I. Найдите в тексте интернациональные слова, переведите их.
II. Выберите в колонке В эквиваленты к словам колонки А.
| A
| B
| | 1.plane
2.curve
3. equation
4. independent variable
5. real number
6. property
7. relation
8. conic section
9. n-dimensional space
10. dependent variable
11.function
12.surface
13.calculus
14.dimension
15.bulk
| a) действительное число
b) отношение
c) плоскость
d) н-мерное пространство
e) исчисление
f) уравнение
g) измерение
h)функция
i) коническое сечение
j) зависимая переменная
k) кривая
l) поверхность
m) свойство
n) объем
o) независимая переменная
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III. Заполните пропуски подходящими по смыслу словами.
1. Appolonius derived the bulk of his geometry of the … from the geometrical equivalents.
a) conic section b) polyhedra
c) sequence d) surface
2. Oresme represented certain laws by graphing the … against the independent one.
a) mental notion b) dependent variable
c) set of theorems d) relation
3. A correspondence between curve in the plane and the … in two variables is used in analytic geometry.
a) equation b) inequality
c) equality d) sequence
4. In the history of mathematics much will be said about of ….
a) fact and concept b) property and relation
c) function and dimension d) surface and plane
5. In Oresme’s work there are the notions of the subject from … to three.
a) one- dimensional space b) five- dimensional spaces
c) six – dimensional spaces d) two dimensional spaces
Text I
A correspondence is similarly established between the algebraic and analytic properties of the equation f (x, y) = 0, and the geometric properties of the associated curve. The task of proving a theorem in geometry will cleverly be shifted to that of proving a corresponding theorem in algebra and analysis.
There is no unanimity of opinion among historians of mathematics concerning who invented Analytic Geometry, nor even concerning what age should be credited with the invention. Much of this difference of opinion is caused by a lack of agreement regarding just what constitutes Analytic Geometry. There are those who, favouring Antiquity as the era of the invention, point out the well-known fact that the concept of fixing the position of a point by means of suitable coordinates was employed in the ancient world by the Egyptians and the Romans in surveying, and by the Greeks in map-making. And, if Analytic Geometry implies not only the use of coordinates but also the geometric interpretation of relations among coordinates then a particularly strong argument in favour of crediting the Greeks is the fact that Appolonius (c. 225 B. C.) derived the bulk of his geometry of the conic sections from the geometrical equaivalents of certain Cartesian equations of these curves, the idea which originated with Menaechmus about 350 B. C.
Others claim that the invention of Analytic Geometry should be credited to Nicole Oresme, who was born in Normandy about 1323 and died in 1382 after a career that carried him from a mathematics professorship to a bishopric. N. Oresme in one of his mathematical tracts, anticipated another aspect of Analytic Geometry, when he represented certain laws by graphing the dependent variable against the independent one, as the latter variable was permitted to take on small increments. Advocates for N. Oresme as the inventor of Analytic Geometry see in his work such accomplishments as the first, explicit introduction of the equation of a straight line and the extension of some of the notions of the subject from two-dimensional space to three, and even four-dimensional spaces. A century after N. Oresme's tract was written, it enjoyed several printings and in this way it may possibly exert some influence on the succeeding mathematicians.
However, before Analytic geometry could assume its present highly practical form, it had to wait the development of algebraic symbolism, and accordingly it may be more correct to agree with the majority of historians, who regard the decisive contributions made in the seventeenth century by the two French mathematicians, R. Descartes (1596-1650) and P. Fermat (1601-1663), as the essential origin of at least the modern spirit of the subject. After the great impetus given to the subject by these two men, we find Analytic Geometry in a form with which we are familiar today. In the history of mathematics a good deal of space will be devoted to R. Descartes and P. Fermat, for these men left very deep imprints on many subjects. Also, in the history of mathematics, much will be said about the importance of Analytic geometry, not only for the development of Geometry and for the theory of curves and surfaces in particular, but as an indespensable force in the development of the calculus, as the influential power in molding our ideas of such farreaching concepts as those of "function" and "dimension".
IV. Выберите правильный ответ на вопрос в соответствии с содержанием текста.
1. Why was not there unanimity of opinion among scientists about the invention of analytic geometry? Because of ….
a) the position of a point b) a lack of agreement
c) suitable coordinates d) a map-making of the Greeks
2. Who derived the bulk of geometry?
a) Appolonius b) Fermat
c) Menaechmus d) Descartes
3. Who left deep imprints on many subjects?
a) R. Descartes and P. Fermat b) Appolonius
c) Menaechmus c) N. Oresme
V. Выберите заголовок для данного текста, в соответствии с его содержанием.
a. Who invented analytic geometry?
b. Analytic geometry
c. Algebraic symbolism
d. R. Descartes and P. Ferma
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