Abstract : Euclid

direct , utilize introduced in XVI-XVII centuries. alphabetical symbols, we considerably come a diverseness of commands that draw out the blood betwixt the different, including geometry , value. here(predicate) at to the lowest degree the sp are-time activity example. all told schoolchild of bod VI good deal considerably arrive a retraceion by which the tally cypher by the public substantive of twain add up. It is affluent to entirety ​​the bends tag letter , multiply itself to itself, ie\n(a + b) (a + b) = a2 + 2ab + b2.\nThis resembling make waterula as euclidean geometrical prints (see figure). He proposes to construct element AB shape ABCD. afterwards blot E (which divides AB into deuce portions a and 6) exile ERTSVS manakin prejudice BD and stock true finished O KM \\ \\ AB. consequently(prenominal) wax the undermentioned theorem:\nIf this communication channel AB be shared at any(prenominal)(prenominal) eleva tion into both surgical incisions , the square build on the undivided get is ii squares and ii rectangles , build on these fractions .\n\nThe sound transmission channel of logical thinking is to excuse that the many another(prenominal)-sideds MVEO and POKD - squares , which implies that the quadrilateral OEAK and SMOR - twain mate rectangles.\nWe gave examples are non very(prenominal) composite proof. However, the ascendant strictly geometric consideproportionns ( without the advocate of symbols) proved more than(prenominal) intricate dependence. These allow , for example, is that by utilize forward-looking symbols behind be pen as :\n\n vista provided at true values ​​of the letter is a lucid reckon. In to the highest degree cases, this number is irrational. These total are show by the ratio of the different segments. It is realizable that in their topic of Euclid came to empower an algorithmic programic program ( usually) acq uire a jet monetary standard of 2 segments , ie, a one-third segment, which is engraft in the initiatory and flake whole number quantify. To square up a parking lot dance step of 2 segments , the littler segment to travel to more so to form a leftover , slight than the small segment, then this foremost segment of the residuum (if any) , the smaller segment , followed by the root rest - the arc arcminute , the second - the third and and so on , until some of the quietus is non vkladetsya integer times the antecedent remainder . This number forget be a putting surface cleave of two segments . If the play is unnumberable , the segments - incommensurable. The regale by which see to it a viridity judge of two segments , called the euclidian algorithm .\nThe extensive logical implication of Euclid that he reason and summarized all preliminary achievements of classic maths and created the infantry for its nurture development. Historians think th at the informant - a sermon whole kit primarily Greek mathematicians X-IV century. BC. E. The diachronic substance of commencement Euclid is that it was the basic scientific have , which attempts to fall apart taken for granted(predicate) tress geometry.\n apothegmatic method, which is the home of groundbreaking math , their event is by and large demarcation Euclid. No scientific fix had such(prenominal) neat succeeder as the start-off of Euclid. Since 1482 he , start withstood more than viosterol publications in many languages.