Get it on Google Play
New! Download Unionpedia on your Android™ device!
Faster access than browser!


Index Euclid

Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry". [1]

79 relations: Alexander the Great, Alexandria, Apollonius of Perga, Arabic, Archimedes, Arthur Surridge Hunt, Autolycus of Pitane, Axiom, Axiomatic system, Bernard Pyne Grenfell, Bill Casselman (mathematician), Catoptrics, Clark University, Conic section, Data (Euclid), Emission theory (vision), Encyclopædia Britannica, Euclid (spacecraft), Euclid of Megara, Euclid's Elements, Euclid's lemma, Euclid's Optics, Euclid's orchard, Euclid's theorem, Euclid–Euler theorem, Euclidean algorithm, Euclidean geometry, Euclidean relation, Eudoxus of Cnidus, European Space Agency, Extended Euclidean algorithm, Floruit, Fundamental theorem of arithmetic, Geometry, Greatest common divisor, Greek mathematics, Hero of Alexandria, History of mathematics, Integer factorization, Library of Alexandria, Library of Congress, List of things named after Euclid, Locus (mathematics), Mathematical proof, Mathematics, Mechanics, Menaechmus, Mersenne prime, Morris Kline, Nicolas Bourbaki, ..., Non-Euclidean geometry, Number theory, Optics, Oxyrhynchus, Pappus of Alexandria, Papyrus Oxyrhynchus 29, Perfect number, Perspective (graphical), Philip of Opus, Plato, Porism, Proclus, Ptolemaic Kingdom, Ptolemy, Ptolemy I Soter, Quadric, Rare Book Room, Ratio, Reason, Rigour, Serapeum of Alexandria, Spacecraft, Spherical astronomy, Spherical geometry, Theaetetus (mathematician), Theon of Alexandria, Thomas Little Heath, Tyre, Lebanon, University of Texas at Austin. Expand index (29 more) »

Alexander the Great

Alexander III of Macedon (20/21 July 356 BC – 10/11 June 323 BC), commonly known as Alexander the Great (Aléxandros ho Mégas), was a king (basileus) of the ancient Greek kingdom of Macedon and a member of the Argead dynasty.

New!!: Euclid and Alexander the Great · See more »


Alexandria (or; Arabic: الإسكندرية; Egyptian Arabic: إسكندرية; Ⲁⲗⲉⲝⲁⲛⲇⲣⲓⲁ; Ⲣⲁⲕⲟⲧⲉ) is the second-largest city in Egypt and a major economic centre, extending about along the coast of the Mediterranean Sea in the north central part of the country.

New!!: Euclid and Alexandria · See more »

Apollonius of Perga

Apollonius of Perga (Ἀπολλώνιος ὁ Περγαῖος; Apollonius Pergaeus; late 3rdearly 2nd centuries BC) was a Greek geometer and astronomer known for his theories on the topic of conic sections.

New!!: Euclid and Apollonius of Perga · See more »


Arabic (العَرَبِيَّة) or (عَرَبِيّ) or) is a Central Semitic language that first emerged in Iron Age northwestern Arabia and is now the lingua franca of the Arab world. It is named after the Arabs, a term initially used to describe peoples living from Mesopotamia in the east to the Anti-Lebanon mountains in the west, in northwestern Arabia, and in the Sinai peninsula. Arabic is classified as a macrolanguage comprising 30 modern varieties, including its standard form, Modern Standard Arabic, which is derived from Classical Arabic. As the modern written language, Modern Standard Arabic is widely taught in schools and universities, and is used to varying degrees in workplaces, government, and the media. The two formal varieties are grouped together as Literary Arabic (fuṣḥā), which is the official language of 26 states and the liturgical language of Islam. Modern Standard Arabic largely follows the grammatical standards of Classical Arabic and uses much of the same vocabulary. However, it has discarded some grammatical constructions and vocabulary that no longer have any counterpart in the spoken varieties, and has adopted certain new constructions and vocabulary from the spoken varieties. Much of the new vocabulary is used to denote concepts that have arisen in the post-classical era, especially in modern times. During the Middle Ages, Literary Arabic was a major vehicle of culture in Europe, especially in science, mathematics and philosophy. As a result, many European languages have also borrowed many words from it. Arabic influence, mainly in vocabulary, is seen in European languages, mainly Spanish and to a lesser extent Portuguese, Valencian and Catalan, owing to both the proximity of Christian European and Muslim Arab civilizations and 800 years of Arabic culture and language in the Iberian Peninsula, referred to in Arabic as al-Andalus. Sicilian has about 500 Arabic words as result of Sicily being progressively conquered by Arabs from North Africa, from the mid 9th to mid 10th centuries. Many of these words relate to agriculture and related activities (Hull and Ruffino). Balkan languages, including Greek and Bulgarian, have also acquired a significant number of Arabic words through contact with Ottoman Turkish. Arabic has influenced many languages around the globe throughout its history. Some of the most influenced languages are Persian, Turkish, Spanish, Urdu, Kashmiri, Kurdish, Bosnian, Kazakh, Bengali, Hindi, Malay, Maldivian, Indonesian, Pashto, Punjabi, Tagalog, Sindhi, and Hausa, and some languages in parts of Africa. Conversely, Arabic has borrowed words from other languages, including Greek and Persian in medieval times, and contemporary European languages such as English and French in modern times. Classical Arabic is the liturgical language of 1.8 billion Muslims and Modern Standard Arabic is one of six official languages of the United Nations. All varieties of Arabic combined are spoken by perhaps as many as 422 million speakers (native and non-native) in the Arab world, making it the fifth most spoken language in the world. Arabic is written with the Arabic alphabet, which is an abjad script and is written from right to left, although the spoken varieties are sometimes written in ASCII Latin from left to right with no standardized orthography.

New!!: Euclid and Arabic · See more »


Archimedes of Syracuse (Ἀρχιμήδης) was a Greek mathematician, physicist, engineer, inventor, and astronomer.

New!!: Euclid and Archimedes · See more »

Arthur Surridge Hunt

Arthur Surridge Hunt, FBA (1 March 1871 – 18 June 1934) was an English papyrologist.

New!!: Euclid and Arthur Surridge Hunt · See more »

Autolycus of Pitane

Autolycus of Pitane (Αὐτόλυκος ὁ Πιταναῖος; c. 360 – c. 290 BC) was a Greek astronomer, mathematician, and geographer.

New!!: Euclid and Autolycus of Pitane · See more »


An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.

New!!: Euclid and Axiom · See more »

Axiomatic system

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.

New!!: Euclid and Axiomatic system · See more »

Bernard Pyne Grenfell

Bernard Pyne Grenfell, FBA (16 December 1869 – 18 May 1926) was an English scientist and Egyptologist.

New!!: Euclid and Bernard Pyne Grenfell · See more »

Bill Casselman (mathematician)

William Allen "Bill" Casselman (born November 27, 1941) is an American Canadian mathematician who works in group theory.

New!!: Euclid and Bill Casselman (mathematician) · See more »


Catoptrics (from κατοπτρικός katoptrikós, "specular", from κάτοπτρον katoptron "mirror") deals with the phenomena of reflected light and image-forming optical systems using mirrors.

New!!: Euclid and Catoptrics · See more »

Clark University

Clark University is an American private research university located in Worcester, Massachusetts.

New!!: Euclid and Clark University · See more »

Conic section

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.

New!!: Euclid and Conic section · See more »

Data (Euclid)

Data (Greek: Δεδομένα, Dedomena) is a work by Euclid.

New!!: Euclid and Data (Euclid) · See more »

Emission theory (vision)

Emission theory or extramission theory (variants: extromission, extromittism) is the proposal that visual perception is accomplished by eye beams emitted by the eyes.

New!!: Euclid and Emission theory (vision) · See more »

Encyclopædia Britannica

The Encyclopædia Britannica (Latin for "British Encyclopaedia"), published by Encyclopædia Britannica, Inc., is a general knowledge English-language encyclopaedia.

New!!: Euclid and Encyclopædia Britannica · See more »

Euclid (spacecraft)

Euclid is a visible to near-infrared space telescope currently under development by the European Space Agency (ESA) and Euclid Consortium.

New!!: Euclid and Euclid (spacecraft) · See more »

Euclid of Megara

Euclid of Megara (also Euclides, Eucleides; Εὐκλείδης ὁ Μεγαρεύς; c. 435 – c. 365 BC) was a Greek Socratic philosopher who founded the Megarian school of philosophy.

New!!: Euclid and Euclid of Megara · See more »

Euclid's Elements

The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.

New!!: Euclid and Euclid's Elements · See more »

Euclid's lemma

In number theory, Euclid's lemma is a lemma that captures a fundamental property of prime numbers, namely: For example, if,,, then, and since this is divisible by 19, the lemma implies that one or both of 133 or 143 must be as well.

New!!: Euclid and Euclid's lemma · See more »

Euclid's Optics

Euclid's Optics (Ὀπτικά), is a work on the geometry of vision written by the Greek mathematician Euclid around 300 BC.

New!!: Euclid and Euclid's Optics · See more »

Euclid's orchard

In mathematics, informally speaking, 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.

New!!: Euclid and Euclid's orchard · See more »

Euclid's theorem

Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers.

New!!: Euclid and Euclid's theorem · See more »

Euclid–Euler theorem

The Euclid–Euler theorem is a theorem in mathematics that relates perfect numbers to Mersenne primes.

New!!: Euclid and Euclid–Euler theorem · See more »

Euclidean algorithm


New!!: Euclid and Euclidean algorithm · See more »

Euclidean geometry

Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.

New!!: Euclid and Euclidean geometry · See more »

Euclidean relation

In mathematics, Euclidean relations are a class of binary relations that formalizes "Axiom 1" in Euclid's Elements: "Magnitudes which are equal to the same are equal to each other.".

New!!: Euclid and Euclidean relation · See more »

Eudoxus of Cnidus

Eudoxus of Cnidus (Εὔδοξος ὁ Κνίδιος, Eúdoxos ho Knídios) was an ancient Greek astronomer, mathematician, scholar, and student of Archytas and Plato.

New!!: Euclid and Eudoxus of Cnidus · See more »

European Space Agency

The European Space Agency (ESA; Agence spatiale européenne, ASE; Europäische Weltraumorganisation) is an intergovernmental organisation of 22 member states dedicated to the exploration of space.

New!!: Euclid and European Space Agency · See more »

Extended Euclidean algorithm

In arithmetic and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common divisor of integers a and b, also the coefficients of Bézout's identity, which are integers x and y such that This is a certifying algorithm, because the gcd is the only number that can simultaneously satisfy this equation and divide the inputs.

New!!: Euclid and Extended Euclidean algorithm · See more »


Floruit, abbreviated fl. (or occasionally, flor.), Latin for "he/she flourished", denotes a date or period during which a person was known to have been alive or active.

New!!: Euclid and Floruit · See more »

Fundamental theorem of arithmetic

In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers and that, moreover, this representation is unique, up to (except for) the order of the factors.

New!!: Euclid and Fundamental theorem of arithmetic · See more »


Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

New!!: Euclid and Geometry · See more »

Greatest common divisor

In mathematics, the greatest common divisor (gcd) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

New!!: Euclid and Greatest common divisor · See more »

Greek mathematics

Greek mathematics refers to mathematics texts and advances written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean.

New!!: Euclid and Greek mathematics · See more »

Hero of Alexandria

Hero of Alexandria (ἭρωνGenitive: Ἥρωνος., Heron ho Alexandreus; also known as Heron of Alexandria; c. 10 AD – c. 70 AD) was a mathematician and engineer who was active in his native city of Alexandria, Roman Egypt.

New!!: Euclid and Hero of Alexandria · See more »

History of mathematics

The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.

New!!: Euclid and History of mathematics · See more »

Integer factorization

In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers.

New!!: Euclid and Integer factorization · See more »

Library of Alexandria

The Royal Library of Alexandria or Ancient Library of Alexandria in Alexandria, Egypt, was one of the largest and most significant libraries of the ancient world.

New!!: Euclid and Library of Alexandria · See more »

Library of Congress

The Library of Congress (LOC) is the research library that officially serves the United States Congress and is the de facto national library of the United States.

New!!: Euclid and Library of Congress · See more »

List of things named after Euclid

This is a list of topics named after the Greek mathematician Euclid.

New!!: Euclid and List of things named after Euclid · See more »

Locus (mathematics)

In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.

New!!: Euclid and Locus (mathematics) · See more »

Mathematical proof

In mathematics, a proof is an inferential argument for a mathematical statement.

New!!: Euclid and Mathematical proof · See more »


Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

New!!: Euclid and Mathematics · See more »


Mechanics (Greek μηχανική) is that area of science concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment.

New!!: Euclid and Mechanics · See more »


Menaechmus (Μέναιχμος, 380–320 BC) was an ancient Greek mathematician and geometer born in Alopeconnesus in the Thracian Chersonese, who was known for his friendship with the renowned philosopher Plato and for his apparent discovery of conic sections and his solution to the then-long-standing problem of doubling the cube using the parabola and hyperbola.

New!!: Euclid and Menaechmus · See more »

Mersenne prime

In mathematics, a Mersenne prime is a prime number that is one less than a power of two.

New!!: Euclid and Mersenne prime · See more »

Morris Kline

Morris Kline (May 1, 1908 – June 10, 1992) was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.

New!!: Euclid and Morris Kline · See more »

Nicolas Bourbaki

Nicolas Bourbaki is the collective pseudonym under which a group of (mainly French) 20th-century mathematicians, with the aim of reformulating mathematics on an extremely abstract and formal but self-contained basis, wrote a series of books beginning in 1935.

New!!: Euclid and Nicolas Bourbaki · See more »

Non-Euclidean geometry

In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.

New!!: Euclid and Non-Euclidean geometry · See more »

Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

New!!: Euclid and Number theory · See more »


Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it.

New!!: Euclid and Optics · See more »


Oxyrhynchus (Ὀξύρρυγχος Oxýrrhynkhos; "sharp-nosed"; ancient Egyptian Pr-Medjed; Coptic Pemdje; modern Egyptian Arabic El Bahnasa) is a city in Middle Egypt, located about 160 km south-southwest of Cairo, in the governorate of Al Minya.

New!!: Euclid and Oxyrhynchus · See more »

Pappus of Alexandria

Pappus of Alexandria (Πάππος ὁ Ἀλεξανδρεύς; c. 290 – c. 350 AD) was one of the last great Greek mathematicians of Antiquity, known for his Synagoge (Συναγωγή) or Collection (c. 340), and for Pappus's hexagon theorem in projective geometry.

New!!: Euclid and Pappus of Alexandria · See more »

Papyrus Oxyrhynchus 29

Papyrus Oxyrhynchus 29 (P. Oxy. 29) is a fragment of the second book of the Elements of Euclid in Greek.

New!!: Euclid and Papyrus Oxyrhynchus 29 · See more »

Perfect number

In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum).

New!!: Euclid and Perfect number · See more »

Perspective (graphical)

Perspective (from perspicere "to see through") in the graphic arts is an approximate representation, generally on a flat surface (such as paper), of an image as it is seen by the eye.

New!!: Euclid and Perspective (graphical) · See more »

Philip of Opus

Philip (or Philippus) of Opus (Φίλιππος Ὀπούντιος), was a philosopher and a member of the Academy during Plato's lifetime.

New!!: Euclid and Philip of Opus · See more »


Plato (Πλάτων Plátōn, in Classical Attic; 428/427 or 424/423 – 348/347 BC) was a philosopher in Classical Greece and the founder of the Academy in Athens, the first institution of higher learning in the Western world.

New!!: Euclid and Plato · See more »


A porism is a mathematical proposition or corollary.

New!!: Euclid and Porism · See more »


Proclus Lycaeus (8 February 412 – 17 April 485 AD), called the Successor (Greek Πρόκλος ὁ Διάδοχος, Próklos ho Diádokhos), was a Greek Neoplatonist philosopher, one of the last major classical philosophers (see Damascius).

New!!: Euclid and Proclus · See more »

Ptolemaic Kingdom

The Ptolemaic Kingdom (Πτολεμαϊκὴ βασιλεία, Ptolemaïkḕ basileía) was a Hellenistic kingdom based in Egypt.

New!!: Euclid and Ptolemaic Kingdom · See more »


Claudius Ptolemy (Κλαύδιος Πτολεμαῖος, Klaúdios Ptolemaîos; Claudius Ptolemaeus) was a Greco-Roman mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology.

New!!: Euclid and Ptolemy · See more »

Ptolemy I Soter

Ptolemy I Soter (Πτολεμαῖος Σωτήρ, Ptolemaĩos Sōtḗr "Ptolemy the Savior"; c. 367 BC – 283/2 BC), also known as Ptolemy of Lagus (Πτολεμαῖος ὁ Λάγου/Λαγίδης), was a Macedonian Greek general under Alexander the Great, one of the three Diadochi who succeeded to his empire.

New!!: Euclid and Ptolemy I Soter · See more »


In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas).

New!!: Euclid and Quadric · See more »

Rare Book Room

Rare Book Room is an educational website for the repository of digitally scanned rare books made freely available to the public.

New!!: Euclid and Rare Book Room · See more »


In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second.

New!!: Euclid and Ratio · See more »


Reason is the capacity for consciously making sense of things, establishing and verifying facts, applying logic, and changing or justifying practices, institutions, and beliefs based on new or existing information.

New!!: Euclid and Reason · See more »


Rigour (British English) or rigor (American English; see spelling differences) describes a condition of stiffness or strictness.

New!!: Euclid and Rigour · See more »

Serapeum of Alexandria

The Serapeum of Alexandria in the Ptolemaic Kingdom was an ancient Greek temple built by Ptolemy III Euergetes (reigned 246–222 BCE) and dedicated to Serapis, who was made the protector of Alexandria.

New!!: Euclid and Serapeum of Alexandria · See more »


A spacecraft is a vehicle or machine designed to fly in outer space.

New!!: Euclid and Spacecraft · See more »

Spherical astronomy

Spherical astronomy or positional astronomy is the branch of astronomy that is used to determine the location of objects on the celestial sphere, as seen at a particular date, time, and location on Earth.

New!!: Euclid and Spherical astronomy · See more »

Spherical geometry

Spherical geometry is the geometry of the two-dimensional surface of a sphere.

New!!: Euclid and Spherical geometry · See more »

Theaetetus (mathematician)

Theaetetus of Athens (Θεαίτητος; c. 417 – 369 BC), possibly the son of Euphronius of the Athenian deme Sunium, was a Greek mathematician.

New!!: Euclid and Theaetetus (mathematician) · See more »

Theon of Alexandria

Theon of Alexandria (Θέων ὁ Ἀλεξανδρεύς; 335 – c. 405) was a Greek scholar and mathematician who lived in Alexandria, Egypt.

New!!: Euclid and Theon of Alexandria · See more »

Thomas Little Heath

Sir Thomas Little Heath (5 October 1861 – 16 March 1940) was a British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer.

New!!: Euclid and Thomas Little Heath · See more »

Tyre, Lebanon

Tyre (صور, Ṣūr; Phoenician:, Ṣūr; צוֹר, Ṣōr; Tiberian Hebrew, Ṣōr; Akkadian:, Ṣurru; Greek: Τύρος, Týros; Sur; Tyrus, Տիր, Tir), sometimes romanized as Sour, is a district capital in the South Governorate of Lebanon.

New!!: Euclid and Tyre, Lebanon · See more »

University of Texas at Austin

The University of Texas at Austin (UT, UT Austin, or Texas) is a public research university and the flagship institution of the University of Texas System.

New!!: Euclid and University of Texas at Austin · See more »

Redirects here:

EucliD, Euclid Of Alexandria, Euclid of Alexandria, Eukleidēs, Euklid, Evclid, Εὐκλείδης.


[1] https://en.wikipedia.org/wiki/Euclid

Hey! We are on Facebook now! »