Помогите перевести текст по геометрии с английского на русский (доказательство теоремы Пифагора)
Proof #2
We start with two squares with sides a and b, respectively, placed side by side. The total area of the two squares is a²+b².
The construction did not start with a triangle but now we draw two of them, both with sides a and b and hypotenuse c. Note that the segment common to the two squares has been removed. At this point we therefore have two triangles and a strange looking shape.
As a last step, we rotate the triangles 90°, each around its top vertex. The right one is rotated clockwise whereas the left triangle is rotated counterclockwise. Obviously the resulting shape is a square with the side c and area c². This proof appears in a dynamic incarnation.
(A variant of this proof is found in an extant manuscript by Thâbit ibn Qurra located in the library of Aya Sofya Musium in Turkey, registered under the number 4832. [R. Shloming, Thâbit ibn Qurra and the Pythagorean Theorem, Mathematics Teacher 63 (Oct., 1970), 519-528]. ibn Qurra's diagram is similar to that in proof #27. The proof itself starts with noting the presence of four equal right triangles surrounding a strangely looking shape as in the current proof #2. These four triangles correspond in pairs to the starting and ending positions of the rotated triangles in the current proof. This same configuration could be observed in a proof by tessellation.)
Proof #2
We start with two squares with sides a and b, respectively, placed side by side. The total area of the two squares is a²+b².
The construction did not start with a triangle but now we draw two of them, both with sides a and b and hypotenuse c. Note that the segment common to the two squares has been removed. At this point we therefore have two triangles and a strange looking shape.
As a last step, we rotate the triangles 90°, each around its top vertex. The right one is rotated clockwise whereas the left triangle is rotated counterclockwise. Obviously the resulting shape is a square with the side c and area c². This proof appears in a dynamic incarnation.
(A variant of this proof is found in an extant manuscript by Thâbit ibn Qurra located in the library of Aya Sofya Musium in Turkey, registered under the number 4832. [R. Shloming, Thâbit ibn Qurra and the Pythagorean Theorem, Mathematics Teacher 63 (Oct., 1970), 519-528]. ibn Qurra's diagram is similar to that in proof #27. The proof itself starts with noting the presence of four equal right triangles surrounding a strangely looking shape as in the current proof #2. These four triangles correspond in pairs to the starting and ending positions of the rotated triangles in the current proof. This same configuration could be observed in a proof by tessellation.)
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Answers & Comments
Начнем с двух квадратов со сторонами а и Ь соответственно, размещенных бок о бок. Общая площадь двух квадратов a² + b².
Строительство не начать с треугольником, но теперь мы обращаем два из них, как со сторонами А и В и гипотенузы с. Следует отметить, что сегмент общим для двух квадратов был удален. Поэтому при данном этапе мы имеем два треугольника и странный вид формы.
В качестве последнего шага, мы вращать треугольники 90 °, каждый вокруг своей верхней вершине. Правая повор