TEXT A. JOHN NAPIER (1550-1617)
Writing about the middle of the eighteenth century, David Hume proclaimed John Napier of Merchiston as the ‘person to whom the title of a great man is more justly due than to any other whom his country ever produced’.” John Napier was a Scottish mathematician and inventor. Napier is famous for creating mathematical logarithms, creating the decimal point, and for inventing Napier's Bones, a calculating instrument. John Napier - Inventor While better known as a mathematician, John Napier was a busy inventor. He proposed several military inventions including: burning mirrors that set enemy ships on fire, special artillery that destroyed everything within a radius of four miles, bulletproof clothing, a crude version of a tank, and a submarine-like device. John Napier invented a hydraulic screw with a revolving axle that lowered water levels in coal pits. Napier also worked on agricultural innovations to improve crops with manures and salt. John Napier - Mathematician As a Mathematician, the highlight of John Napier's life was the creation of logarithms and the decimal notation for fractions. His other mathematical contributions included: a mnemonic for formulas used in solving spherical triangles, two formulas known as Napier's analogies used in solving spherical triangles, and the exponential expressions for trigonometric functions. In 1621, English mathematician and clergyman, William Oughtred used Napier's logarithms when he invented the slide rule. Oughtred invented the standard rectilinear slide rule and circular slide rule. Napier's Bones Napier's bones were multiplication tables written on strips of wood or bones. The invention was used for multiplying, dividing, and taking square roots and cube roots. Napier's invention led directly to the slide rule, first built in England in 1632 and still in use in the 1960's by the NASA engineers of the Mercury, Gemini, and Apollo programs which landed men on the moon. Exercise 2. Answer the following questions. 1. What is John Napier famous for? 2. What inventions did he propose? 3. What was John Napier’s contribution to mathematics? 4. What are Napier’s bones? How can they be used?
Exercise 3. Make all types of questions to the following sentence. Napier also worked on agricultural innovations to improve crops with manures and salt.
Exercise 4. Translate from Russian into English. Математик, изобретатель, десятичный знак, вычислительная машина, военные разработки, сельскохозяйственные разработки, дробь, вклад в, тригонометрическая функция, логарифмическая линейка, квадратный корень.
Exercise 5. Match up:
Exercise 6. Translate the following sentences into English. 1. Джон Непер, шотландский математик и изобретатель, известен за изобретение логарифмических таблиц. 2. Непер также занимался военными и сельскохозяйственными разработками. 3. Главным событием в жизни Непера-математика было изобретение логарифмов и десятичная система счисления дробей. 4. В 1621 году Уильям Отред воспользовался логарифмами Непера при разработке логарифмической линейки.
Exercise 7. Give a summary of the text. Exercise 8. Read and translate the text. TEXT B. BLAISE PASCAL (1623 – 1662) French inventor, Blaise Pascal was one of the most reputed mathematician and physicist of his time. A genuis from a young age, Blaise Pascal composed a treatise on the communication of sounds at the age of twelve, and at the age of sixteen he composed a treatise on conic sections. Blaise Pascal's Inventions The Pascaline The idea of using machines to solve mathematical problems can be traced at least as far as the early 17th century. Mathematicians who designed and implemented calculators that were capable of addition, subtraction, multiplication, and division included Wilhelm Schickhard, Blaise Pascal, and Gottfried Leibnitz. In 1642, at the age of nineteen Blaise Pascal invented his numerical wheel calculator called the Pascaline to help his father a French tax collector count taxes. The Pascaline had eight movable dials that added up to eight figured long sums and used base ten. When the first dial (one's column) moved ten notches - the second dial moved one notch to represent the ten's column reading of 10 - and when the ten dial moved ten notches the third dial (hundred's column) moved one notch to represent one hundred and so on. Pascal built 50 of this gear-driven one-function calculator (it could only add) but couldn't sell many because of their exorbitant cost and because they really weren't that accurate. Up until the present age when car dashboards went digital, the odometer portion of a car's speedometer used the very same mechanism as the Pascaline to increment the next wheel after each full revolution of the prior wheel. Pascal was a child prodigy. At the age of 12, he was discovered doing his version of Euclid's thirty-second proposition on the kitchen floor. Pascal went on to invent probability theory, the hydraulic press, and the syringe. Roulette Machine Blaise Pascal introduced a very primitive version of the roulette machine in the 17th century. The roulette was a by-product of Blaise Pascal's attempts to invent a perpetual motion machine. Wrist Watch The first reported person to actually wear a watch on the wrist was the French mathematician and philosopher, Blaise Pascal. With a piece of string, he attached his pocket watch to his wrist.
Exercise 9. Answer the following questions. 1. When did the idea of using machines to solve mathematical problems first appear? Who did it belong to? 2. What were first calculators capable of? 3. What device did Pascal invent to help his father? How did it work? 4. Did Pascal’s calculator have any disadvantages? 5. How did roulette machine come to life? 6. Who was the first person to wear a watch on the wrist? Exercise 10. Prove that Blaise Pascal was a child prodigy. Exercise 11. Make all types of questions to the following sentence. In 1642, at the age of nineteen Blaise Pascal invented his numerical wheel calculator called the Pascaline to help his father a French tax collector count taxes. Exercise 12. Translate from Russian into English. Математик, физик, научный труд, восходит к 17 веку, сложение, вычитание, умножение, деление, сборщик налогов, приборная панель, теория вероятности, вечный двигатель, запястье. Exercise 13. Match up:
Exercise 14. Translate the following sentences into English. 1. Паскаль, один из самых выдающихся математиков и физиков своего времени, является автором научного труда о коническом сечении. 2. Первые вычислительные машины выполняли сложение, вычитание, умножение и деление. 3. В возрасте девятнадцати лет Паскаль изобрел …, чтобы помочь отцу-сборщику налогов считать налоги. 4. Он создал 50 калькуляторов, выполнявших только одну функцию, но не смог продать много устройств из-за непомерной стоимости и, кроме того, они были не точными. 5. Рулетка была побочным продуктом при изобретении вечного двигателя. 6. Первым человеком, который надел часы на запястье, был французский математик и философ Паскаль.
Exercise 15. Give a summary of the text. Exercise 16. Imagine that you are Blaise Pascal. You are taking part in a scientific conference and you have to prepare a speech about your invention (numerical wheel calculator). Do it using the following phrases and word combinations. I would like to begin with The key thing I'd like to start with is The subject of my speech is I'm going to deal with I'd like to fix (draw) your attention on (to) the following questions Assume that These assumptions call attention to On the other hand It is safe to say that In order to go more thoroughly into this problem It is essential for In addition to As mentioned above It is necessary to determine here It should be stressed here Here is an illustrative explanation of. Previous investigations show From the viewpoint of..... Perhaps it will be polemic to In this sense I would like to emphasize I would like to raise some questions related to Thus, we come to the following conclusion Thank you for attention
Exercise 17. Read and translate the text. TEXT C. GOTTFRIED WILHELM LEIBNIZ (1646–1716) Leibniz was a polymath almost without peer. He was a mathematician, jurist, historian, scientist, diplomat, poet, inventor, and courtier. His father was a professor of philosophy at Leipzig University, but Leibniz turned down an academic career. He entered into the employ of Baron Boineburg in Frankfurt, while also continuing his study in the law and pursuing his interest in physics, especially of motion. Just a few years after Pascal, the German Gottfried Wilhelm Leibniz (co-inventor with Newton of calculus) managed to build a four-function (addition, subtraction, multiplication, and division) calculator that he called the stepped reckoner because, instead of gears, it employed fluted drums having ten flutes arranged around their circumference in a stair-step fashion. Although the stepped reckoner employed the decimal number system (each drum had 10 flutes), Leibniz was the first to advocate use of the binary number system which is fundamental to the operation of modern computers. Leibniz is considered one of the greatest of the philosophers but he died poor and alone.
Exercise 18. Answer the following questions. 1. What was Leibniz? 2. Did he follow his father’s footsteps in his career? 3. What was stepped reckoner? How did it work? 4. Who were Lebniz’s co-inventors of this kind of calculator? Exercise 19. Prove that Leibnitz was a polymath. Exercise 20. Make all types of questions to the following sentence. His father was a professor of philosophy at Leipzig University, but Leibniz turned down an academic career. Exercise 21. Translate from Russian into English. a) эрудит, отвергать, движение, двоичная система, десятичная система, основной, современный компьютер; b) Лейбниц отказался от карьеры ученого. Несколько лет спустя Лейбницу и Паскалю удалось создать калькулятор, выполняющий четыре функции: сложение, вычитание, умножение и деление. Лейбниц выступал сторонником двоичной системы, которая является основой работы современных компьютеров. Лейбниц считается одним из выдающихся философов, но умер он в бедности и одиночестве. Exercise 22. a) Fill in the gaps, read and translate the text.
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