Урок 4. Geometry. Exercises

Упражнение 4. Найдите в тексте английские эквиваленты следующих слов и выражений.

1 Египтян больше всего интересовало… The Egyptians were mostly concerned with

2. Распространяться - spread [spred]

3. Привести в логическую последовательность - put into a logical sequence

4. Книга Евклида, называемая «Начала» - The book by Euclid called Elements

5. За последние годы - In recent years

6. Обсудить свойства точки - to discuss properties of the point

7. Эти точки обычно называют  - These points are commonly referred to as

Упражнение 5. Найдите в тексте синонимы следующих слов.

To better – to improve; to name – to mean, to denote – to define, to be called – to be referred to, drawing – picture.

Упражнение 6. Выпишите из текста предложения с герундием.

Упражнение 7. Определите, к каким частям речи относятся подчеркнутые слова.

1.       The Egyptians were mostly concerned with applying geometry to their everyday problems. (Gerund)

2.       In what fields can applied geometry be used? (Participle II)

3.       Computers like the one pictured (Participle II) in this book are capable of solving (Gerund) a system with a hundred or more if necessary.

4.       In factoring (noun) as in all other algebraic processes, the first step is always to make a careful study of the given expression.

5.       This results (verb) in the product of two or more factors being equal to zero. (Participle I)

6.       In other words, you change two or the three signs without changing the value of the fraction. (Gerund)

7.       You have already learned to use parentheses ( ) as a means for indicating that one group of terms is to be multiplied by another group of terms. (Gerund)

8.       Knowing the properties of equality will help you decide whether a sentence is true or false. (Gerund)

9.       The product may be found by multiplying the factors contained in this mathematical sentence. (Gerund, Participle II)

10.   While solving (Gerund) equations one (Pronoun) must be very careful with the signs one uses.

11.   Before trying (Gerund) to multiply terms containing (Participle I) letters, let us summarize the basic facts you will need to remember for performing multiplication. (Gerund)

Упражнение 8. Назовите слова, от которых образованы следующие производные.

1. application, applicable, applicant, apply, applied – to apply
2. solution, solvable (разрешимый), solve, solvent (раствор), solvability (разрешимость, растворимость), soluble (разрешимый, растворимый) – to solve
3. change, changeability, changeable (изменчивый), changeful (переменчивый), changeless (неизменный), change-over (переход) – to change
4. performance, perform, performer, performing – to perform
5. localize, locally, locate, location, locative (местный), locality (местоположение), local – to locate
6. information, informative, informant (осведомитель), inform, informed – to inform

Упражнение 9. Найдите сказуемое в следующих предложениях. Переведите предложения на русский язык.

1. His book called "Elements” is one of the most famous books of mathematics.
2. Think of a point as an exact location in space.
3. When writing about points you represent the points by dots.
4. The dots below mark points and are referred to as point A, point B and point C.
5. It is possible to draw the complete picture of such an extension but it can be represented as follows.
6. Let us agree on using the word "line” to mean a straight line.

Упражнение 10. Переведите следующие предложения на русский язык.

1. Both geometry and algebra deal with equations.

Как геометрия, так и алгебра имеют дело с уравнениями.

2. One can easily measure the amount of work performed.

Можно легко измерить выполненную работу.

3. Mathematical measurements have many practical uses.

Математические размеры имеют широкое практическое использование.

4. Nowadays information spreads all over the world within a few hours.

Сегодня информация распространяется по всему свету в течение нескольких часов.

5. This method can be applied for measuring volumes.

Этот метод может быть использован для измерения объемов.

6. One, two, three, four and so on make a sequence of numbers.

1, 2, 3, 4 и т.д. составляют последовательность чисел.

7. I cannot imagine how one can draw this line without a ruler.

Я не могу представить, как можно начертить эту линию без линейки.

8. It is possible to find the location of the object in space.

Возможно определить местоположение объекта в пространстве.

9. We were to study the shape and the dimensions of those objects.

Мы должны были изучить форму и размеры этих объектов.

10. Knowing fundamental rules is important.

Знание фундаментальный правил очень важно.

11. Drawing a long straight line without a ruler is not easy.

Нелегко начертить длинную прямую линию без линейки.

Упражнение 11. Составьте план текста.

Упражнение 12. Скажите, правильны ли следующие утверждения.

1. Geometry includes only the study of the shape and size of the earth and all things on it. (F)
2. A point has dimensions, that’s why we can see it, feel it and move it. (F)
3. A dot is only a picture of a point and not the point itself. (T)
4. Geometry is a young subject and the ideas about geometry have not been put into a logical sequence so far. (F)
5. While solving equations it is not important to be very careful with the signs one uses. (F)
6. Mathematical measurements hardly have any practical uses. (F)
7. Neither geometry nor algebra deals with equations. (F)
8. One can easily measure the amount of work performed. (T)

Упражнение 13. Заполните пропуски предлогами, где необходимо

1. Points В and E are referred… as endpoints… the line segment. (to, as)
2. When we write… points, we represent them… dots. (x, x)
3. We can draw a straight line… two points… using a ruler. (between, x)
4. You haven’t mentioned all the properties… the point, you have mentioned only some… them. (of, of)
5. The most fundamental idea… the study… geometry is a point. (in, of)
6. What are practical ways… measuring the areas and volumes … objects? (of, of)
7. …300 B.C. all the known facts… the Greek geometry were put … a logical sequence… Euclid. (in, about, into, by)
8. Let’s extend this line segment… the right and… the left. (to, to)
9. …describing this object use geometrical terminology. (when)

Упражнение 14. Переведите следующие предложения из действительного залога в страдательный.

1. Euclid put all the known facts about the Greek geometry into a logical sequence.

(All the known facts about the Greek geometry were put into a logical sequence by Euclid)

2. Euclid wrote several books and called them "Elements”.

Several books were written by Euclid and called "Elements”.

3. Now we shall discuss all the properties of a point.

All the properties of a point will be discussed by us.

4. You represent points by dots, don’t you?

Points are represented by dots, aren’t they?

5. You extended the line segment only to the right, didn’t you?

The line segment was extended only to the right, wasn’t it?

6. We call the number AB the length of the segment AB.

The number AB is called the length of the segment AB.

7. We can represent the complete picture of such an extension as follows.

The complete picture of such an extension can be represented as follows.

8. In the drawing below we indicated several rays.

Several rays were indicated in the drawing below.

9. We shall introduce the first three postulates in the next chapter.

The first three postulates will be introduced in the next chapter.

10. We shall also note other properties and prove them on the basis of our postulates.

Other properties will be noted and proved on the basis of our postulates.

11. If we place the edge of an ordinary ruler on any two points on a large flat surface, its entire edge will lie on the surface.

If the edge of an ordinary ruler is placed on any two points on a large flat surface, the entire edge will lie on the surface.

12. We usually provide appropriate diagrams for the exercises.

Appropriate diagrams are usually provided for the exercises.

Упражнение 15. Замените косвенные вопросы прямыми и задайте их своим товарищам.

Ask your friend: 1) When all the known facts about the Greek geometry were put into a logical sequence by Euclid.

2. What Euclid called his books;

3. What we include in the study of geometry;

4. if a point has any properties;

5. if a point has dimensions;

6. if a point can be moved or seen;

7. in what way we represent points when writing about them;

8. what a line segment is;

9. whether a segment can be extended indefinitely.

Упражнение 16. Дайте краткое описание точки.

Упражнение 17. Составьте план текста.

Упражнение 18. В нескольких словах передайте основное содержание текста.