Read these logarithms to your partner. Listen as s/he is reading and check. Take turns.


log (6) = log 3 + log 2 log (18) = log 6 + log 3
log (3) = log 6 – log2 log (9) = log 27 – log 3
log (8) = 3 log 2 log (27) = 4 log 3
log (2) = log (3) =

Unit 8


Reading and Vocabulary

Match the definitions/explanations in A (1–5) with the words in B (a–e):

1 figures about length, height etc of something a volumes
2 a measurement of the amount of space that a substance or object fills b sequence
3 well-aimed, correctly c set
4 a group of similar things that belong together or are related on some way d measurement(s)
5 the order that something happens or exists in, or the order it is supposed to happen or exists in e accurately

2. Read the text and complete it with a word from the task 1 [B (a–e)].

    Geometry is the Greek name for the science which the early Egyptians began to develop about 5000 years ago. The word geometry is derived from two Greek words: ‘geo’ meaning ‘earth’ and ‘metron’ meaning ‘measure’. So geometry is a science dealing with the 1 _____ of lines, surfaces and solids. Plane geometry deals with plane figures. It is geometry of two dimensions.

    Solid geometry deals with figures in space. It is geometry of three dimensions.

    The geometry known to the Egyptians consisted principally of rules and formulas for finding areasand 2 _____ . The Egyptians were principally interested in the practical application of their rules.

    After a time Greek philosophers and teachers developed and perfected the proofs of the Egyptians. The most important of the early Greek teachers was Pythagoras who was born about 569 before our era.

    The best known name connected with geometry is Euclid. Euclid was a teacher of geometry in Alexandria. He used to say that geometry trained the habits of expressing thoughts 3 _____. In 350 B.C. Euclid compiled out of the disorganized geometry of his day a 4 _____ of rules concerning space and shape. This set of rules seemed so basic and true that no one changed it for 2 thousand tears. One of his most important textbooks is called ‘The Elements’. This book has been used as a basis for all textbooks on geometry since his time. All the known facts about Greek geometry were put up into the logical 5_____ by Euclid. So for over 20 centuries Euclidean geometry was the ruling theory. Even to-day most textbooks on geometry follow the plan of Euclid`s writings and use his diagrams, methods of proof and ways geometrical truths.

    In the 19 th century the Russian mathematician Lobachevsky succeed in solving the problem which the mathematicians of the world had failed to solve for more than 2000 years – he created non-Euclidean geometry, one of the greatest masterpieces of mathematics. Later Lobachevsky’s new masterpiece Pan-geometry appeared. Few discoveries in world science can equal this Lobachevsky`s discovery. Today Lobachevsky’s name is known all over the world. As Lobachevsky was a revolutionary in science, he is often called Copernicus of geometry. The famous mathematicians Bolyai and Riemann developed non-Euclidean geometry too.

    Geometry is a branch of mathematics that is constantly used by the builder, the engineer, the navigator, the astronomer. Without geometry the world and our lives in it would be totally different from what they are now. So geometry is an indispensable tool of mankind.


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