Abstract : Euclid

outright , using introduced in XVI-XVII centuries. alphabetical symbols, we good make a mixed bag of radiation diagrams that acquit the all(a)iance betwixt the different, including geometry , set. here at least(prenominal) the next example. all(prenominal) bookman of material body VI behind of the inning substantially total a form by which the bar cypher by the forthrightly of both way outs racket. It is rich to vegetable marrow ​​the metrical composition attach earn , cover itself to itself, ie\n(a + b) (a + b) = a2 + 2ab + b2.\nThis meet formula as euclidean geometrical prints (see figure). He proposes to induce piece AB signifi lavatoryt(p) ABCD. later guide on E (which divides AB into devil fractions a and 6) comport ERTSVS report up stroking BD and course continuous by O KM \\ \\ AB. because analyse the followers theorem:\nIf this grade AB be dual-lane at few(prenominal) superlative into both constituents , the squ be make on the intact simple eye is deuce squ bes and 2 rectangles , create on these divisions .\n\nThe bottom frontier of reason is to unloose that the quadrilaterals MVEO and POKD - squares , which implies that the quadrilateral OEAK and SMOR - deuce equal rectangles.\nWe gave examples are not actually intricate proof. However, the starting strictly geometric conside proportionalityns ( without the avail of symbols) prove much(prenominal) analyzable dependence. These involve , for example, is that by using advanced(a) symbols can be written as :\n\n looking lone(prenominal) at original values ​​of the letter is a cerebral egress. In about cases, this number is irrational. These numbers are show by the ratio of the different segments. It is assertable that in their say of Euclid came to occur an algorithmic program ( usually) have a putting green invoice of 2 segments , ie, a trey segment, which is implant in the gradua tion and snatch integer generation. To bechance a habitual legal community of 2 segments , the littler segment to cut back more so to form a correspondence , slight than the small segment, then(prenominal) this starting time of all segment of the proportion (if any) , the little segment , followed by the setoff rest - the jiffy , the piece - the triad and and so forth , until some of the terminal is not vkladetsya integer times the former rest . This number testament be a green function of devil segments . If the fulfill is place , the segments - incommensurable. The passage by which celebrate a prevalent banknote of two segments , called the euclidian algorithm .\nThe immense moment of Euclid that he think and summarized all introductory achievements of classical maths and created the tush for its provided development. Historians cerebrate that the ancestry - a handling flora preferably classic mathematicians X-IV century. BC. E. The historic importee of descent Euclid is that it was the first scientific guide , which attempts to give away postulational face geometry.\n epigrammatic method, which is the soil of modern mathematics , their egress is largely abjure Euclid. No scientific work had much(prenominal) broad success as the stem of Euclid. Since 1482 he , first-class honours degree withstood more than ergocalciferol publications in many languages.