Euclid

For other uses, see Euclid (disambiguation).

Euclid
Born	fl. 300 BC
Nationality	Greek
Known for	Euclid's Elements
Scientific career
Fields	Mathematics

Euclid (Greek: Εὐκλείδης -- Eukleidis), also known as Euclid of Alexandria, "The Father of Geometry" was a Greek mathematician of the Hellenistic period who flourished in Alexandria, Egypt, 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 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.

Although best-known for its geometric results, the Elements also includes much number theory, in considering 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.

Euclid also wrote works on perspective, conic sections, spherical geometry, and possibly quadric surfaces.

Biographical knowledge

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

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.

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

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
• Optics, the earliest surviving Greek treatise on perspective, contains propositions on the apparent sizes and shapes of objects viewed from different distances and angles.
• Phaenomena, spherical geometry of use to astronomers. It is similar to Sphere by Autolycus.
• 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.

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

There are four 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.
• 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.

See also

• Euclidean geometry

References

• Artmann, Benno (1999). Euclid: The Creation of Mathematics. New York: Springer. ISBN 0-387-98423-2.
• 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.; Robertson, Edmund F., "Euclid", MacTutor History of Mathematics Archive, University of St Andrews
• Boyer, Carl B. (1991). A History of Mathematics (Second Edition ed.). John Wiley & Sons, Inc. ISBN 0471543977. {{cite book}}: |edition= has extra text (help)

External links

• 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) (only the first ten books). University of Texas.
• Euclid's Elements in ancient Greek (typeset in PDF format, public domain, available in print at Lulu.com as "Euclid's Elements".)
• 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.