BC, was educated at Plato's academy in Athens and stayed there until invited to teach at Ptolemy I's newly founded university in Alexandria in Egypt. It is there he is believed to have stayed until the time of his death.
All mentions of Euclid describe him as fair, kind, patient, someone who had no problem praising others' work, and someone who was ready and willing to help others. However, he was also known to be sarcastic at times. When one of his students, like most high school students, complained that he would never have any use in his daily life for the mathematics he was learning on he had left school, Euclid was quick to respond. He told his slave to give the boy a coin because "he must make a gain out of what he learns." Another story has Ptolemy wanting Euclid to give him a shortcut to learning geometry, rather than leaning all the theorems. Euclid replied, "There is no royal road to geometry," and told the king to study.
Exactly how much of Euclid's original work is in The Elements, a collection of Greek mathematics and geometry, is unknown. Many of the theorems found can be traced to former thinkers including, Eudoxus, Thales, Hippocrates, and Pythagoras. On the other hand, the layout of The Elements belongs to him alone. Each volume lists a number of definitions and assumptions followed by theorems, which are followed by proofs using those definitions and postulates. Every statement was proven, no matter how obvious.
The Element was arranged in thirteen books.
Euclid structured each book into four groups.
Book I - VI -- Plane geometry Books one and two lay down the basic properties of triangles, parallels, parallelograms, rectangles, and squares. Book three deal with the properties of the circle. Book four dealt with the problems of circle and is thought to set out work of the followers of Pythagoras. The work of Eudoxus is laid out on proportion applied to commensurable and incommensurable magnitudes in book five, while book six look at applications of the results of book five to plane geometry.
Book VII - IX -- Theory of Numbers Books seven to nine dealt with theory of numbers. Book seven is a self-contained introduction to number theory. It contains the Euclidean algorithm for finding the greatest common divisor of two numbers. Book eight looked at numbers in geometrical progression.
Book X -- Incommensurables Book ten covered mainly the work of Theaetetus and dealt with the theory of irrational numbers. Euclid altered the proofs of several theorems in this book so that they fitted the new definition of proportion given by …show more content…
Eudoxus.
Book XI - XIII -- Solid Geometry Three-dimensional geometry is covered in books eleven through thirteen. The basic definitions needed for this subject is covered in book thirteen. The theorems follow a fairly similar pattern to the two-dimensional analogues previously given in books one and four. The bottom lines of book twelve are that circles are to one another as the squares of their diameters and that spheres are to each other as the cubes of their diameters. The "method of exhaustion"� invented by Eudoxus is used by Euclid to prove the theorems. The Elements concludes with book thirteen which discusses the properties of the five regular polyhedra and gives proof that there are precisely five. This book appears to be based largely on an earlier treatise by Theaetetus.
The first printed copy came out in 1482 and was the geometry textbook and logic primer by the 1700s.
During the period Euclid was highly respected as a mathematician and Elements was considered one of the greatest mathematical works of all time. The publication was used in schools up to 1903.
In his time, Euclid was attacked by many of his colleagues for being too detailed and including self-evident data, such as one side of a triangle can not be longer than the sum of the other two sides. Today, most mathematicians attack Euclid for the exact opposite reason. They feel he was not thorough enough. In Elements, there are missing areas which were forced to be filled in by following mathematicians. In addition, several errors and questionable ideas have been found.
Euclid also wrote other books, some of which have survived through the time and some of which have not. A few that have survived are: Data, which was a companion volume to the first six books of The Elements, written for beginners. It looks at what properties of figures can be deduced when other properties are given. It includes geometric methods for the solution of quadratics; Division of Figures, a collection of thirty-six propositions relating to the division of plane configurations. It survived only in Arabic translations; Phaenomena, on spherical geometry, which is similar to the work by Autolycus; and Optics, an early work on perspective including optics, catoptrics and
dioptrics.
Euclid may not have been a first class mathematician but holds the distinction of being one of the first person to attempt to standardize mathematics and set it upon a foundation of proofs. His work acted as a springboard for future generations