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Euclid (; grc-gre,
Εὐκλείδης Euclid (; grc, Εὐκλείδης – ''Eukleídēs'', ; fl. 300 BC), sometimes called Euclid of Alexandria to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the "founder of geometry Geometr ...
; 300 BC), sometimes called Euclid of Alexandria to distinguish him from
Euclid of Megara Euclid of Megara (; also Euclides, Eucleides; el, Εὐκλείδης ὁ Μεγαρεύς; c. 435 – c. 365 BC) was a Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially t ...

Euclid of Megara
, was a Greek mathematician, often referred to as the "founder of
geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position of figures. A mat ...

geometry
" or the "father of geometry". He was active in
Alexandria Alexandria ( or ; ar, الإسكندرية ; arz, اسكندرية ; Coptic Coptic may refer to: Afro-Asia * Copts, an ethnoreligious group mainly in the area of modern Egypt but also in Sudan and Libya * Coptic language, a Northern Afro-Asia ...

Alexandria
during the reign of Ptolemy I (323–283 BC). His '' Elements'' is one of the most influential works in the
history of mathematics The history of mathematics deals with the origin of discoveries in and the . Before the and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the states ...
, serving as the main textbook for teaching
mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ...
(especially
geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position of figures. A mat ...

geometry
) from the time of its publication until the late 19th or early 20th century. In the ''Elements'', Euclid deduced the theorems of what is now called
Euclidean geometry Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematics , Greek mathematician Euclid, which he described in his textbook on geometry: the ''Euclid's Elements, Elements''. Euclid's method consists in assuming a sma ...
from a small set of
axiom An axiom, postulate or assumption is a statement that is taken to be , to serve as a or starting point for further reasoning and arguments. The word comes from the Greek ''axíōma'' () 'that which is thought worthy or fit' or 'that which comm ...

axiom
s. Euclid also wrote works on perspective,
conic section In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...
s,
spherical geometry Image:Triangles (spherical geometry).jpg, 300px, The sum of the angles of a spherical triangle is not equal to 180°. A sphere is a curved surface, but locally the laws of the flat (planar) Euclidean geometry are good approximations. In a small tr ...
,
number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of devoted primarily to the study of the s and . German mathematician (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen ...

number theory
, and
mathematical rigour Rigour (British English British English (BrE) is the standard dialect of the English language English is a West Germanic languages, West Germanic language first spoken in History of Anglo-Saxon England, early medieval England, wh ...
.


Etymology

The
English English usually refers to: * English language English is a West Germanic languages, West Germanic language first spoken in History of Anglo-Saxon England, early medieval England, which has eventually become the World language, leading lan ...

English
name ''Euclid'' is the anglicized version of the Greek name Εὐκλείδης, which means "renowned, glorious".


Biography

Very few original references to Euclid survive, so little is known about his life. He was likely born around 325 BC, although the place and circumstances of both his birth and death are unknown and may only be estimated relative to other people mentioned with him. He is mentioned by name, though rarely, by other Greek mathematicians from
Archimedes Archimedes of Syracuse (; grc, ; ; ) was a Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its popula ...

Archimedes
(c. 287 BC – c. 212 BC) onward, and is usually referred to as "ὁ στοιχειώτης" ("the author of ''Elements''"). The few historical references to Euclid were written by
Proclus Proclus Lycius (; 410/411/ 7 Feb. or 8 Feb. 412 –17 April 485 AD), called Proclus the Successor, Proclus the Platonic Successor, or Proclus of Athens (Greek: Προκλου Διαδοχου ''Próklos Diádochos'', ''"''in some Manuscript ...
c. 450 AD, eight centuries after Euclid lived. A detailed biography of Euclid is given by Arabian authors, mentioning, for example, a birth town of
Tyre Tyre may refer to: * Tire, the outer part of a wheel Places * Tyre, Lebanon, a city ** See of Tyre, a Christian diocese seated in Tyre, Lebanon ** Tyre Hippodrome, a UNESCO World Heritage site * Tyre District, Lebanon * Tyre, New York, a town in t ...
. This biography is generally believed to be fictitious. If he came from Alexandria, he would have known the
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. There are also signs of Harpocrates. It ...
, and the
Library of Alexandria The Great Library of Alexandria in Alexandria, Egypt, was one of the largest and most significant libraries of the ancient world. The Library was part of a larger research institution called the Musaeum, Mouseion, which was dedicated to the ...

Library of Alexandria
, and may have worked there during his time. Euclid's arrival in Alexandria came about ten years after its founding by
Alexander the Great Alexander III of Macedon ( grc-gre, Αλέξανδρος}, ; 20/21 July 356 BC – 10/11 June 323 BC), commonly known as Alexander the Great, was a king (''basileus ''Basileus'' ( el, βασιλεύς) is a Greek term and title A title ...

Alexander the Great
, which means he arrived c. 322 BC. Proclus introduces Euclid only briefly in his ''Commentary on the Elements''. According to Proclus, Euclid supposedly belonged to
Plato Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was an Classical Athens, Athenian philosopher during the Classical Greece, Classical period in Ancient Greece, founder of the Platonist school of thought and the Platoni ...

Plato
's "persuasion" and brought together the ''Elements'', drawing on prior work of
Eudoxus of Cnidus Eudoxus of Cnidus (; grc, Εὔδοξος ὁ Κνίδιος, ''Eúdoxos ho Knídios''; ) was an ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from ...
and of several pupils of Plato (particularly Theaetetus and
Philip of OpusPhilip (or Philippus) of Opus ( el, Φίλιππος Ὀπούντιος), was a philosopher and a member of the Academy An academy ( Attic Greek: Ἀκαδήμεια; Koine Greek Koine Greek (, , Greek approximately ;. , , , lit. "Common Gree ...
.) Proclus believes that Euclid is not much younger than these, and that he must have lived during the time of
Ptolemy I Ptolemy I Soter (; gr, Πτολεμαῖος Σωτήρ, ''Ptolemaîos Sōtḗr'' "Ptolemy the Savior"; c. 367 BC – January 282 BC) was a companion and historian of Alexander the Great Alexander III of Macedon ( grc-gre, Αλέξανδ ...
(c. 367 BC – 282 BC) because he was mentioned by Archimedes. Although the apparent 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 Archimedes wrote his. Proclus later retells a story that, when Ptolemy I asked if there was a shorter path to learning geometry than Euclid's ''Elements'', "Euclid replied there is no royal road to geometry." This anecdote is questionable since it is similar to a story told about
Menaechmus:''There is also a Menaechmus in Plautus Titus Maccius Plautus (; c. 254 – 184 BC), commonly known as Plautus, was a Ancient Rome, Roman playwright of the Old Latin period. His comedy, comedies are the earliest Latin literature, Latin literary ...
and Alexander the Great. Euclid died c. 270 BC, presumably in Alexandria. In the only other key reference to Euclid,
Pappus of Alexandria Pappus of Alexandria (; grc-gre, Πάππος ὁ Ἀλεξανδρεύς; AD) was one of the last great Greek mathematicians of antiquity, known for his ''Synagoge'' (Συναγωγή) or ''Collection'' (), and for Pappus's hexagon theorem ...
(c. 320 AD) briefly mentioned that Apollonius "spent a very long time with the pupils of Euclid at Alexandria, and it was thus that he acquired such a scientific habit of thought" c. 247–222 BC. Because the lack of biographical information is unusual for the period (extensive biographies being available for most significant Greek mathematicians several centuries before and after Euclid), some researchers have proposed that Euclid was not a historical personage, and that his works were written by a team of mathematicians who took the name Euclid from
Euclid of Megara Euclid of Megara (; also Euclides, Eucleides; el, Εὐκλείδης ὁ Μεγαρεύς; c. 435 – c. 365 BC) was a Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially t ...

Euclid of Megara
(à la Bourbaki). However, this hypothesis is not well accepted by scholars and there is little evidence in its favor.


''Elements''

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 proof A mathematical proof is an inferential argument In logic Logic is an interdisciplinary field which studies truth and reasoning Reason is the capacity of consciously making sense of things, applying logic Logic (from Ancient Greek ...
s that remains the basis of mathematics 23 centuries later. There is no mention of Euclid in the earliest remaining copies of the ''Elements''. Most of the copies say they are "from the edition of Theon" or the "lectures of Theon", while the text considered to be primary, held by the Vatican, mentions no author. Proclus provides the only reference ascribing the ''Elements'' to Euclid. Although best known for its geometric results, the ''Elements'' also includes
number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of devoted primarily to the study of the s and . German mathematician (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen ...

number theory
. It considers the connection between
perfect numbers In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number. The ...
and
Mersenne primes In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minims (religious order), Minim friar, who studie ...
(known as the
Euclid–Euler theorem The Euclid–Euler theorem is a theorem In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, c ...
), the infinitude of prime numbers,
Euclid's lemma In number theory, Euclid's lemma is a lemma that captures a fundamental property of prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A na ...
on factorization (which leads to the
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 An integer (from the Latin wikt:integer#Latin, ''integer'' meaning "wh ...
on uniqueness of prime factorizations), and the
Euclidean algorithm In mathematics, the Euclidean algorithm,Some widely used textbooks, such as I. N. Herstein's ''Topics in Algebra'' and Serge Lang's ''Algebra'', use the term "Euclidean algorithm" to refer to Euclidean division or Euclid's algorithm, is an effi ...
for finding the
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. For two integers ''x'', ''y'', the greatest common divisor of ''x'' and ''y'' is ...

greatest common divisor
of two numbers. The geometrical system described in the ''Elements'' was long known simply as ''
geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position of figures. A mat ...

geometry
'', and was considered to be the only geometry possible. Today, however, that system is often referred to as ''
Euclidean geometry Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematics , Greek mathematician Euclid, which he described in his textbook on geometry: the ''Euclid's Elements, Elements''. Euclid's method consists in assuming a sma ...
'' to distinguish it from other so-called ''
non-Euclidean geometries In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). I ...
'' discovered in the 19th century.


Fragments

The
Papyrus Oxyrhynchus 29 Papyrus Oxyrhynchus 29 (P. Oxy. 29) is a fragment of the second book of the ''Euclid's Elements, Elements'' of Euclid in Ancient Greek, Greek. It was discovered by Bernard Grenfell, Grenfell and Arthur Surridge Hunt, Hunt in 1897 in Oxyrhynchus. T ...
(P. Oxy. 29) is a fragment of the second book of the '' Elements'' of Euclid, unearthed by
Grenfell Grenfell may refer to: Buildings * Grenfell Tower, building in London, UK * Grenfell Centre, Adelaide, Australia, an office block * Grenfell railway station, New South Wales, Australia * Grenfell Campus, Memorial University of Newfoundland, Canad ...
and
Hunt Hunting is the practice of seeking, pursuing and capturing or killing wildlife Wildlife traditionally refers to undomesticated animal species (biology), species, but has come to include all organisms that grow or live wild in an area ...
1897 in
Oxyrhynchus Oxyrhynchus (; grc-gre, Ὀξύρρυγχος, Oxýrrhynchos, sharp-nosed; ancient Egyptian language, Egyptian ''Pr-Medjed''; cop, or , ''Pemdje''; ar, البهنسا, ''Al-Bahnasa'') is a city in Middle Egypt located about 160 km sou ...

Oxyrhynchus
. More recent scholarship suggests a date of 75–125 AD. The fragment contains the statement of the 5th proposition of Book 2, which in the translation of T. L. Heath reads: Bill Casselman
One of the oldest extant diagrams from Euclid
/ref>


Other works

In addition to the ''Elements'', at least five works of Euclid have survived to the present day. They follow the same logical structure as ''Elements'', with definitions and proved propositions. * ''
Data Data (; ) are individual facts A fact is something that is truth, true. The usual test for a statement of fact is verifiability—that is whether it can be demonstrated to correspond to experience. Standard reference works are often used ...
'' 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 Arabic (, ' or , ' or ) is a Semitic language The Semitic languages are a branch of the Afroasiatic language family originating in the Middle East The Middle East is a list of transcontinental countries, transcontinental region ...

Arabic
translation, concerns the division of geometrical figures into two or more equal parts or into parts in given
ratio In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to ...

ratio
s. It is similar to a first-century AD work by
Heron of Alexandria The herons are long-legged, long-necked, freshwater and coastal bird Birds are a group of warm-blooded vertebrates constituting the class (biology), class Aves , characterised by feathers, toothless beaked jaws, the Oviparity, laying of ...
. * ''
Catoptrics Catoptrics (from grc-gre, κατοπτρικός ''katoptrikós'', "specular", from grc-gre, κάτοπτρον ''katoptron'' "mirror") deals with the phenomena of and s using s. A catoptric system is also called a ''catopter'' (''catoptre'') ...
'', which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. The attribution is held to be anachronistic however by J J O'Connor and E F Robertson who name
Theon of Alexandria Theon of Alexandria (; grc, Θέων ὁ Ἀλεξανδρεύς;  335 – c. 405) was a Greeks, Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's ''Euclid's Elements, Elements'' and wrot ...
as a more likely author. * ''Phaenomena'', a treatise on
spherical astronomy Spherical astronomy, or positional astronomy, is a branch of observational astronomy used to locate astronomical object In astronomy, an astronomical object or celestial object is a naturally occurring physical entity, association, or stru ...
, survives in Greek; it is quite similar to ''On the Moving Sphere'' by
Autolycus of Pitane ''De sphaera quae movetur liber'' Autolycus of Pitane ( el, Αὐτόλυκος ὁ Πιταναῖος; c. 360 – c. 290 BC) was a Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), off ...
, who flourished around 310 BC. * ''
Optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of optical instruments, instruments that use or Photodetector, detect it. Optics usually describes t ...
'' 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 that 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 these results to be important in astronomy and included Euclid's ''Optics'', along with his ''Phaenomena'', in the ''Little Astronomy'', a compendium of smaller works to be studied before the ''Syntaxis'' (''Almagest'') of
Claudius Ptolemy Claudius Ptolemy (; grc-koi, Κλαύδιος Πτολεμαῖος, ''Klaúdios Ptolemaîos'' ; la, Claudius Ptolemaeus; AD) was a mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics ...
.


Lost works

Other works are credibly attributed to Euclid, but have been lost. * ''Conics'' was a work on
conic section In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...
s that was later extended by
Apollonius of Perga Apollonius of Perga ( grc-gre, Ἀπολλώνιος ὁ Περγαῖος ''Apollonios o Pergeos''; la, Apollonius Pergaeus; ) was an Ancient Greece, Ancient Greek geometer and astronomer known for his work on conic sections. Beginning from the ...
into his famous work on the subject. It is likely that the first four books of Apollonius's work come directly from Euclid. According to Pappus, "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. * ''
Porism A porism is a mathematical proposition or corollary. In particular, the term porism has been used to refer to a direct consequence of a proof, analogous to how a corollary refers to a direct consequence of a theorem. In modern usage, a porism is a ...
s'' 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 Reason is the capacity of consciously applying logic Logic is an interdisciplinary field which studies truth and reasoning Reason is the capacity of consciously making sense of things, applying logic Logic (from Ancient Greek, Greek: ...

reasoning
. * ''Surface Loci'' concerned either
loci Locus (plural loci) is Latin for "place". It may refer to: Entertainment * Locus (comics), a Marvel Comics mutant villainess, a member of the Mutant Liberation Front * Locus (magazine), ''Locus'' (magazine), science fiction and fantasy magazine ...
(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 Mechanics (Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximat ...

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. ''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.


Legacy

The
European Space Agency , owner = , headquarters = Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, most populous city of France, with an estimated population of 2,175,601 residents , in an area ...

European Space Agency
's (ESA)
Euclid Euclid (; grc-gre, Εὐκλείδης Euclid (; grc, Εὐκλείδης – ''Eukleídēs'', ; fl. 300 BC), sometimes called Euclid of Alexandria to distinguish him from Euclid of Megara, was a Greek mathematician, often referre ...
spacecraft A spacecraft is a vehicle or machine designed to fly in outer space. A type of artificial satellite alt=, A full-size model of the Earth observation satellite ERS 2 ">ERS_2.html" ;"title="Earth observation satellite ERS 2">Earth obse ...

spacecraft
was named in his honor. The minor planet Euclides is named after him.


See also

*
Axiomatic method In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
*
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. More formally, Euclid's orchard is the set of line segments from to , whe ...
*
Euclidean relationIn mathematics, Euclidean relations are a class of binary relations that formalize ":wikisource:Page:First_six_books_of_the_elements_of_Euclid_1847_Byrne.djvu/26, Axiom 1" in Euclid's Elements: "Magnitudes which are equal to the same are equal to eac ...
*
Extended Euclidean algorithm In arithmetic Arithmetic (from the Ancient Greek, Greek wikt:en:ἀριθμός#Ancient Greek, ἀριθμός ''arithmos'', 'number' and wikt:en:τική#Ancient Greek, τική wikt:en:τέχνη#Ancient Greek, έχνη ''tiké échne', 'art' ...
* List of things named after Euclid * Oliver Byrne (mathematician)


References


Works cited

* Artmann, Benno (1999). ''Euclid: The Creation of Mathematics''. New York: Springer. . * * * With extensive bibliography. * * As reproduced in th
Perseus Digital Library
* Heath, Thomas L. (1981). ''A History of Greek Mathematics'', 2 Vols. New York: Dover Publications. . * Kline, Morris (1980). ''Mathematics: The Loss of Certainty''. Oxford: Oxford University Press. . * * *
Proclus Proclus Lycius (; 410/411/ 7 Feb. or 8 Feb. 412 –17 April 485 AD), called Proclus the Successor, Proclus the Platonic Successor, or Proclus of Athens (Greek: Προκλου Διαδοχου ''Próklos Diádochos'', ''"''in some Manuscript ...
, ''A commentary on the First Book of Euclid's Elements'', translated by Glenn Raymond Morrow, Princeton University Press, 1992. . * *


Further reading

* * * * *


External links

* * *
Euclid's Elements
All thirteen books, with interactive diagrams using Java.
Clark University Clark University is a private Private or privates may refer to: Music * "In Private "In Private" was the third single in a row to be a charting success for United Kingdom, British singer Dusty Springfield, after an absence of nearly two d ...

Euclid's Elements
with the original Greek and an English translation on facing pages (includes PDF version for printing).
University of Texas The University of Texas at Austin, shortened to UT Austin, UT, or Texas, is a public In public relations and communication science, publics are groups of individual people, and the public (a.k.a. the general public) is the totality of s ...
.
Euclid's Elements, books I–VI
in English pdf, in a Project Gutenberg Victorian textbook edition with diagrams.
Euclid's Elements
All thirteen books, in several languages as Spanish, Catalan, English, German, Portuguese, Arabic, Italian, Russian and Chinese.

1482, Venice. From
Rare Book Room Rare Book Room is an educational website Educational technology (commonly abbreviated as EduTech, or EdTech) is the combined use of computer hardware, software, and Education sciences, educational theory and practice to facilitate learning. When ...

Rare Book Room
.
''Elementa''
888 AD, Byzantine. From
Rare Book Room Rare Book Room is an educational website Educational technology (commonly abbreviated as EduTech, or EdTech) is the combined use of computer hardware, software, and Education sciences, educational theory and practice to facilitate learning. When ...

Rare Book Room
.
Texts on Ancient Mathematics and Mathematical Astronomy
PDF scans (Note: many are very large files). Includes editions and translations of Euclid's ''Elements'', ''Data'', and ''Optica'', Proclus's ''Commentary on Euclid'', and other historical sources.
"The elements of geometrie of the most auncient Philosopher Euclide of Megara"
(1570) from th

in the Rare Book and Special Collection Division at the
Library of Congress The Library of Congress (LC) is the research library A library is a collection of materials, books or media that are easily accessible for use and not just for display purposes. It is responsible for housing updated information in order ...

Library of Congress
. {{DEFAULTSORT:Euclid 4th-century BC births 4th-century BC Egyptian people 4th-century BC Greek people 4th-century BC writers 3rd-century BC deaths 3rd-century BC Egyptian people 3rd-century BC Greek people 3rd-century BC writers Ancient Alexandrians Ancient Greek mathematicians Geometers Number theorists Philosophers of mathematics 3rd-century BC mathematicians