Presentation Biography of Euclid
Similar presentations show another presentation on the topic: “Euclid is an ancient Greek mathematician. Young mathematician lived at the beginning of the 3rd century BC Naukhat’s son, known for the name“ Geometers ”, an old time scientist,“ - 1 Euclid - Ancient Greek mathematician 2 Young mathematician lived at the beginning of the III century BC Naukht’s son, known for the name “Geometers”, an old time scientist, in its origin, the Greek, at the place of residence of the Syrian, originally from the shooting range.
He moved to Alexandria. There he founded a mathematical school and wrote for her students his fundamental work, united under the general name of “Beginning” about a year BC. The 1st book formulates the initial provisions of geometry, and also contains fundamental theorems of planimetry, including the theorem on the sum of the angles of the triangle and the Pythagoras theorem.
The 2nd book sets out the basics of geometric algebra. In the 4th book, the correct polygons are considered, and the construction of the right fifteen-angle belongs, apparently, Euclid himself. These three books are apparently written on the basis of the compositions of the archite that have not reached us. The book discusses quadratic irrationality and sets out the results obtained by Teetet.
The book contains the basics of stereometry. In the book, by exhaustion of the Evdox method, theorems related to the area of the circle and volume of the ball are proved, the relations of the volume of pyramids, cones, prisms and cylinders are displayed. The book was based on the results obtained by Teetet in the field of correct polyhedra. I and I do not belong to Euclid, they were written later: I am in the 2nd century.
Book I suggested the definitions of concepts used in the future. They are intuitive because they are defined in terms of physical reality: "The point is that which has no parts." Further, Euclid proves in book I the elementary properties of triangles, among which are conditions of equality. Then, some geometric constructions are described, such as the construction of the bisector of the angle, the middle of the segment and the perpendicular to the straight line.
Book I also includes the theory of parallel and the calculation of the areas of some flat figures of triangles, parallelograms and squares. Book II laid the foundations of the so -called geometric algebra, dating back to the Pythagoras school. All values in it are represented geometrically, and operations on numbers are carried out geometrically. The numbers are replaced by segments of a straight line.
The theory of proportions, developed in the book V, was equally well attached to the commensurate values and to incommensurable quantities. Euclid included in the concept of “magnitude” of length, area, volumes, weights, angles, temporary intervals, etc. Refusing to use geometric evidence, but also avoiding an appeal to arithmetic, he did not attribute to the values of numerical values.
Part is a size of a size smaller from a larger if it measures a large one. The multiple is large from the smaller if it is measured less. The attitude is some dependence of two homogeneous values in quantity. They say that the values are related to each other, if they, taken multiplying, can surpass each other. They say that the quantities are in the same respect: the first to the second and third to the fourth, if equivalent to the first and third at the same time, or at the same time are equal, or at the same time less than the equally equal second and fourth, each for any multiplicity, if we take them in the appropriate order.
The values of the same attitude, albeit called proportional. In book VII determines the equality of relations of integers, or, from a modern point of view, the theory of rational numbers is built. Of the many properties of the numbers studied by Euclide, evenness, divisibility, etc. Book X is read with difficulty; It contains a classification of quadratic irrational values that are represented there geometrically straight and rectangles.
Book XI is dedicated to stereometry. In the book XII, which also rises to Eudox, using the method of exhausting the area of curvilinear figures, are compared with the areas of polygons. The subject of the book XIII is the construction of the right polyhedra. The construction of Platon bodies, which, apparently ended with the "beginning", gave the basis to rank Euclid to the followers of Plato's philosophy.
Euclid also owns phenomena dedicated to elementary spherical astronomy, optics and capoprick, a small treatise of the canon section contains ten tasks of musical intervals, a collection of tasks for dividing the area of divisions about the divisions in the Arabic translation. The presentation in all these essays, as well as the beginning, is subordinated to strict logic, and theorems are derived from the accurately formulated physical hypotheses and mathematical postulates.
Many works of Euclid are lost, we know about their existence in the past only by links in the works of other authors.