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VI. Укажите правильный перевод подчеркнутой части предложения.

II. Заполните пропуски подходящими по смыслу словами.

1.Here is the double … a>b>c.

a) equality b) inequality

c) triangle d)rectangle

2. Who can do without the figure of the …, the circle with its centre, or with the cross of three perpendicular axes?

a) triangle b) rectangle

c) axes d) circle

3. On the diagram there is the cross of three perpendicular ….

a) axes b) rectangles

c) triangles d) inequalities

4. Geometric … are graphic formulas and no mathematician can do without them.

a) figures b) segments

c) circles d) axes

5. Students draw segments and … closed in one another.

a) points b) rectangles

c) formulas d) symbols

Text V

To the new concepts correspond, necessarily, new signs. These we choose in such a way that they remind us of the phenomena of the external world. Likewise the geometric figures are signs or symbols of space intrusion and are used as such by all mathematicians. Who does not always use along with the double inequality a>b>c the picture or drawing of three points following one another on a straight-line as the geometrical idea of "betweenness"? Who does not make use of drawings of segments and rectangles closed in one another, when it is required to prove with perfect rigour a difficult theorem on the continuity of functions or the existence of points of condensation? Who can do without the figure of the triangle, the circle with its centre, or with the cross of three perpendicular axes? The arithmetical symbols are written diagrams and the geometric figures are graphic formulas and no mathematician can do without them or avoid them.

Some remarks upon the difficulties which mathematical problems may offer and the means of overcoming and coping with them may be worth discussing. If we do not manage andare not able to solve a mathematical problem the reason often consists in our failure to recoenize the more general standpoint from which the problem under study appears only as a single link in a chain of related problems. After finding this standpoint, the problem becomes more accessible to our investigations and we possess then a method which is applicable also to related problems. This way for finding general methods is certainly the most fruitful and the most certain; for who seeks for methods without having: a definite problem in mind seeks for the most part in vain.

In dealing with mathematical problems, specialization plays, to my mind a still more important part than. generalization. Perhaps in mostcases where we seek in vain the answer to a question, the cause of the failure lies in the fact that problems simpler and easier than the one at issue were either not at all or incompletely solved. All depends, then, on finding out these easier problems, and on solving them by means of devices as perfect as possible and of concepts capable of generalization. This rule is one of the most important levers for overcoming mathematical difficulties and I think, that it is used wherever it is possible, though sometimes unconsciously.

IV. Выберите правильный ответ на вопрос в соответствии с содержанием текста.

1. What do the new concepts correspond?

a) new signs b) new symbols

c) new solutions d) new problems

2. What does the formula a>b>c mean?

a) It is a double inequality b) It is a double equality

c) It is an equation d) It is triangle

3. What are the arithmetical symbols?

a) graphic formulas b) written diagrams

c) double inequality d) algebraic figures

4. When does the problem become more accessible to our investigations?

a) after finding proper standpoint.

b) after finding the solution of concepts.

c) after making drawing.

5. What does the solution of the problem depend on?

a) on it’s formulation.

b) on it’s source.

c) on finding out easier problems and on their solving.

d) on it’s difficulties.

V. Выберите заголовок для данного текста, в соответствии с его содержанием.

a. The phenomena of the external world

b. The double inequality a>b>c

c. Mathematical symbols

d. Mathematical symbols and the rule for overcoming mathematical difficulties

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