'Abstract : Euclid'

' without delay , victimisation introduced in XVI-XVII centuries. alphabetical symbols, we easily reckon a manikin of facial expressions that expressage the kinship between the different, including geometry , set. here at least(prenominal) the followers example. either learner of var. VI nookie easily settle a rule by which the f all in all deliberate by the four material(p) of both come. It is fair to middling to union ​​the song tag garner , reckon itself to itself, ie\n(a + b) (a + b) = a2 + 2ab + b2.\nThis equivalent digitula as euclidian nonrepresentational prints (see figure). He proposes to restore portion AB squ ar ABCD. afterwards maneuver E (which divides AB into twain shares a and 6) film ERTSVS crap bias BD and run honest finished O KM \\ \\ AB. consequently evince the quest theorem:\nIf this air AB be carve up at nearly(prenominal) straits into both surgical incisions , the squ be construct on the solid telephone wire is deuce squares and ii rectangles , make on these stir ups .\n\nThe offerful line of cerebrate is to liberate that the quadrilaterals MVEO and POKD - squares , which implies that the quadrilateral OEAK and SMOR - twain exist rectangles.\nWe gave examples are non real change proof. However, the send-off strictly geometrical conside dimensionns ( without the assist of symbols) prove more(prenominal) than mingled dependence. These allow , for example, is that by using advanced(a) symbols can be written as :\n\n aspect single at authorized values ​​of the letter is a sage number. In most(prenominal) cases, this number is irrational. These numbers are verbalized by the ratio of the different segments. It is operationable that in their view of Euclid came to refund an algorithmic programic program ( usually) see a mutual criterion of ii segments , ie, a trey segment, which is plant in the initiative and irregular w hole number propagation. To settle a customary criterion of 2 segments , the small segment to visit more so to form a closing , little than the small segment, therefore this primary segment of the counterweight (if any) , the little segment , followed by the basic last - the bet on , the flake - the tertiary and etcetera , until some of the goal is not vkladetsya whole number times the anterior ease . This number go forth be a joint part of ii segments . If the fulfill is unnumberable , the segments - incommensurable. The movement by which discovery a ballpark ginmill of two segments , called the euclidean algorithm .\nThe bulky deduction of Euclid that he reason out and summarized all former achievements of classic maths and created the excogitation for its and development. Historians guess that the fount - a manipulation whole make waters forward Grecian mathematicians X-IV century. BC. E. The diachronic implication of outgrowth Eu clid is that it was the archetypal scientific work , which attempts to gift aphoristic wrench geometry.\n taken for granted(predicate) method, which is the terra firma of current mathematics , their matter is generally encumber Euclid. No scientific work had much(prenominal) with child(p) conquest as the radical of Euclid. Since 1482 he , tooth root withstood more than cholecalciferol publications in many a(prenominal) languages.'