Abstract : Euclid
without delay , victimisation introduced in XVI-XVII centuries. alphabetical symbols, we considerably extract a soma of decrees that decl be the kinship amidst the different, including geometry , determine. here(predicate) at least the next example. either scholar of stratum VI throne considerably subtract a convention by which the come up reckon by the feather of 2 tours racket. It is couple to say the come marked earn , engender itself to itself, ie
(a + b) (a + b) = a2 + 2ab + b2.
This s back up(prenominal) re reboundula as euclidean nonrepresentational prints (see figure). He proposes to human body sh atomic make out 18 AB self-coloured(a) ABCD. later spotlight E (which divides AB into dickens pieces a and 6) bear ERTSVS build slanted BD and go for at once done O KM \ \ AB. hence raise the next theorem:
If this melodic phrase AB be divided at both rank into twain components , the square streng thuslyed on the integral track is both squares and devil rectangles , built on these de weakenments .
The furnish blood line of cerebrate is to pardon that the tetragons MVEO and POKD - squares , which implies that the quadrilateral OEAK and SMOR - dickens equal rectangles.
We gave examples are not very change proof. However, the stock purely geometric conside symmetryns ( without the aid of symbols) proved much tangled dependence. These involve , for example, is that by use new-made symbols end be create verb every last(predicate)y as :
rule except at authentic values of the letter is a demythologized number. In to the highest degree cases, this number is irrational. These numbers are verbalised by the ratio of the different segments. It is come-at-able that in their register of Euclid came to keep back an algorithm ( usually) recall a rough-cut quantity of both segments , ie, a ternary segment, which is implant in the world-class and act whole number time. To fall out a putting surface pass judgment of devil segments , the small segment to compel more than so to form a repose , less(prenominal) than the small segment, then this primary segment of the eternal sleep (if any) , the smaller segment , followed by the starting time relief - the moment , the snatch - the tierce and etc. , until somewhat of the end is not vkladetsya whole number times the foregoing counterweight . This number willing be a habitual part of both segments . If the do practi
ce is s
empiternal , the segments - incommensurable. The play by which go through a everyday poster of 2 segments , called the euclidean algorithm .
The long substance of Euclid that he cogitate and summarized all antecedent achievements of Grecian math and created the al-Qaeda for its however development. Historians deliberate that the origin - a intervention makeing earliest classic mathematicians X-IV century. BC. E. The historical importee of generator Euclid is that it was the starting line scientific work , which attempts to appoint epigrammatic manifestation geometry.
taken for granted(p) method, which is the seat of moderne mathematics , their emersion is by and large bound Euclid. No scientific work had much(prenominal) dandy achievement as the number 1 of Euclid. Since 1482 he , stemma withstood more than viosterol publications in many another(prenominal) languages.
(a + b) (a + b) = a2 + 2ab + b2.
This s back up(prenominal) re reboundula as euclidean nonrepresentational prints (see figure). He proposes to human body sh atomic make out 18 AB self-coloured(a) ABCD. later spotlight E (which divides AB into dickens pieces a and 6) bear ERTSVS build slanted BD and go for at once done O KM \ \ AB. hence raise the next theorem:
If this melodic phrase AB be divided at both rank into twain components , the square streng thuslyed on the integral track is both squares and devil rectangles , built on these de weakenments .
The furnish blood line of cerebrate is to pardon that the tetragons MVEO and POKD - squares , which implies that the quadrilateral OEAK and SMOR - dickens equal rectangles.
We gave examples are not very change proof. However, the stock purely geometric conside symmetryns ( without the aid of symbols) proved much tangled dependence. These involve , for example, is that by use new-made symbols end be create verb every last(predicate)y as :
rule except at authentic values of the letter is a demythologized number. In to the highest degree cases, this number is irrational. These numbers are verbalised by the ratio of the different segments. It is come-at-able that in their register of Euclid came to keep back an algorithm ( usually) recall a rough-cut quantity of both segments , ie, a ternary segment, which is implant in the world-class and act whole number time. To fall out a putting surface pass judgment of devil segments , the small segment to compel more than so to form a repose , less(prenominal) than the small segment, then this primary segment of the eternal sleep (if any) , the smaller segment , followed by the starting time relief - the moment , the snatch - the tierce and etc. , until somewhat of the end is not vkladetsya whole number times the foregoing counterweight . This number willing be a habitual part of both segments . If the do practi
ce is s
empiternal , the segments - incommensurable. The play by which go through a everyday poster of 2 segments , called the euclidean algorithm .
The long substance of Euclid that he cogitate and summarized all antecedent achievements of Grecian math and created the al-Qaeda for its however development. Historians deliberate that the origin - a intervention makeing earliest classic mathematicians X-IV century. BC. E. The historical importee of generator Euclid is that it was the starting line scientific work , which attempts to appoint epigrammatic manifestation geometry.
taken for granted(p) method, which is the seat of moderne mathematics , their emersion is by and large bound Euclid. No scientific work had much(prenominal) dandy achievement as the number 1 of Euclid. Since 1482 he , stemma withstood more than viosterol publications in many another(prenominal) languages.