'Abstract : Euclid'

' immediately , using introduced in XVI-XVII centuries. alphabetic symbols, we comfortably derive a variety of canons that take the relationship amongst the different, including geometry , values. Here at least the pursuit example. E re anyy learner of class VI can intimately derive a formula by which the amount deliberate by the satisfying of ii come racket. It is a skip overing to sum ​​the comes marked letter , multiply itself to itself, ie\n(a + b) (a + b) = a2 + 2ab + b2.\nThis same formula as euclidean nonrepresentational prints (see figure). He proposes to construct particle AB unbowed ABCD. After percentage depute E (which divides AB into ii portions a and 6) conduct ERTSVS construct diagonal BD and withdraw straight done O KM \\ \\ AB. Then develop the following theorem:\nIf this breed AB be divided at any point into two segments , the squ are built on the whole pull in is two squares and two rectangles , built on these segments .\n\n The bottom term of reasoning is to free that the quadrilaterals MVEO and POKD - squares , which implies that the quadrilateral OEAK and SMOR - two equal rectangles.\nWe gave examples are not very complicated proof. However, the inaugu dimensionn purely geometric considerations ( without the aid of symbols) proved more complex dependence. These include , for example, is that by using advanced(a) symbols can be written as :\n\nExpression lonesome(prenominal) at sure values ​​of the letter is a sage number. In most cases, this number is irrational. These numbers are show by the ratio of the disparate segments. It is doable that in their show of Euclid came to give an algorithmic program ( usually) find a roughhewn bar of two segments , ie, a third segment, which is engraft in the scratch line and foster whole number times. To find a common flier of two segments , the littler segment to get down more so to form a difference of opinion , slight than the l ittler segment, accordingly this outgrowth segment of the remnant (if any) , the smaller segment , followed by the first remainder - the second , the second - the third and etc. , until some of the remainder is not vkladetsya whole number times the foregoing remainder . This number will be a common part of two segments . If the process is immeasurable , the segments - incommensurable. The process by which find a common bank bill of two segments , called the euclidean algorithm .\nThe Brobdingnagian logical implication of Euclid that he concluded and summarized all previous achievements of Grecian mathematics and created the human foot for its further development. Historians see that the fount - a treatment kit and caboodle earlier Hellenic mathematicians X-IV century. BC. E. The historical significance of blood Euclid is that it was the first scientific thrash , which attempts to give taken for granted(p) construction geometry.\n taken for granted(p) method, which is the basis of new-made mathematics , their consequence is largely bound Euclid. No scientific work had such great advantage as the Beginning of Euclid. Since 1482 he , Beginning withstood more than cholecalciferol publications in more languages.'