Mathematical Thought From Ancient to Modern Times, Volume 1, Volum 1Oxford University Press, 1. mars 1990 - 432 sider This comprehensive history traces the development of mathematical ideas and the careers of the mathematicians responsible for them. Volume 1 looks at the disciplines origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the 19th century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study. |
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... Babylonian algebra asks for a number which, added to its reciprocal, yields a given number. In modern notation, the Babylonians sought x and such that These two equations yield a quadratic equation in x, namely,. Babylonian Algebra.
... Babylonian algebra asks for a number which, added to its reciprocal, yields a given number. In modern notation, the Babylonians sought x and such that These two equations yield a quadratic equation in x, namely,. Babylonian Algebra.
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Morris Kline. These two equations yield a quadratic equation in x, namely, x2 – bx + 1 = 0. They formed then ; then ; and were which yield the answers. In effect, the Babylonians had the quadratic formula. Other problems, such as finding ...
Morris Kline. These two equations yield a quadratic equation in x, namely, x2 – bx + 1 = 0. They formed then ; then ; and were which yield the answers. In effect, the Babylonians had the quadratic formula. Other problems, such as finding ...
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... equation in x, with the x and x3 terms missing so that it can be and was solved as a quadratic in x2 . Problems leading to a cube root also occurred. The modern formulation of one such problem would be 12x = z, y = x, xyz = where V is ...
... equation in x, with the x and x3 terms missing so that it can be and was solved as a quadratic in x2 . Problems leading to a cube root also occurred. The modern formulation of one such problem would be 12x = z, y = x, xyz = where V is ...
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... equations involving one or more unknowns, especially quadratic equations, constituted a start in algebra. Their development of a systematic way of writing whole numbers and fractions enabled them to carry arithmetic to a fairly advanced ...
... equations involving one or more unknowns, especially quadratic equations, constituted a start in algebra. Their development of a systematic way of writing whole numbers and fractions enabled them to carry arithmetic to a fairly advanced ...
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... equations, such as = b, are considered. Even when two unknowns occur, the type is ax2 so that after eliminating y, the equation in x reduces to the first type. Some concrete problems involving arithmetic and geometric progressions also ...
... equations, such as = b, are considered. Even when two unknowns occur, the type is ax2 so that after eliminating y, the equation in x reduces to the first type. Some concrete problems involving arithmetic and geometric progressions also ...
Innhold
Euclid and Apollonius | |
The Work of Desargues | 4-3 |
The Work of Pascal and La Hire | 4-4 |
The Emergence of New Principles | 4-5 |
Progress inMathematics Proper | 4-7 |
The Status of the Number System and Arithmetic | 4-250 |
Symbolism | 4-262 |
The Solution of Third and Fourth Degree Equations | 4-267 |
The Theory of Equations | 4-276 |
The Binomial Theorem and Allied Topics | 4-280 |
The Theory of Numbers | 4-282 |
The Relationship of Algebra to Geometry | 4-288 |
The Beginnings of Projective Geometry | 4-298 |
The Merits and Defects of the Elements | 4-10 |
Coordinate Geometry | 4-15 |
The Reemergence of Arithmetic | 4-78 |
The Demise of the Greek World | 4-135 |
The Mathematics of the Hindus and Arabs | 4-152 |
The Medieval Period in Europe | 4-177 |
Progress in Physical Science | 4-193 |
Summary | 4-196 |
The Renaissance 1 Revolutionary Inuences in Europe | 4-199 |
The New Intellectual Outlook | 4-202 |
The Spread of Learning | 4-205 |
Humanistic Activity in Mathematics | 4-206 |
The Clamor for the Reform of Science | 4-210 |
The Rise of Empiricism | 4-215 |
Mathematical Contributions in the Renaissance 1 Perspective | 4-221 |
Geometry Proper | 4-225 |
Algebra | 4-228 |
Trigonometry | 4-230 |
The Major Scientific Progress in the Renaissance 6 Remarks on the Renaissance | 4-244 |
and Algebra | 4-249 |
The Rebirth of Geometry | 14-1 |
The Problems Raised by the Work on Perspective | 14-2 |
René Descartes | 14-3 |
Descartess Work in Coordinate Geometry | 14-4 |
SeventeenthCentury Extensions | 14-5 |
The Importance of Coordinate Geometry Coordinate | 14-21 |
The Mathematization of Science 1 Introduction | 14-54 |
Descartess Concept of Science | 14-55 |
Galileos Approach to Science | 14-57 |
The Function Concept | 14-69 |
The Creation of the Calculus 1 The Motivation for the Calculus | 14-78 |
Early SeventeenthCentury Work on the Calculus | 14-80 |
The Work of Newton | 14-98 |
The Work of Leibniz | 14-118 |
A Comparison of the Work of Newton and Leibniz | 14-130 |
The Controversy over Priority | 14-132 |
Some Immediate Additions to the Calculus | 14-133 |
The Soundness of the Calculus 383 | 14-136 |
List of Abbreviations Index | 24 |
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Mathematical Thought From Ancient to Modern Times, Volume 1, Volum 3 Morris Kline Begrenset visning - 1990 |
Mathematical Thought From Ancient to Modern Times, Volume 1, Volum 3 Morris Kline Ingen forhåndsvisning tilgjengelig - 1990 |
Mathematical Thought From Ancient to Modern Times, Volum 1 Morris Kline Ingen forhåndsvisning tilgjengelig - 1990 |
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