
- •Навчальний посібник
- •First term
- •Second term
- •Mathematics as a science
- •Mathematics
- •Task 17
- •Isaak Newton
- •Age problem
- •Self-assessment Be ready to speak on the topic "Mathematics as an independent science" using the following as a plan:
- •Check your active vocabulary on the topic:
- •Translate into English and be ready to give illustrative examples:
- •Fill in the gaps using a word from the list:
- •Arithmetic operations
- •Four basic operations of arithmetic
- •Two Characteristics of Addition
- •Self-assessment
- •Rational numbers
- •Rational and irrational numbers
- •Rational and irrational numbers
- •What is a number that is not rational?
- •Self-assessment
- •Properties of rational numbers
- •Properties of rational numbers
- •Properties of rational numbers
- •Reciprocal Fractions
- •Reducing Fractions to Lowest Terms
- •A Visit to a Concert
- •Self-assessment
- •Geometry
- •Meaning of geometry
- •Points and Lines
- •The history of geometry
- •Strange figures.
- •Measure the water.
- •Self-assessment
- •Simple closed figures
- •Simple closed figures
- •Simple closed figures
- •Problems of Cosmic and Cosmetic Physics
- •How to find the hypotenuse
- •Geometry Challenges
- •Self-assessment
- •Functional organization of computer
- •Computers
- •An a is a b that c
- •Find the numbers
- •Hundreds and hundreds
- •Tasks for self-assessment
- •Computer programming
- •Now read the description below. Do you like it? Why/Why not?
- •Instruction, instruct, instructed, instructor
- •Programming languages
- •Testing the computer program
- •Genius’s answer
- •A witty answer
- •The oldest profession
- •Tasks for self-assessment
- •Additional texts for reading
- •Read the text and summarise the main ways of expressing numbers in English.
- •Expressing numbers in english
- •Expressing millions
- •Ways of expressing the number 0
- •Fractional numbers
- •Writing full stops and commas in numbers
- •A short introduction to the new math
- •Algorithm
- •Mathematical component of the curriculum
- •Some facts on the development of the number system
- •The game of chess
- •Computers in our life
- •Is "laptop" being phased out?
- •The Main Pieces of Hardware
- •Text 10
- •Programs and programming languages
- •Text 11
- •All about software Categories of applications software explained
- •Systems Software
- •Applications Software
- •All the Other 'Ware Terminology
- •Malware
- •Greyware
- •Text 12
- •Advantages and disadvantages of the internet
- •Advantages
- •Disadvantages
- •Text 13
- •Text 14
- •Thinking about what we’ve found
- •Meta-Web Information
- •Text 15
- •Computer-aided instruction
- •Text 16
- •Teacher training
- •Іменник Утворення множини іменників
- •Правила правопису множини іменників
- •Окремі випадки утворення множини іменників
- •Присвійний відмінок
- •Практичні завдання
- •Артикль
- •Вживання неозначеного артикля
- •Вживання означеного артикля
- •Відсутність артикля перед обчислюваними іменниками
- •Вживання артикля з власними іменниками
- •Практичні завдання
- •Прикметник
- •Практичні завдання
- •Числівник
- •Практичні завдання
- •Займенник Особові займенники
- •Присвійні займенники
- •Зворотні займенники
- •Вказівні займенники
- •Питальні займенники
- •Неозначені займенники
- •Кількісні займенники
- •Практичні завдання
- •Прийменник
- •Дієслово
- •Неозначені часи indefinite tenses
- •Теперішній неозначений час the present indefinite tense active
- •Вживання Present Indefinite Active
- •Майбутній неозначений час the future indefinite tense active
- •Практичні завдання
- •Did you have a meeting yesterday?
- •I had an exam last week.
- •I didn't have an exam last week. Did you?
- •Тривалі часи дієслова continuous tenses
- •Теперішній тривалий час The present continuous tense active
- •Минулий тривалий час The past continuous tense active
- •Майбутній тривалий час The future continuous tense active
- •Практичні завдання
- •Перфектні часи perfect tenses
- •Теперішній перфектний час The present perfect tense active
- •Минулий перфектний час The perfect past tense active
- •Майбутній перфектний час The future perfect tense active
- •Практичні завдання
- •Узгодження часів sequence of tenses
- •Практичні завдання
- •Модальні дієслова modal verbs
- •Практичні завдання
- •Типи питальних речень question types
- •Практичні завдання
- •Пасивний стан дієслова passive voice
- •Практичні завдання
- •Check yourself
- •Читання буквосполучень
- •Читання голосних буквосполучень
- •Читання деяких приголосних та їхніх сполучень
- •Irregular verbs
- •Indefinite Tenses
- •Continuous Tenses
- •Perfect Tenses
- •Perfect Continuous Tenses
- •List of Proper Names
- •Sources of used materials
- •Contents
Isaak Newton
Sir Isaak Newton (1643–1727) was a brilliant English mathematician and physicist. It is justly believed that he is one of the great men of science in the history of mankind. __________(1)
Newtonean theory of universal gravitation and his formulation of the basic concepts and principles of mechanics are known as his two great achievements that have made possible the creation of a physical picture of the Universe which remained unshaken until the beginning of the 20th century. It is very important for us to examine, in some details, the concepts he introduced and clarified in the course of his work.__________ (2)
Ever since Galileo had invented his telescope men had been studying the motions of the planets with ever increasing interest and accuracy. In particular, a great deal of observed data had been collected by Tycho Brahe, a Danish astronomer (1546–1601). From these Kepler deduced his famous three laws describing the motion of the planets about the Sun. They amounted to:
The planets describe ellipses, with the Sun being at a focus.
The radius vector joining the Sun with the planet describes equal areas in equal times, that is the rate of description of sectorial area is constant.
The cubes of the mean distances of the planets from the Sun are proportional to the squares of their times of revolution. _________ (3)
Newton was able to show that these laws were compatible with the assumption that each planet possesses acceleration towards the Sun which is inversely proportional to the square of their distance from it. Furthermore, he believed that this .acceleration was of the same nature as the acceleration of bodies falling near the Earth's .surface. This generalization led him to the concept that all bodies taken in pairs induce in each other mutual acceleration. Translating it into terms of force required a new principle and Newton supplied this principle in his law of "action and reaction" – and this in its turn provides us with a notion of mass not possessed by any of Newton's predecessors. This concept distinguishes between mass and weight. _______ (4)
The laws of motion which Newton published in his "Principia" amount to the following:
Law I. Every body preserves in its state of rest or of uniform motion in a straight line unless it is compelled to alter that state by impressed force.
Law II. Change of momentum is proportional to the impressed force and takes place along the line of action of that force.
Law III. Action and reaction are always equal and opposite; that is to say, the actions of two bodies upon each other are equal and directly opposite._______ (5)
Task 27
True-false test
1. Isaak Newton was a Danish mathematician and physicist.
2. Physical picture of the Universe in 18 – 19th centuries was based on Newtonean discoveries.
3. Telescope was invented by a Danish astronomer.
4. Newton's predecessors were well acquainted with a notion of mass.
5. Newton’s laws were connected with motion.
Task 28
Read the text again and fill in the gaps in the text with the following:
Newton stated his 3 laws of motion in his book.
Newton's predecessors collected a great deal of observed data.
Sir Isaak Newton is an outstanding English scientist.
Newtonians concepts were a base for a physical picture of the Universe in those times.
Newton got married when he was 40.
Newton supplied mankind with a notion of mass not possessed by any of his predecessors.
Enjoy yourself!