. ... Hippias can also refer to a son of Pisistratus and a tyrant of Athens. ... Hippocrates of Chios was an ancient Greek mathematician (geometer) and astronomer, who lived c. ... Hypatia, as depicted in Raphaels The School of Athens. ... Hypsicles (ca. ... Marinus (Μαρίνος ο Νεαπολίτης) was neo-Platonist philosopher born in Neapolis (modern Nablus), Palestine in the mid 5th century CE. He was probably a Samaritan, or possibly a Jew. ... Greek mathematician and geometer said to have been the tutor of Alexander the Great. ... Menelaus of Alexandria (c. ... Nicomachus (Gr. ... Oenopides of Chios was an ancient Greek mathematician (geometer) and astronomer, who lived around 450 BCE. He was born shortly after 500 BC on the island of Chios, but mostly worked in Athens. ... Pappus of Alexandria is one of the most important mathematicians of ancient Greek time, known for his work Synagoge or Collection (c. ... Perseus (c. ... Philolaus (circa 480 BC – circa 405 BC) was a Greek mathematician and philosopher. ... 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Zeno of Sidon, Epicurean philosopher of the 1st century BC and contemporary of Cicero. ... Zenodorus (ca. ... Almagest is the Latin form of the Arabic name (al-kitabu-l-mijisti, i. ... The Archimedes Palimpsest is a palimpsest on parchment in the form of a codex which originally was a copy of an otherwise unknown work of the ancient mathematician, physicist, and engineer Archimedes of Syracuse and other authors. ... Arithmetica, an ancient text on mathematics written by classical period Greek mathematician Diophantus in the second century AD is a collection of 130 algebra problems giving numerical solutions of determinate equations (those with a unique solution), and indeterminate equations. ... Apollonius of Perga [Pergaeus] (ca. ... The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems... Aristarchuss 3rd century BC calculations on the relative sizes of the Earth, Sun and Moon, from a 10th century CE Greek copy On the Sizes and Distances [of the Sun and Moon] is the only extant work written by Aristarchus of Samos, an ancient Greek astronomer who lived circa... On Sizes and Distances [of the Sun and Moon] (Peri megethoon kai apostèmátoon) is a text by the ancient Greek astronomer Hipparchus. ... Autolycus of Pitane (c. ... For other uses, see Academy (disambiguation). ... Inscription regarding Tiberius Claudius Balbilus of Rome (d. ... Cyrene (Greek Κυρήνη, Kurene) was an ancient Greek colony in present-day Libya, the oldest and most important of the five Greek cities in the region. ... Babylonian clay tablet YBC 7289 with annotations. ... This article or section is in need of attention from an expert on the subject. ... For a timeline of events in mathematics, see timeline of mathematics. ... In the history of mathematics, Islamic mathematics or Arabic mathematics refers to the mathematics developed by the Islamic civilization between 622 and 1600. ... This article is under construction. ...

  Results from FactBites:
 
Euclid - Wikipedia, the free encyclopedia (736 words)
Euclid also wrote works on perspective, conic sections, spherical geometry, and possibly quadric surfaces.
In particular, Euclid's proof of the infinitude of prime numbers is in Book IX, Proposition 20.
Euclid's elements, with the original Greek and an English translation on facing pages (includes PDF version for printing) (only the first nine books).
Euclid, Ohio - Wikipedia, the free encyclopedia (807 words)
Euclid borders Cleveland on the west, South Euclid and Richmond Heights on the south, Willowick, Wickliffe, and Willoughby Hills on the east, and Lake Erie on the north.
Euclid Beach Park was originally part of Euclid, until the boundaries were redrawn in the early 1900's.
Euclid is situated near the junction of Interstate 90, Interstate 271 and Ohio Route 2, giving easy access by car to downtown Cleveland, Lake County, and most of the East suburbs.
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