Euclid fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician and is often referred to as the Father of Geometry. He was active in Alexandria during the reign of Ptolemy I (323 BC – 283 BC). His work Elements is the most successful textbook in the history of mathematics. In it, the principles of what is now called Euclidean geometry were deduced from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and rigor.
Easton Press Euclid books
Euclid's Elements of Geometry - 2002
Franklin Library Euclid books
Works of Archimedes, Apollonius, Euclid and Nicomachus - Great
Books of the Western World - 1985
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Who was Euclid?
Little is known about Euclid's life, as there are only a handful of references to him. In fact, the key references to Euclid were written centuries after he lived, by Proclus and Pappus of Alexandria. Proclus introduces Euclid only briefly in his Commentary on the Elements, written in the fifth century, where he writes that Euclid was the author of the Elements, that he was mentioned by Archimedes, and that when Ptolemy the First asked Euclid if there was no shorter road to geometry than the Elements, he replied, "there is no royal road to geometry." Although the purported 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 those of Archimedes. In addition, the "royal road" anecdote is questionable since it is similar to a story told about Menaechmus and Alexander the Great. In the only other key reference to Euclid, Pappus briefly mentioned in the fourth century 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." It is further believed that Euclid 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, and only roughly estimated in proximity to contemporary figures mentioned in references. No likeness or description of Euclid's physical appearance made during his lifetime survived antiquity. Therefore, Euclid's depiction in works of art is the product of the artist's imagination.
Euclid meaning
The English name 'Euclid' is the anglicized version of the Ancient Greek name Eukleídes (Εὐκλείδης). It is derived from 'eu-' (εὖ; 'well') and 'klês' (-κλῆς; 'fame'), meaning "renowned, glorious". In English, by metonymy, 'Euclid' can mean his most well-known work, Euclid's Elements, or a copy thereof, and is sometimes synonymous with 'geometry'.
Elements of Geometry
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.
There is no mention of Euclid in the earliest remaining copies of the Elements, and 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. The only reference that historians rely on of Euclid having written the Elements was from Proclus, who briefly in his Commentary on the Elements ascribes Euclid as its author.
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
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.
Lost works
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.
Source and additional information: Euclid