Render the text in English using the words and phrases supplied below.

Основоположником алгебры, как особой науки, нужно считать среднеазиатского ученого Мухаммеда из Хорезма, известного под арабским прозвищем аль-Хваризми (Хорезмиец). Его алгебраический труд, составленный в 9 в. н.э., носит название «Книга восстановления и противопоставления». «Восстановлением» Мухаммед называет перенос вычитаемого из одной части уравнения в другую, где оно становится слагаемым; «противопоставлением» – собирание неизвестных в одну сторону уравнения, а известных – в другую сторону. По - арабски «восстановление» называется «ал-джебр». Отсюда название «алгебра».

Эта книга также сыграла решающую роль в распространении индийской позиционной нумерации в арабских странах.

В 12 веке «Алгебра» аль-Хваризми стала известна в Европе и была переведена на латинский язык. С этого времени начинается развитие алгебры в европейских странах. В 13 веке индийская нумерация получает преобладание в Италии. В других странах Западной Европы она утверждается в 16 веке. Европейцы, заимствовавшие индийскую нумерацию от арабов, называли ее «арабской». Это исторически неправильное название удерживается и поныне.

Kitab al-Jabr wa-l-Muqabala (Arabic for " The Compendious Book on Calculation by Completion and Balancing"); transfer of the subtrahend; summand

Unit 4

1. Learn to use these words:

to encounter - to experience or to meet unexpectedly

When did you first encounter these difficulties?

complex, complicated - having many parts, difficult

The film's plot was so complex that I couldn't follow it. This machine looks a bit complicated for my liking. The rules are rather complicated to follow.

to link, to connect, to join - put together, unite, connect

to arrange - to plan, to organize, to put in a particular order

They arranged to have dinner the following month. His books are neatly arranged in alphabetical order.

according to (rules) - in a way that agrees with

According to Sarah they're not getting very well at the moment. You're all put in different groups according to your abilities. Did it all go according to plan? " From each according to his abilities, to each according to his needs". (Karl Marx) The counterexample shows that what should be impossible according to the theory is actually found.

item - smth which is part of a list or group of things, subjects to be considered

We will consider all of these items in turn. Several items of clothing lay on the floor.

occasionally - not happening often or regularly

I'm in London occasionally - about once a month.

character - a letter, number or other mark or sign used in writing or printing

The paper was covered in a string of characters.

to regard - to consider, to have an opinion about

This possibility is regarded as an unwanted one. The notion of an information system is not to be regarded as an absolute notion. Her parents always regarded her as the cleverest of their children.

to implement, implementation - to put (a plan or system) into operation

The changes to the national health system will be implemented next year.

to remove - to take away(from a place)

She angrily asked him to remove himself from the room. It got so hot that he removed his tie and jacket. Oil spills have been traditionally removed physically from sea surface.

queue - a line of people waiting for smth

There was a long queue for tickets. To get into the museum you have to stand in a queue.

frequently - happening often, common

The buses run less frequently on Saturdays.

to adjust - to change smth slightly to make it more correct, effective or suitable

She adjusted her skirt, took a deep breath and walked into the room. I can't adjust to living on my own. Her eyes slowly adjusted to the gloom.

to imply - to communicate (an idea or feeling) without saying it directly; to involve smth

I am not implying anything about your cooking, but could we eat out tonight? Socialism implies equality.