- •Contents
- •General comprehension questions:
- •Isaac Newton; Fibonacci; Lioville; Birkhoff; Hilbert; Archimedes; Pythagoras; Giloramo Cardano; Leibniz; Abraham de Moivre; Leonard Euler; Caspar Wessel; Hamilton.
- •General comprehension questions:
- •Learn to read the following formulas:
- •Vocabulary
- •1. A list of words to remember:
- •2. Fill in the gaps in the sentences with these words.
- •Vocabulary
- •1. A list of words to remember:
- •2. Translate the following sentences into English:
- •3. Can you solve the following problems and explain how you obtained the solution?
- •Forms of the Infinitive
- •Functions of the Infinitive in the sentence
- •Attributive Clauses
- •Integrating Factors
- •Unit 3.
- •General comprehension questions:
- •Learn to read the following formulas:
- •Vocabulary
- •1. A list of words to remember:
- •2. Fill in the gaps in the sentences with these words.
- •The Fundamental Theorem of Algebra
- •The Number I
- •Vocabulary
- •1. A list of words to remember:
- •2. Translate the following sentences into English:
- •3. Translate the following text into English.
- •Participles and their forms
- •Functions of participles in the sentence
- •The complex plane
- •1. General comprehension questions:
- •2. Learn to read the following formulas:
- •Vocabulary
- •1. A list of words to remember:
- •2. Fill in the gaps in the sentences with these words.
- •8.1. Euclidean Linear Transformations
- •3. Translate the following text into English.
- •The Gerund and its forms
- •Functions of the Gerund in the sentence
- •Families of circles
Functions of participles in the sentence
The Participle can be used in sentences in different syntactic functions:
a) as part of the predicate (in the Continuous and Perfect tenses, in both active and passive forms):
Considerable changes are currently taking place in the organization of research.
This equation is obtained by differentiating…
Up to this point I have discussed….
b) as predicative: both participle 1 (simple) and participle II can be used as predicatives after a link verb (e.g., be):
The idea itself was surprising.
She was disappointed.
Note that with participle II the verb get can be used instead of be in modern English:
The subject somehow got taught.
c) as an attribute (participle 1 simple – active and passive; and participle II):
We obtained a large variation of values ranging from several to tens of thousands of degrees.
In the chapters that follow we shall try to survey the problems listed above.
Participles can be used in pre-position (when they precede nouns), or in post-position (when they follow them).
The use of single participle 1 in pre-position may present a problem, for not every participle can function this way. In fact, only those participles that indicate a permanent or characteristic feature can be usually used in pre-position. For example, we can say a beginning student (=a freshman), but not *a beginning method, rather – a method for beginning… Participle 1 in preposition is incompatible with anything taking place or being true only at the moment of speech or over a short period of time.
Participle 1 with accompanying words is widely used in post-position instead of an attributive clause:
People coming to see the experiment could not believe their eyes. (=People who came)
However, we cannot replace a clause with a participial phrase when the clause contains a verb that describes mental states – know, believe, like, etc.:
Those who believe it will believe anything.
An exception may be made when a participial phrase denotes the cause of an event (and be used in the function of an adverbial modifier):
Knowing how dangerous the experiment was, she decided not to carry it out.
The basic principles determining the use of participle II are the same as those operating with single participle 1. We can say the used equipment (=not new), but we can hardly say *the used approach, rather – the approach used.
A participial phrase used in preposition is always detached and has an additional meaning of an adverbial modifier:
Annoyed by his words, she went out of the room.
Participle II in post-position can be used either in a phrase, or singly:
The side effects complicating this picture can be ignored.
Money lent is money spent. (proverb)
There are a number of participles which are normally used in post-position: the place visited; the items taken/left; the letters received/shown; all the people involved/questioned; the grant obtained; the drawbacks found/discovered.
These participles usually refer to something dynamic, not permanent.
d) as an adverbial modifier of time, cause, comparison, manner/attendant circumstances, condition and concession.
Participle II in this function is always preceded by a conjunction.
Adverbial modifier of time.
When there is no change of the subject, we can use the participle instead of an adverbial clause of time:
Finishing his report, he reviewed all the results obtained.
You should be very careful when/while dealing with such substances.
When kept at 00C, this substance preserves its properties.
When exposed to air, this substance explodes.
All things considered, we are led to the conclusion that the whole process takes about 10 minutes.
Participle 1 as an adverbial modifier of time can be preceded by the conjunctions when and while; participle II is introduced by when, while and once.
Adverbial modifier of cause.
Both participle 1 (simple active and passive) and participle II can be used in this function:
Not knowing the data, he couldn’t solve the problem.
He changed his mind, realizing that everything was useless.
Occupied by his thoughts, he didn’t hear my question.
Sentences with participle 1 as an adverbial modifier of cause belong to formal style:
Being ill, he could not go to work. (=As he was ill…)
Having heard the news, she could not continue the meeting.
Adverbial modifier of comparison.
Both participle 1 simple and participle II are introduced by the conjunctions as if, as though:
She continued talking as if trying to convince them.
He nodded as if convinced by what was said.
Adverbial modifier of manner/ attendant circumstances.
Participle 1 can have both functions, which sometimes combine:
She came knocking on the door. (manner or attendant circumstances)
Participle II denoting manner is introduced by as:
In the coming year the technology will be greatly improved, as stated in many reports.
Fill in the application form as instructed.
Adverbial modifier of condition.
Participle II is used here after the conjunction if:
The thing is very fragile. If dropped, it can break into very small pieces.
If asked, he always helped me.
Driving at this speed, we’ll be there in no time.
Adverbial modifier of concession.
Participle 1 and II as adverbial modifiers of concession are introduced by the conjunctions while, though:
While liking mathematics, he didn’t choose it as his major.
Though discouraged by the lack of support, he went on trying.
e) as parenthesis. Both participle 1 and participle II are used in parenthetical expressions (set phrases): frankly/generally speaking, judging by experience, stated/put bluntly, etc.
Put bluntly, he had no chance of winning.
Taking everything into consideration, she had a right to do it.
Participles can also function as a part of participial constructions (for details see Unit 3.)
Exercise 3. Identify the forms and the functions of the participles in the following sentences.
1) He asked this question smiling but irritated.
2) She appreciated his help and couldn’t see him so disappointed.
3) I had to spend all my day trying to complete the calculations.
4) Suddenly she looked at me as if surprised.
5) When cooled down to a very low temperature, gas becomes liquefied.
6) Within the framework of this theory our results can be explained quite satisfactorily.
7) The process occurring in this case is well known.
8) The data obtained are against this assumption.
9) For details the reader is referred to the paper by Goldman and co-workers published in 2010.
10) Frankly speaking, our attempts were fruitless.
11) For the time being, this question remains unanswered.
12) Though puzzled, he tried to answer the question asked.
13) Absorbed in her book, she didn’t hear my question.
14) The method used appeared to be quite effective.
15) Having discussed everything they decided to continue their cooperation.
Exercise 4. Translate the following sentences into English using the participles (in different forms and functions).
Метод, предлагаемый автором этой статьи, несколько устарел.
Результаты опытов доказывают правильность нашего предположения.
Эти статьи охватывают широкий круг проблем, обсуждаемых в последние годы.
При оценке новых научных результатов нужно глубокое знание предмета.
Обсуждая эти результаты, мы должны принять во внимание, что нам не удалось проверить их другими методами.
При сравнении с теоретическими расчетами наши результаты показали небольшое отклонение, которое можно игнорировать.
В начале статьи должен быть приведен краткий обзор данных, имеющихся в литературе.
Суммированные результаты дают более общую картину данного явления.
Так как их статья была опубликована раньше, в ней отсутствуют некоторые полученные результаты.
Additional text. Read it and retell in English. You may need to write down the formulas and base your retelling on them. Pay attention to the vocabulary and correct pronunciation.
