Euclid was likely born c. 325 BC. Although the place and circumstances of both his birth and death are unknown. Later historian try to estimate it roughly relative to other people mentioned with him.
Later Euclid’s arrival in Alexandria came about ten years after its founding by Alexander the Great, which means he arrived c. 322 BC.
Euclid is not much younger than these, and that he must have lived during the time of Ptolemy I (c. 367 BC – 282 BC) as Archimedes mentioned him.
Although Archimedes citation of Euclid has been judged to be an interpolation of Eulid works. Historian still believed that Euclid wrote his works before Archimedes wrote his. Euclid died c. 270 BC, presumably in Alexandria.
Euclidean geometry is an axiomatic system, in which all theorems (“true statements”) are derived from a small number of simple axioms.
Until the advent of non-Euclidean geometry, mathematician considered these axioms to be obviously true in the physical world, so that all the theorems would be equally true.
Euclid gives five postulates (axioms) for plane geometry, stated in terms of constructions:
Let the following be postulated:
Draw a straight line from any point to any point.
Produce [extend] a finite straight line continuously in a straight line.
To describe a circle with any centre and distance [radius].
That all right angles are equal to one another.
[The parallel postulate]: That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.
In mathematics, the Euclidean algorithm, or Euclid’s algorithm, is an efficient method for computing the greatest common divisor (GCD) of two numbers, the largest number that divides both of them without leaving a remainder.
The Euclidean algorithm has many theoretical and practical applications. Later Mathematician used it for reducing fractions to their simplest form and for performing division in modular arithmetic.
Computations using this algorithm form part of the cryptographic protocols. Later it is now used to secure internet communications, and in methods for breaking these cryptosystems.
The Elements is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.
It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions.
The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines.
Elements is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science. Mathematician didn’t surpass its logical rigor until the 19th century.
Euclidean space, in geometry, a two- or three-dimensional space in which the axioms and postulates of Euclidean geometry apply. Also, a space in any finite number of dimensions, in which coordinates (one for each dimension) designated points.
Euclidean space is the only conception of physical space for over 2,000 years. It remains the most compelling and useful way of modeling the world as we experienced it.
Though non-Euclidean spaces, such as those that emerge from elliptic geometry and hyperbolic geometry, have led scientists to a better understanding of the universe and of mathematics itself, Euclidean space remains the point of departure for their study.
In addition to the Elements, at least five works of Euclid have survived to the present day. They follow the same logical structure as Elements
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, concerns the division of geometrical figures into two or more equal parts or into parts in given ratios. It is similar to a first-century AD work by Heron of Alexandria.
Catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. However J J O’Connor and E F Robertson names Theon of Alexandria as a more likely author.
Phaenomena, a treatise on spherical astronomy, survives in Greek; it is quite similar to On the Moving Sphere by Autolycus of Pitane, who flourished around 310 BC.
Optics is the earliest surviving Greek treatise on perspective. In its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye.