Brief biography Euclid

Bibliography Biography The ancient Greek thinker Euclid became the first mathematician of the Alexandrian school and the author of one of the most ancient theoretical mathematical treatises. The biography of this scientist is much less known than about his work. So, in the well -known work of “Beginning”, Euclid outlined stereometry, planimetry, aspects of the theory of numbers, created a base for the subsequent development of mathematics.

The biography of Euclid allegedly began in the year BC is an approximate date, the exact year of birth is unknown in Alexandria. Some researchers suggest that the future mathematician was born in a dash, and spent most of the adulthood in Damascus. Euclid probably came from a rich family, since he studied at the Plato Athenian school at that time such education was available only to wealthy citizens.

The scientists managed to establish a portrait of Euclid that the author of the “began” was younger than the famous followers of Plato, who lived and created a century from a century, but older than Archimedes, who was born in the year and died in the year BC. Euclid understood the philosophical concept of Plato and shared its main provisions. The above information about the personality and life paths of Euclid is drawn by researchers from the comments of Proche, written by him to the first book “Beginning”.

The statements of Stobe and Papp of the personality of the ancient Greek thinker are also known. Stobey allegedly said that in response to the student’s question about the benefit from science, Euclid ordered the slave to give him several coins. Papp noted that the scientist knew how to be kind and soft with any person who could at least to some extent be useful for the development of mathematical sciences.

The portrait of Euclid, the preserved data about Euclid is so small and doubtful that there is a version of the assignment of the pseudonym "Euclid" to the whole collectives of scientists from ancient Alexandria. Euclid Alexandria is confused with the Greek philosopher Euclid from Megar, a student of Socrates, who lived in a century BC. In the Middle Ages, Euclid from Megar was even considered the author of the “beginning”.

Euclid spent a considerable part of his free time in the Alexandrian library - the temple of knowledge founded by Ptolemy. Within the walls of this institution, the ancient Greek scientist took up the unification of arithmetic laws, geometric principles and the theory of irrational numbers in geometry. Euclid described the results of his works in the book “Beginning” - an essay that made a great contribution to the development of mathematics.

The book of Euclid "Beginning" the book consists of fifteen volumes: in the book I, the author talks about the properties of parallelograms and triangles, completing the presentation by using the Pythagorean theorem when calculating the parameters of rectangular triangles. The book under number II describes the principles and patterns of geometric algebra and dates back to the baggage of knowledge accumulated by the Pythagoreans.

During the creation of these volumes, the author could turn to the use of the work of Hippocrates of Khios. In the V book, the ancient Greek mathematician examined the general theory of proportions developed by Evdox Knidsky. In the materials of the VI book, the author attaches a general theory of the proportions of Evdox of Knid to the theory of such figures.

When writing these volumes, the mathematician again turned to the materials created and collected by the Pythagoreans - representatives of the doctrine, in which the number occupies the central role. In these works, the author speaks of geometric progressions and proportions, proves the infinity of many prime numbers, studies even, introduces the concept of the GCD of the greatest common divider.

The algorithm for finding such a divider is currently called the Euclidean algorithm. The famous work of Euclid "began" Tom under the number X is the most complex and voluminous work in the composition of "beginnings", which contains a classification of irrationalities. The authorship of this book is also unknown for certain: it could write both Euclid himself and Theetet of Athens.

On the pages of the XI book, the mathematician talks about the basics of stereometry. Book XII contains evidence of theorems of the volume of cones and pyramids, relations of the area of ​​circles. To build these evidence, the exhaust method is used. Most researchers agree that this book was also not written by Euclid. The likely author is Evdox Knidsky. Evdox British materials of the XIII Books contain information about the construction of five correct polyhedraries of Platon Tel.

Some of the constructions given in the volume could be developed by Theetet of Athens. So, the penultimate volume of “began” was written by the gypsyl who also lived in Alexandria, but later Euclid, and the latter was written by Isidor Miletsky, who built the temple of St. Sophia in Constantinople at the beginning of the sixth century BC. Before the appearance of Euclid's “beginnings” works with the same name, the essence of which was the sequential presentation of key facts of theoretical arithmetic and geometry, were compiled by Leont, Hippocrates of the Khios, Fevdius.

All of them practically disappeared from everyday life after the appearance of the work of Euclid.For two thousand years, fifteen volumes of “beginnings” acted as a basic textbook on geometry. The work was translated into Arabic, then into English. Euclid's book “Beginning” a significant part of the materials that the author included in labor is not his own discoveries, but previously known theories.

The essence of the work of Euclid was the processing of the material, its systematization and information of disparate data. Euclid began some books with a list of definitions, in the first book there is also a list of axioms and postulates. The postulates of Euclids are divided into two groups: general concepts, including generally recognized scientific statements, and geometric axioms.

So, in the first group there are such statements: "If two values ​​are separately equal to the same third, then they are equal to each other." In the second group, for example, the following statements are: "From any point to any point you can draw a straight line." He also wrote a number of works on the Cathoptric of the new optics industry, which, to a large extent, approved the mathematical function of mirrors.

The scientist devoted several works to the study of conical sections. The mathematician also developed assumptions and hypotheses regarding the trajectory of the movement of bodies and laws of mechanics. He became the author of key tools with which the geometry operates - the so -called "Euclidean constructions." Many works of this ancient Greek thinker have not survived to this day.

Philosophy in ancient times philosophy was closely woven with many other branches of scientific knowledge. So, geometry, astronomy, arithmetic and music were considered mathematical sciences, the understanding of which is necessary for a qualitative study of philosophy. Euclid developed Plato's teachings about four elements, which are brought into line with four correct multi -graders: the element of fire personifies the tetrahedron; The element of the Earth is associated with a cube; The water element is associated with the icosahedron.

The philosopher Euclid in this context of the “beginning” can be considered as a kind of doctrine of the construction of “Platon bodies”, that is, five correct polyhedra. The teaching contains all the necessary prerequisites, evidence and ligaments. The proof of the possibility of building such bodies ends in the assertion of the fact that there are no other correct bodies, with the exception of the data of five,.

Almost every Euclid theorem in the “Bage” also corresponds to the indicators of the doctrine about the proof of Aristotle. So, the author consistently derives the investigations from the causes, forming a chain of logical evidence. Moreover, it proves even a general statement, which also corresponds to the teachings of Aristotle. Personal life came to us only some information about the work of Euclid in science, but practically nothing is known about his personal life.

There is a legend that King Ptolemy, who decided to study the geometry, was annoyed by its complexity. Then he turned to Euclid and asked him to point out an easier path to knowledge, to which the thinker replied: "There is no royal road to geometry." The expression later became winged. Euclid founded a mathematical school at the Alexandrian library, there is evidence that under the Alexandrian library, this ancient Greek scientist founded a private mathematical school.

The same enthusiasts of science studied in it as Euclid himself. Even at the sunset of his life, Euclid helped students in writing work, creating their own theories and developing appropriate evidence. There is no exact data on the appearance of the scientist. Its portraits and sculptures are the fruit of the imagination of their creators, an invented image, transmitted from generation to generation.

Death presumably, Euclid died in the years BC. The exact causes of death are not known. The scientist’s heritage survived him for two thousand years and inspired many great people a century after his death. There is an opinion that the politician Abraham Lincoln loved to quote the statements of Euclid in his speeches and had several volumes “began” with him. The statue of Euclida scientists of subsequent years based the works on the works of Euclid.

Thus, the Russian mathematician Nikolai Lobachevsky used the materials of the ancient Greek thinker to develop hyperbolic geometry, or Lobachevsky's geometry.

The format of mathematics, which was created by Euclid, is now known as "Euclidean Geometry." The scientist also created a device for determining the height of the tone of the string and studied interval ratios, contributing to the creation of keyboards.