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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... solved verbally. The words uś (length), sag (breadth), and aša (area) were often used for the unknowns, not because the unknowns necessarily represented these geometric quantities, but probably because many algebraic problems came from ...
... solved verbally. The words uś (length), sag (breadth), and aša (area) were often used for the unknowns, not because the unknowns necessarily represented these geometric quantities, but probably because many algebraic problems came from ...
Side
... 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 some known volume. To find x here we must extract a cube root. The ...
... 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 some known volume. To find x here we must extract a cube root. The ...
Side
... solved x2 + y2 = 2z2 in integers. 6. Babylonian. Geometry. The role of geometry in Babylonia was insignificant. Geometry was not a separate mathematical discipline. Problems involving division of a field or the sizes of bricks needed for ...
... solved x2 + y2 = 2z2 in integers. 6. Babylonian. Geometry. The role of geometry in Babylonia was insignificant. Geometry was not a separate mathematical discipline. Problems involving division of a field or the sizes of bricks needed for ...
Side
... solving particular physical problems. Apart from a few special facts, such as the calculation of the radius of a circle circumscribing a known isosceles triangle, the substance of Babylonian geometry was a collection of rules for the ...
... solving particular physical problems. Apart from a few special facts, such as the calculation of the radius of a circle circumscribing a known isosceles triangle, the substance of Babylonian geometry was a collection of rules for the ...
Side
... solving them was essentially what we do. when we calculate according to a formula. Thus an almost literal translation of the geometrical problem of finding the volume of the frustum of a pyramid reads: “If you are told: a truncated ...
... solving them was essentially what we do. when we calculate according to a formula. Thus an almost literal translation of the geometrical problem of finding the volume of the frustum of a pyramid reads: “If you are told: a truncated ...
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, Volum 1 Morris Kline Ingen forhåndsvisning tilgjengelig - 1990 |
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Alexandrian algebra angle Apollonius applied Arabs Archimedes Aristotle arithmetic astronomy Babylonians base became bodies Book calculation called century Chap chord circle civilization classical concept conic consider construction contained continued course Definition determined diameter Diophantus earth Egyptian Elements empire equal equations Euclid Europe example existence fact Figure fractions geometry given gives Greek Hence Hindus History ideas important interest irrational Italy knowledge known later learning length less magnitudes mathematicians mathematics means measured mechanics method motion moving nature numbers objects observations obtained original parallel period philosophy physical plane positive practical problems proof proportion Proposition proved Ptolemy Pythagoreans ratio reason rectangle Roman roots says segment shows side solution solved sphere square straight line symbols theorems theory thought treated triangle trigonometry University volumes whole writings