# Dictionary Definition

Euclid n : Greek geometer (3rd century BC)

# Extensive Definition

Euclid (Greek: ),
fl. 300 BC, also known
as Euclid of Alexandria and the "Father of Geometry", was a
Greek
mathematician of the Hellenistic
period who was active in Alexandria,
almost certainly during the reign of Ptolemy I
(323
BC–283
BC). His Elements
is the most successful textbook in the history
of mathematics. In it, the principles of what is now called
Euclidean
geometry are deduced from a small set of axioms. Euclid also wrote works on
perspective,
conic
sections, spherical
geometry, and rigor.

## 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. The date and
place of Euclid's birth and the date and circumstances of his death
are unknown.

Some writers in the Middle Ages
confused him with Euclid of
Megara, a Greek Socratic philosopher who lived
approximately one century earlier.

## The 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 proofs that remains the basis of mathematics 23 centuries later.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.

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.

## Other works

In addition to the Elements, at least five works
of Euclid have survived to the present day.

- 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. The attribution to Euclid is doubtful. Its author may have been 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 BC.
- 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 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.

All of these works follow the basic logical
structure of the Elements, containing definitions and proved
propositions.

There are also 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'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.
- 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. 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.

## References

- Artmann, Benno (1999). Euclid: The Creation of Mathematics. New York: Springer. ISBN 0-387-98423-2.

- [p. 52].

- 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.

- .

## External links

- A short list of Mathematicians born in Egypt
- Euclid's elements, All thirteen books, with interactive diagrams using Java. Clark University
- Euclid's elements, with the original Greek and an English translation on facing pages (includes PDF version for printing). University of Texas.
- Euclid's elements, All thirteen books, in Spanish and Catalan.
- Elementa Geometriae 1482, Venice. From Rare Book Room.
- Elementa 888 AD, Byzantine. From Rare Book Room.
- Euclid biography by Charlene Douglass With extensive bibliography.
- Euclid's Elements. Heiberg's edition of the Greek with Latin translation (public domain). PDF scans of all 13 books.

Euclid in Arabic: إقليدس

Euclid in Asturian: Euclides

Euclid in Azerbaijani: Evklid

Euclid in Bengali: ইউক্লিড

Euclid in Bosnian: Euklid

Euclid in Breton: Euklides

Euclid in Bulgarian: Евклид

Euclid in Catalan: Euclides

Euclid in Czech: Eukleidés

Euclid in Danish: Euklid

Euclid in German: Euklid

Euclid in Modern Greek (1453-): Ευκλείδης

Euclid in Spanish: Euclides

Euclid in Esperanto: Eŭklido

Euclid in Extremaduran: Uclidi

Euclid in Persian: اقلیدس

Euclid in French: Euclide

Euclid in Galician: Euclides

Euclid in Classical Chinese: 歐几里得

Euclid in Korean: 에우클레이데스

Euclid in Armenian: Էվկլիդես

Euclid in Croatian: Euklid

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Euclid in Indonesian: Euklides

Euclid in Icelandic: Evklíð

Euclid in Italian: Euclide

Euclid in Hebrew: אוקלידס

Euclid in Kara-Kalpak: Evklid

Euclid in Georgian: ევკლიდე

Euclid in Kirghiz: Евклид

Euclid in Latin: Euclides

Euclid in Latvian: Eiklīds

Euclid in Lithuanian: Euklidas

Euclid in Lombard: Eucliit da Megara

Euclid in Hungarian: Euklidész

Euclid in Maltese: Ewklide

Euclid in Mongolian: Евклид

Euclid in Dutch: Euclides van Alexandrië

Euclid in Japanese: エウクレイデス

Euclid in Norwegian: Euklid av Alexandria

Euclid in Piemontese: Uclid

Euclid in Polish: Euklides

Euclid in Portuguese: Euclides

Euclid in Romanian: Euclid

Euclid in Russian: Евклид

Euclid in Albanian: Euklidi

Euclid in Sicilian: Euclidi

Euclid in Simple English: Euclid

Euclid in Slovak: Euklides

Euclid in Slovenian: Evklid

Euclid in Serbian: Еуклид

Euclid in Serbo-Croatian: Euklid

Euclid in Finnish: Eukleides

Euclid in Swedish: Euklides

Euclid in Tamil: யூக்ளிட்

Euclid in Thai: ยุคลิด

Euclid in Vietnamese: Euclid

Euclid in Tajik: Эвклид

Euclid in Turkish: Öklid

Euclid in Ukrainian: Евклід

Euclid in Urdu: اقلیدس

Euclid in Volapük: Eukleides

Euclid in Yiddish: אוקלידוס

Euclid in Chinese: 欧几里德