5. Перепишите предложения и переведите их, обращая внимание на перевод неопределенных и отрицательных местоимений.

1. Never try to prove what nobody doubts.

2. This paper will consider some minor aspects of the problem.

3. Don’t tell anybody. It is a secret.

4. Any problem is expressed in mathematical terms.

5. Everybody knows this familiar theorem.

6. We can seek the solution nowhere.

6. Перепишите предложения. Найдите в них сказуемые, выпишите их, определите видо-временную форму и укажите инфинитив. Переведите предложения.

Образец: There was nobody in the room.

was – Past Simple – (be)

В комнате никого не было.

1. The problems contain formulae, equations, and calculations.

2. This publication was the first significant arithmetic book in England.

3. The coordinates of any point that lies on the curve will satisfy the equation.

4. Lobachevsky wrote a number of works in the field of algebra and mathematical analysis.

5. There will be only one specific point corresponding to each positive and negative real number.

6. Symbolic language is one of the basic characteristics of modern maths.

7. Поставьте данные предложения в вопросительную и отрицательную формы.

1. She usually compares the experimental results.

2. They introduced this concept in 1960.

3. In the introduction they will outline the present state of research.

4. We made a comparison between some earlier results and recent data.

8. Составьте предложения.

1. me / forget / send / a / to / don’t / post-card.

2. rich / did / want / he / to / and / be / famous?

3. the / any / were / letters / on / there / table ?

4. Paris / ago / left / she / town / her / two / for / years.

5. will / tonight / go / bed / late / he / to.

6. more / the / petrol / was / year / than / is / expensive / it / last.

9. Прочитайте текст, перепишите и письменно переведите 1, 5, 6, 7, 8 абзацы.

N. I. Lobachevsky

There are scientists who seem to be born scientists. And their life is not always a bed of roses; sometimes their life turns really tragic. Lobachevsky’s life is a good example and a proof of this statement.

Nicholai Ivanovich Lobachevsky, the distinguished Russian mathematician and creator of non-Euclidean geometry, was born on December 1, 1792 near Nizhny Novgorod in a poor family. After his father’s death in 1797 the family moved to Kazan where he studied and graduated from the University.

He became interested in mathematics when he was still a schoolboy and remained true to this science all his life long.

N. I. Lobachevsky spent forty years at Kazan University occupying the position of dean of the Faculty of Physics and Mathematics and rector of the University. He gave lectures on mathematics, physics, and astronomy. N. Lobachevsky did a lot to make Kazan University a first-rate educational institution of that time. At the same time he was engaged in extensive researches in mathematics.

On February 23, 1826 a great event took place at Kazan University. N. I. Lobachevsky presented his paper “A Brief Outline of the Principles of Geometry Demonstrating the Theorem of Parallel Lines”¹. That day a new geometrical system, the so-called non-Euclidian geometry, was born. It required intellectual courage to attack the theory, which was the basis of geometry for 2,000 years.

Lobachevsky challenged the parallel postulate that “through a point not on a line L there is no more than one line parallel to L” and suggested another: “through a point outside a line L there are an infinite number of lines parallel to L.” He constructed in all details a geometry, which is valid for pseudospherical surfaces, in which this postulate does not hold true.

With this discovery of non-Euclidian geometry, mathematicians realized that there are geometries different from Euclid’s, which are equally valid.

In the years that followed Lobachevsky wrote a number of works in the fields of algebra and mathematical analysis. However, they were recognized only twelve years after his death.

The tsarist government didn’t value his contribution to the development of mathematics. Instead the government dismissed him from his job as head of the University of Kazan at the age of fifty-four with no explanation to a mathematician so great and well-known throughout the world. Lobachevsky survived this disgrace but he became blind.

Non-Euclidian geometry is of great importance in the study of the foundations of mathematics. Lobachevsky’s ideas greatly influenced the development not only of geometry and other mathematical sciences, but also mechanics, physics and astronomy.

Note:

¹ – “Сжатое изложение основ геометрии с доказательством теоремы о параллельных”.