Euclid's Elements

Euclid's Elements (Ancient Greek: Στοιχεῖα Stoicheia) is a mathematical and geometric treatise consisting of 13 books written by the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates (axioms), propositions (theorems and constructions), and mathematical proofs of the propositions. The thirteen books cover Euclidean geometry and the ancient Greek version of elementary number theory. The work also includes an algebraic system that has become known as geometric algebra, which is powerful enough to solve many algebraic problems, including the problem of finding the square root of a number. The Elements is the second oldest extant Greek mathematical treatises after Autolycus' On the Moving Sphere, and it is the oldest extant axiomatic deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science. According to Proclus the term "element" was used to describe a theorem that is all-pervading and helps furnishing proofs of many other theorems. The word 'element' is in the Greek language the same as 'letter'. This suggests that theorems in the Elements should be seen as standing in the same relation to geometry as letters to language. Later commentators give a slightly different meaning to the term 'element', emphasizing how the propositions have progressed in small steps, and continued to build on previous propositions in a well-defined order.

Euclid

Euclid (/ˈjuːklɪd/; Greek: Εὐκλείδης, Eukleidēs Ancient Greek: [eu̯.klěː.dɛːs]; fl. 300 BCE), sometimes called Euclid of Alexandria to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the "father of geometry". He was active in Alexandria during the reign of Ptolemy I (323–283 BCE). His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. In the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor.

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

Life

Very few original references to Euclid survive, so little is known about his life. The date, place and circumstances of both his birth and death are unknown and may only be estimated roughly relative to other figures mentioned alongside him. He is rarely mentioned by name by other Greek mathematicians from Archimedes onward, who usually call him "ὁ στοιχειώτης" ("the author of Elements"). The few historical references to Euclid were written centuries after he lived, by Proclus c. 450 AD and Pappus of Alexandria c. 320 AD.