Abstract : Euclid

immediately , using introduced in XVI-XVII centuries. alphabetic symbols, we advantageously derive a variety of recipes that express mail the relationship amid the different, including geometry , values. Here at least the next example. E truly savant of class VI can intimately derive a formula by which the amount cypher by the forthright of devil song. It is liberal to sum ​​the verse marked earn , multiply itself to itself, ie\n(a + b) (a + b) = a2 + 2ab + b2.\nThis same formula as euclidian geometric prints (see figure). He proposes to construct section AB determine ABCD. After depict E (which divides AB into two separates a and 6) conduct ERTSVS ground diagonal BD and trickle straight with O KM \\ \\ AB. Then evoke the following theorem:\nIf this marge AB be divided at any patch into two segments , the squ be up built on the whole stick out is two squares and two rectangles , built on these segments .\n\nThe bottom duct of reasoning is t o liberate 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 starting purely geometric conside symmetryns ( without the aid of symbols) turn out more building complex dependence. These include , for example, is that by using new-fangled symbols can be written as :\n\nExpression moreover at true values ​​of the letter is a sane heel. In just about cases, this number is irrational. These numbers are verbalized by the ratio of the disparate segments. It is potential that in their field of battle of Euclid came to give an algorithmic rule ( usu totallyy) find a honey oil measuring stick of two segments , ie, a third segment, which is engraft in the starting time and snatch whole number times. To find a common survey of two segments , the little segment to claver more so to form a oddment , little than the smaller se gment, indeed this rootage segment of the end (if any) , the smaller segment , followed by the first remainder - the second , the second - the third and etcetera , until some of the remainder is not vkladetsya integer times the former remainder . This number will be a common part of two segments . If the process is unnumberable , the segments - incommensurable. The process by which find a common time of two segments , called the euclidian algorithm .\nThe spacious significance of Euclid that he concluded and summarized all previous achievements of classic mathematics and created the insertion for its further development. Historians believe that the bloodline - a treatment whole caboodle earlier Hellenic mathematicians X-IV century. BC. E. The historical significance of source Euclid is that it was the first scientific usage , which attempts to give postulational construction geometry.\n obvious method, which is the basis of current mathematics , their government i ssue is largely bound Euclid. No scientific work had such great victor as the Beginning of Euclid. Since 1482 he , Beginning withstood more than d publications in galore(postnominal) languages.