DESCARTES’ AND FERMAT'S COORDINATE GEOMETRYBefore 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 maths a good deal of space will be devoted to R. Descartes and R Fermat, for these men left very deep imprints on many subjects. Also, in the history of maths, 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 indispensable force in the development of the calculus, as the influential power in molding our ideas of such far-reaching concepts as those of "function" and "dimension". Thus, applied maths in the modern sense of the term was not the creation of the engineer or the engineering-minded mathematician. Of the two great thinkers who founded this subject one was a profound philosopher, the other was a scientist in the realm of ideas. The former, Rene Descartes, devoted himself to critical and profound thinking about the nature of truth, and the physical structure of the universe. The latter, JI Fermat, lived an ordinary life as a lawyer and civil servant, but in his spare time he was busy creating arm offering to the world his famous theorems. The work of both men in many fields will be immortal. Descartes proposed to generalize and extend the methods used by mathematicians in order to make them applicable to all investigations. In essence, the method will be an axiomatic deductive construction for all thoughts. The conclusions will be theorems derived from axioms. Guided by the methods of the geometers Descartes carefully formulated the rules that would direct him in his search for truth. His story of the search for method and the application of the method to problems of philosophy was presented in his famous Discourse on Method. Vocabulary
1. Answer the following questions: 1) What is the two great mathematicians’ contribution to math science? 2) Why is analytic geometry so important? 3) What do you know about each of these great thinkers? 4) Are their methods applicable to all investigations? 5) Are you familiar with their ideas and what do you think they are for mathematics? 6) What did Rene Descartes devote himself to?
2. Find Russian equivalents for the English word combinations: Profound thinking; the nature of truth; curves and surfaces; indispensable force; decisive contribution; a good deal of space; influential power; the realm of ideas; to offer to the world; immortal work; to generalize and extend the methods; in order to make them applicable; deductive construction; to derive from axioms.
3. Translate from Russian into English. 1) Он посвятил себя критическому и глубокому мышлению о природе истины. 2) Труды Ферма и Декарта бессмертны. 3) Декарт предложил обобщить методы, используемые математиками, что применять их во всех исследованиях. 4) Эти великие люди дали большой толчок развитию аналитической геометрии. 5) Прикладная математика в современном смысле этого термина не была творением инженера или инженерно-мыслящего математика.
4. Find suitable adjectives for the following nouns: Construction, thinking, ideas, concepts, importance, methods, term, spirit, historian, space, force, contributions, nature, universe.
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