Table of Contents

## Euclid Theories

Euclid theories changes the world. Euclid is often referred to as “the father of geometry” because he composed an original treatise on geometry that solidified many earlier results into a single magnum opus; his book provided a common language and systematized many existing approaches to studying geometry.

For example, he defined an angle as “the inclination to one another of two lines which meet each other” or “the inclination to one another of two lines in a plane which meet together”. This definition proved useful and has been popularized by other mathematicians ever since.

## Euclid Theory Of Light

Euclid proposed that light is a stream of tiny particles (he called them “corpuscles”) that move in straight lines. Like the atoms of Democritus, these particles are indivisible and immutable.

He did not believe that light was made up of waves because he thought that it would be impossible for such waves to exist without also having some kind of particle making them travel through space. The particle theory of light was replaced by the wave theory in the 19th century.

## Euclid’s Theory Of Equality

Euclid’s theory of equality is a theory of equality that is used in set theory and the philosophy of mathematics. It is named after the Greek mathematician Euclid of Alexandria (c. 300 BC), who first stated it in his book Elements.

Euclid’s theory states that:

Two objects are equal if they are identical.

Two objects are unequal if they are not identical.

The first part is known as the identity axiom, while the second part is known as the non-identity axiom. The two parts together are sometimes called ‘Euclid’s axiom’.

In modern set theory, this theory is equivalent to the axiom of extensionality, which states that two sets are equal if and only if their elements are equal.

## Euclid Theory Of Numbers

Euclid’s theory of numbers is a collection of propositions that were put together by the famous Greek mathematician, Euclid.

The theory shows how numbers can be demonstrated using other numbers, and is considered to be one of the earliest forms of abstract math. The theory contains many theorems including:

-Every prime number is odd, except 2.

-If one number divides another evenly, it will also divide evenly into the difference of those two numbers.

-If a number is divisible by any prime number, it is also divisible by the square of that prime number.

-There are an infinite amount of prime numbers.

## Euclidean Geometry

Euclidean geometry is a branch of mathematics that studies Euclidean spaces, which are the spaces that satisfy Euclid’s fifth postulate: “Given a line segment and a point not on the line segment, there is exactly one line through the point parallel to the given line segment.”

This branch is named for Euclid of Alexandria, who was one of the first writers to describe this geometry. The term “Euclidean geometry” is also used to refer to plane geometry and solid geometry.

It is the study of two- and three-dimensional shapes such as circles, lines, squares, and triangles. Examples of problems include finding the perimeter or area of triangles or rectangles.

## Euclid Elements

Euclid’s Elements is influential works in mathematics. It contains the foundations of geometry and has been referred to as “the most successful and influential textbook ever written”.

Euclid’s Elements is a 13-book collection of elementary geometry, originally written in Greek by the mathematician Euclid c. 300 BC.

It consists of definitions, postulates (axioms), propositions, and proofs of the propositions. The first five books deal with plane geometry; the remaining six with solids (spheres, cones, cylinders, prisms and pyramids).

Euclid’s Elements was long considered a model for clarity and rigor by logicians; it was given pride of place in university courses because of its logical development from incontrovertible principles.

In recent years its reputation has been somewhat tarnished by the discovery that some of its proofs are invalid. However it still retains some value as an exposition on basic principles and reasoning methods in mathematics.

## Euclidean Algorithm

In mathematics, the Euclidean algorithm is a method of finding the greatest common divisor of two integers, also called their gcd (for greatest common divisor).

The algorithm was described by Euclid in his Elements around 300 BC. It can be used to reduce fractions to their simplest forms, which is useful for simplifying formulas involving fractions. This makes it a useful tool in algebra and number theory.

The Euclidean algorithm consists of a series of steps that can be performed independently at each step. At each step, one of the two numbers is divided by its remainder so far (the modulus) and the remainder is subtracted from the other number until they differ by less than the modulus.

## Euclid Achievements

Euclid’s work Elements is the most influential textbook of all time. He collected, refined, and enlarged the knowledge of previous mathematicians to create a comprehensive account of mathematics.

The Elements was so effective that it was still in use until the 20th century. In fact, it has been said that most of modern mathematics can be derived from Euclid’s work.

Euclid’s work was not limited to geometry; he also wrote about number theory and mathematical logic. His other works include Data, Optics and Phenomena.

Although Euclid is often referred to as “The Father of Geometry,” this is not strictly true. The Ancient Babylonians, Egyptians and Greeks all had geometrical knowledge before him.

However, Euclid systematized the knowledge of his predecessors and recorded the discoveries of his contemporaries in a single convenient volume.