Английский язык = English. Учебное пособие-2

Gradually, over the centuries, geometric concepts became more generalized and people began to use geometry to solve more diffi cult, abstract problems. However, even though people in those times knew that certain relationships existed between things, they did not have a scientifi c means of proving how or why.

That changed during the Classical Period of the ancient Greek civilization (490–323 BC). Because the ancient Greeks were interested in philosophy and wanted to understand the world around them, they developed a system of logical thinking (or deduction) to help them discover the truth. This methodology resulted in the discovery of many important geometric theorems and principles and in the proving of other geometric principles that had been known by earlier civilizations. For example, the Greek mathematician Pythagoras was the fi rst person that we know of to have proved the theorem

type that we still know, use and study today.

until the 7

century AD, when Islamic mathematicians were active in the fi eld. Ibrahim ibn Sinan and Abu Sahl al-Quhi continued the work of the Greeks, while others used geometry to solve problems in other fi elds, such as optics, astronomy, timekeeping and mapmaking. Omar Khayyam’s comments on problems in Euclid’s work eventually led to the development of non-Euclidean geometry in the 19

century.

6. Two points determine a straight line. (Disjunctive)

9. Rene Descartes and Pierre de Fermat created analytic geometry.

quadrilaterals, etc. Some two-dimensional shapes are formed by bounded curves, for example, circle and ellipse.

angles.

6. It is a shape surrounded by four congruent squares.

a point outside the base.

8. It is a shape with four straight sides and four angles of 90°.

Despite having been studied for decades, the question remains: Who or what is making them?

claim – утверждение; woodcut – гравюра на дереве; oat stalks – стебли овса; fl ying saucer – летающая тарелка; swampy area – болотистая местность.

point.

a claim repeated in many books and websites devoted to the mystery.

6. Some two-dimensional shapes formed by bounded curves, for

1. A new device … now. a) is designing c) are designing b) is being designed d) design

2. Our laboratory … an important experiment now. a) are carrying out c) is carrying out b) was carrying out d) were carrying out

3. We … the data at 3 o’clock yesterday. a) were recording c) is being recording b) was recording d) are recording

7. They are busy now. They … an important question. a) is discussing c) will be discussing b) was discussing d) are discussing

8. The children … in the garden now. a) were sitting c) are sitting b) is sitting d) will be sitting

9. The documents … at 5 o’clock yesterday. a) being checked c) were checked b) were being checked d) was being checked

угольник. 3. Профессор попросил студента решить уравнение. 4. Торт имеет квадратную форму. 5. Дорожка вела к небольшому озеру. 6. Этот вопрос о свойствах твердых тел. 7. В этом треугольнике все стороны равны. 8. Что такое овал? 9. Аксиома – это утверждение, которое не требует доказательств. 10. Отрезок разделен на десять равных частей.

5. concept [ˈkɑːnsept] n. понятие, общее представление, идея, кон-

Professional advancement, advancement of science, ambitious blueprint, change of weather, to change the course, heat of combustion, key concept, general concept, to be made for the convenience, to create diffi culties, an electrical current, to collect data, to develop a new technique, a stage of development, a child’s development, unexpected discovery, to make eff orts, enhancement of effi ciency, to repair, an engine, liquid fuel, to improve one’s vocabulary, a positive infl uence, the invention of the telephone, a tremendous pace, a ray of light, steam generator, sewing thread, to utilize the tool.