Science Awakening I - gebonden uitgave, pocketboek

EAN (ISBN-13): 9789001931025
ISBN (ISBN-10): 9001931022
Gebonden uitgave
pocket book
Verschijningsjaar: 1975
Uitgever: SPRINGER NATURE

Boek bevindt zich in het datenbestand sinds 2007-05-25T06:17:32+02:00 (Amsterdam)
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ISBN/EAN: 9789001931025

ISBN - alternatieve schrijfwijzen:
90-01-93102-2, 978-90-01-93102-5
alternatieve schrijfwijzen en verwante zoekwoorden:
Auteur van het boek: bartel van der waerden
Titel van het boek: science awakening

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Gegevens van de uitgever

Auteur: B. L. Van Der Waerden
Titel: Science Awakening I
Uitgeverij: Springer; Springer Netherland
306 Bladzijden
Verschijningsjaar: 1988-04-10
Dordrecht; NL
Gewicht: 0,660 kg
Taal: Engels
85,59 € (DE)
87,99 € (AT)
106,71 CHF (CH)
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306 p. 47 illus.

BB; History, general; Hardcover, Softcover / Geschichte; Geschichte; Verstehen; Evolution; Nation; Transformation; history of science; History; Geschichtsschreibung, Historiographie; Auseinandersetzen; BC; EA

I. The Egyptians.- Chronological Summary.- The Egyptians as the “inventors” of geometry.- The Rhind papyrus.- For whom was the Rhind papyrus written?.- The class of royal scribes.- The technique of calculation.- Multiplication.- Division.- Natural fractions and unit fractions.- Calculation with natural fractions.- Further relations between fractions.- Duplication of unit fractions.- Division once more.- The (2: n) table.- The red auxiliaries.- Complementation of a fraction to 1.- “Aha-calculations”.- Applied calculations.- The development of the computing technique.- Hypothesis of an advanced science.- The geometry of the Egyptians.- Inclination of oblique planes.- Areas.- Area of the hemisphere.- Volumes.- What could the Greeks learn from the Egyptians?.- II. Number systems, digits and the art of computing.- The sexagesimal system.- How did the sexagesimal system originate?.- Oldest Sumerian period (before 3000 B.C.).- Later Sumerian period (about 2000 B.C.).- Sumerian technique of computation.- Table of 7 and of 16,40.- Normal table of inverses.- Squares, square roots and cube roots.- The Greek notation for numbers.- Counting boards and counting pebbles.- Calculation with fractions.- Sexagesimal fractions.- Hindu numerals.- Number systems; Kharosti and Brahmi.- The invention of the positional system.- The date of the invention.- Poetic numbers.- Aryabhata and his syllable-numbers.- Where does the zero come from?.- The triumphal procession of the Hindu numerals.- The abacus of Gerbert.- III. Babylonian mathematics.- Chronological summary.- Babylonian algebra.- First example (MKT I, p. 113).- Interpretation.- Second example (MKT I, p. 280).- Third example (MKT I, p. 323).- Fourth example (MKT I, p. 154).- Fifth example (MKT III, p. 8, no. 14).- Quadratic equations (MKT III, p. 6).- Sixth example (MKT III, p. 9, no. 18).- Seventh example (MKT I. p. 485).- Eighth example (MKT I, p. 204).- Geometrical proofs of algebraic formulas?.- Ninth example (MKT I, p. 342).- A lesson-text (MKT II, p. 39).- Babylonian geometry.- Volumes and areas.- Frustra of cones and of pyramids (MKT, pp. 176 and 178).- The “Theorem of Pythagoras” (MKT II, p. 53).- Babylonian theory of numbers.- Progressions (MKT I, p. 99).- Plimpton 322: Right triangles with rational sides.- Applied mathematics.- Summary.- Greek Mathematics.- IV. The age of Thales and Pythagoras.- Chronological summary.- Hellas and the Orient.- Thales of Milete.- Prediction of a solar eclipse.- The geometry of Thales.- From Thales to Euclid.- Pythagoras of Samos.- The travels of Pythagoras.- Pythagoras and the theory of harmony.- Pythagoras and the theory of numbers.- Perfect numbers.- Amicable numbers.- Figurate numbers.- Pythagoras and geometry.- The astronomy of the Pythagoreans.- Summary.- The tunnel on Samos.- Antique measuring instruments.- V. The golden age.- Hippasus.- The Mathemata of the Pythagoreans.- The theory of numbers.- The theory of the even and the odd.- Proportions of numbers.- The solution of systems of equations of the first degree.- Geometry.- “Geometric Algebra”.- Why the geometric formulation?.- Lateral and diagonal numbers.- Anaxagoras of Clazomenae.- Democritus of Abdera.- Oenopides of Chios.- Squaring the circle.- Antiphon.- Hippocrates of Chios.- Solid geometry in the fifth century, and Perspective.- Democritus.- Cone and pyramid.- Plato on solid geometry.- The duplication of the cube.- Theodorus of Cyrene.- Theodorus and Theaetetus.- Theodorus on higher curves and on mixtures.- Hippias and his Quadratrix.- The main lines of development.- VI. The century of Plato.- Archytas of Taras.- The duplication of the cube.- The style of Archytas.- Book VIII of the Elements.- The Mathemata in the Epinomis.- The duplication of the cube.- According to Menaechmus.- Theaetetus.- Analysis of Book X of the Elements.- The theory of the regular polyhedra.- The theory of proportions in Theaetetus.- Eudoxus of Cnidos.- Eudoxus as an astronomer.- The exhaustion method.- The theory of proportions.- Theaetetus and Eudoxus.- Menaechmus.- Dinostratus.- Autolycus of Pitane.- On the rotating sphere.- On the rising and setting of stars.- Euclid.- The “Elements”.- The “Data”.- On the division of figures.- Lost geometrical writings.- Euclid’s work on applied mathematics.- VII. The Alexandrian Era (330–200 B.C.).- Aristarchus of Samos.- Archimedes’ measurement of the circle.- Tables for the lengths of chords.- Archimedes.- Stories about Archimedes.- Archimedes as an astronomer.- The works of Archimedes.- The “Method”.- The quadrature of the parabola.- On sphere and cylinder I.- On sphere and cylinder II.- On spirals.- On conoids and spheroids.- The notion of integral in Archimedes.- The book of Lemmas.- The construction of the regular heptagon.- The other works of Archimedes.- Eratosthenes of Cyrene.- Life.- Chronography and measurement of a degree.- Duplication of the cube.- Theory of numbers.- Medieties.- Nicomedes.- The trisection of the angle.- The duplication of the cube in Nicomedes.- Apollonius of Perga.- The theory of the epicycle and of the excenter.- Conica.- The conic sections before Apollonius.- The ellipse as a section of a cone according to Archimedes.- How were the symptoms derived originally?.- A question and an answer.- The derivation of the symptoms according to Apollonius.- Conjugate diameters and conjugate hyperbolas.- Tangent lines.- The equation referred to the center.- The two-tangents theorem and the transformation to new axes.- Cones of revolution through a given conic.- The second book.- The third book.- Loci involving 3 or 4 straight lines.- The fifth book.- The sixth, seventh and eighth books.- Further works of Apollonius.- VIII. The decay of Greek mathematics.- External causes of decay.- The inner causes of decay.- 1. The difficulty of geometric algebra.- 2. The difficulty of the written tradition.- The commentaries of Pappus of Alexandria.- The epigones of the great mathematicians.- 1. Diocles.- The cissoid.- 2. Zenodorus.- Isoperimetric figures.- 3. Hypsicles.- The fourteenth book of the Elements.- Anaphora.- History of trigonometry.- Plane trigonometry.- Spherical trigonometry.- Menelaus.- Transversal proposition.- Heron of Alexandria.- Metrics.- Diophantus of Alexandria.- Arithmetica.- Diophantine equations.- The precursors of Diophantus.- Connection with Babylonian and Arabic algebra.- The algebraic symbolism.- From Book II.- From Book III.- From Book IV.- From Book V.- From Book VI.- Pappus of Alexandria.- A porism of Euclid.- The theorem on the complete quadrangle.- Theorem of Pappus.- Theon of Alexandria.- Hypatia.- The Athens school. Proclus Diadochus.- Isidore of Milete and Anthemius of Tralles.