# Mathematics and Euclid

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.

- EuclidA fitting example is the problem of integer factorization, which goes back to Euclid, but which had no practical application before its use in the RSA cryptosystem (for the security of computer networks).

- Mathematics8 related topics

## Axiom

Statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.

Statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.

As used in mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms".

The root meaning of the word postulate is to "demand"; for instance, Euclid demands that one agree that some things can be done (e.g., any two points can be joined by a straight line).

## Euclid's Elements

The Elements ( Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. undefined 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions.

## Greek mathematics

Greek mathematics refers to mathematics texts written during and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly extant from the 7th century BC to the 4th century AD, around the shores of the Eastern Mediterranean.

It has been customary to credit almost half of the material in Euclid's Elements to the Pythagoreans, as well as the discovery of irrationals, attributed to Hippassus (c.

## Geometry

Geometry is, with arithmetic, one of the oldest branches of mathematics.

Euclid took an abstract approach to geometry in his Elements, one of the most influential books ever written.

## Non-Euclidean geometry

In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry.

Euclid's fifth postulate, the parallel postulate, is equivalent to Playfair's postulate, which states that, within a two-dimensional plane, for any given line l and a point A, which is not on l, there is exactly one line through A that does not intersect l. In hyperbolic geometry, by contrast, there are infinitely many lines through A not intersecting l, while in elliptic geometry, any line through A intersects l.

## History of mathematics

The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past.

It was there that Euclid (c.

## Apollonius of Perga

Ancient Greek geometer and astronomer known for his work on conic sections.

Ancient Greek geometer and astronomer known for his work on conic sections.

Beginning from the contributions of Euclid and Archimedes on the topic, he brought them to the state prior to the invention of analytic geometry.

For such an important contributor to the field of mathematics, scant biographical information remains.

## Conic section

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.

Euclid (fl.