I. Найдите в тексте интернациональные слова, переведите их.
II. Выберите в колонке В эквиваленты к словам колонки А.
| А
| В
| | 1. property
2. natural number
3. proof
4. concept
5. right triangle
6. abstraction
7. solid geometry
8. deductive aspect of geometry
9. rational doctrines
10. pure mathematics
| a) концепция
b) правильный треугольник
d) свойство
c) натуральное число
e) пространственная геометрия
f) доказательство
g) дедуктивный аспект геометрии
h) чистая математика
i) абстракция
j) рациональные доктрины
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III. Заполните пропуски подходящими по смыслу словами.
1. Under Plato’s influence they emphasized … to the extent of ignoring all practical applications.
a) geometry b) axioms
c) pure mathematics d) new theory
2. They proved the fundamental theorems of a plane and ….
a) curve b) plane geometry
c) symbol d) solid geometry
3. The Egyptians were able to prove the … property.
a) right angle b) theorem
c) information d) number
4. The ancient’s knew the … of some theorems.
a) subjects b) proofs
c) groups d) columns
Text IV
The "Pythagorean" theorem isone of the most important propositions in the entire realm of geometry. There is no doubt, however, that the "Pythagorean property": c2 =a2 + b2 was known priortothe time of Pythagoras; there existed clay tablet texts which contained columns of figures related to Pythagorean triples. The frequent textbook reference to Egyptian "rope-stretchers" and their knotted surveying ropes as proof that these ancients knew the theorem was erroneous. While it isknown that the Egyptians realized as early as 2000 B. C. that 42+ 32=52, there is no evidence that the Egyptians knew or were able to prove the right angle property of the figure involved. Pythagoras is credited with the proof of this property which is true for all right trianges, and for all natural numbers. Although much of this information was known to the ancients of earlier times, the deductive aspect of geometry was exploited and advanced considerably in the work of the Pythagoreans.
The mysticism of this celebrated school aroused the suspicion and dislike of the people who finally drove the Pythagoreans out Crotona. A Greek seaport in Southern Italy and burnt their buildings. Pythagoras was murdered but his followers were scattened to other Greek centres and continued his teachings. The Pythagoreans were credited with giving the subject of mathematics special and independent status. They were the first group to treat mathematical concepts as abstractions and they distinguished mathematical theory from practices or calculations. They proved the fundamental theorems of plane and solid geometry and of “arithmetica”- the theory of numbers.
More widely known than the Pythagoreans was the Academy of Plato which had Aristotle as its most distinguished students. The latter then founded his own school at the time of Plato’s death pupils were the most famous philosophers, mathematicians and astronomers of their age. Under Plato’s influence they emphasized pure mathematics to the extent of ignoring all practical applications and they added immensely to the range of mathematics.
IV. Выберите правильный ответ на вопрос в соответствии с содержанием текста.
1. What is one of the most important proportions in the entire realm of geometry?
a) theory of proportions b) theory of numbers
c) the “Pythagorean” theorem d) numeration system
2. What was the “Pythagorean property?”
a) rational approximation b) ratio of two integers
c) sum of the angles is equal to two right angles d) c2 =a2 + b2
3. What was the “Pythagorean property” true for?
a) diagonals b) right angles
c) right triangle and all natural numbers d) irrational numbers
4. What was considerably advanced in the work of the Pythagoreans?
a) written documentation b) numeration system
c) incommensurable quantities d) deductive aspect of
geometry
5. What did they distinguish mathematical theory from?
a) deductive aspect b) theory of number
c) practice or calculation d)geometrical
magnitudes
6. Who was the most distinguished student in the Academy of Plato?
a) Plato b) Aristotle
c) Pythagoras d) Cantor
V. Выберите заголовок для данного текста в соответствии с его содержанием.
a. The “Pythagorean property”
b. The Pythagorean theorem
c. The academy of Plato
d. Aristotle – the founder of his own school
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