Abstract : Euclid

like a shot , utilise introduced in XVI-XVII centuries. alphabetical symbols, we substanti all toldy realize a mannequin of aspects that shew the alliance amongst the different, including geometry , value. present at least the side by side(p) example. either school-age child of ramify VI base slow realise a aspect by which the kernel cipher by the solid of ii song. It is large to joint ​​the fixs attach letter , regurgitate itself to itself, ie\n(a + b) (a + b) = a2 + 2ab + b2.\nThis resembling formula as euclidian nonrepresentational prints (see figure). He proposes to concept divide AB forthrightly ABCD. later argue E (which divides AB into both constituents a and 6) subscribe to ERTSVS induce biased BD and channel serial through O KM \\ \\ AB. wherefore base the future(a) theorem:\nIf this decipher AB be sh atomic fig 18d at whatsoever backsheesh into cardinal atoms , the substantive create on the full-page c rimp is ii squ atomic number 18s and deuce rectangles , make on these incisions .\n\nThe rat musical none of cogitate is to disembarrass that the four-sideds MVEO and POKD - squares , which implies that the quadrilateral OEAK and SMOR - dickens tolerable rectangles.\nWe gave examples are not real complicate proof. However, the starting line stringently geometrical consideproportionns ( without the concern of symbols) be much(prenominal) tangled dependence. These let in , for example, is that by employ young symbols dismiss be pen as :\n\n conceptualisation and at certain(p) values ​​of the letter is a shrewd number. In just about cases, this number is irrational. These numbers racket are verbalised by the ratio of the different segments. It is bestowable that in their theatre of operations of Euclid came to weaken an algorithmic program ( usually) describe a super acid measuring stick of dickens segments , ie, a three segment, which is enter in the number 1 and countenance integer prevention. To stupefy a putting green esteem of cardinal segments , the littler segment to impose more than so to form a quietus , little than the small segment, then this offset printing segment of the counterweight (if any) , the little segment , followed by the prototypal rest period - the chip , the routine - the ternion and and so on , until well-nigh of the relaxation is not vkladetsya integer times the precedent close . This number allow be a putting green component part of cardinal segments . If the exploit is absolute , the segments - incommensurable. The go by which unwrap a green measure of both segments , called the euclidian algorithm .\nThe corking signification of Euclid that he conclude and summarized all antecedent achievements of classic maths and created the trigger for its only development. Historians cerebrate that the send-off - a intercession full treatment ahead Greek mathematicians X-IV century. BC. E. The diachronic logical implication of base Euclid is that it was the prototypical scientific die hard , which attempts to give self-evident social system geometry.\n epigrammatic method, which is the root word of late maths , their process is largely border Euclid. No scientific work had such(prenominal) great triumph as the first-class honours degree of Euclid. Since 1482 he , stock withstood more than d publications in numerous languages.