История греческой математики, том I (2012)

PRZEDMIOTEM OFERTY JEST KOD DOSTĘPOWY DO KSIĄŻKI ELEKTRONICZNEJ (EBOOK)

KSIĄŻKA JEST DOSTĘPNA NA ZEWNĘTRZNEJ PLATFORMIE. KSIĄŻKA NIE JEST W POSTACI PLIKU.

"As it is, the book is indispensable; it has, indeed, no serious English rival." Times Literary Supplement. "Sir Thomas Heath, foremost English historian of the ancient exact sciences in the twentieth century." Professor W. H. Stahl "Indeed, seeing that so much of Greek is mathematics, it is arguable that, if one would understand the Greek genius fully, it would be a good plan to begin with their geometry." The perspective that enabled Sir Thomas Heath to understand the Greek genius deep intimacy with languages, literatures, philosophy, and all the sciences brought him perhaps closer to his beloved subjects and to their own ideal of educated men, than is common or even possible today. Heath read the original texts with a critical, scrupulous eye, and brought to this definitive two-volume history the insights of a mathematician communicated with the clarity of classically taught English. "Of all the manifestations of the Greek genius none is more impressive and even awe-inspiring than that which is revealed by the history of Greek mathematics." Heath records that historywith the scholarly comprehension and comprehensiveness that marks this work as obviously classic now as when it first appeared in 1921. The linkage and unity of mathematics and philosophy suggest the outline for the entire history. Heath covers in sequence Greek numerical notation, Pythagorean arithmetic, Thales and Pythagorean geometry, Zeno, Plato, Euclid, Aristarchus, Archimedes, Apollonius, Hipparchus and trigonometry, Ptolemy, Heron, Pappus, Diophantus of Alexandria and the algebra. Interspersed are sections devoted to the history and analysis of famous problems: squaring the circle, angle trisection, duplication of the cube, and an appendix on Archimedes' proof of the subtangent property of a spiral. The coverage is everywhere thorough and judicious;but Heath is not content with plain exposition: It is a defect in the existing histories that, while they state generally the contents of, and the main propositions proved in, the great treatises of Archimedes and Apollonius, they make little attempt to describe the procedure by which the results are obtained. I have therefore taken pains, in the most significant cases, to show the course of the argument in sufficient detail to enablea competent mathematician to grasp the method used and to apply it, if he will, to other similar investigations. Mathematicians, then, will rejoice to find Heath back in print and accessible after many years. Historians of Greek culture and science can renew acquaintance with a standard reference; readers in general will find, particularly in the energetic discourses on Euclid and Archimedes, exactly what Heath means by impressive and awe-inspiring.

• Autorzy: Sir Thomas Heath
• Wydawnictwo: Dover Publications
• Data wydania: 2012
• Wydanie:
• Liczba stron: 461
• Forma publikacji: ePub (online)
• Język publikacji: angielski
• ISBN: 9780486162690

• Cover
• Title Page
• Copyright Page
• Preface
• Contents
• I. Introductory
• The Greeks and mathematics
• Conditions favouring development of philosophy among the Greeks
• Meaning and classification of mathematics
• (?) Arithmetic and logistic
• (ß) Geometry and geodaesia
• (?) Physical subjects, mechanics, optics, &c.
• Mathematics in Greek education
• II. Greek Numerical Notation and Arithmetical Operations
• The decimal system
• Egyptian numerical notation
• Babylonian systems
• (?) Decimal. (ß) Sexagesimal
• Greek numerical notation
• (?) The Herodianic’ signs
• (ß) The ordinary alphabetic numerals
• (?) Mode of writing numbers in the ordinary alphabetic notation
• (?) Comparison of the two systems of numerical notation
• (?) Notation for large numbers
• (i) Apollonius’s tetrads’
• (ii) Archimedes’s system (by octads)
• Fractions
• (?) The Egyptian system
• (ß) The ordinary Greek form, variously written
• (?) Sexagesimal fractions
• Practical calculation
• (?) The abacus
• (ß) Addition and subtraction
• (?) Multiplication
• (i) The Egyptian method
• (ii) The Greek method
• (iii) Apollonius’s continued multiplications
• (iv) Examples of ordinary multiplications
• (?) Division
• (?) Extraction of the square root
• (?) Extraction of the cube root
• III. Pythagorean Arithmetic
• Numbers and the universe
• Definitions of the unit and of number
• Classification of numbers
• Perfect’ and Friendly’ numbers
• Figured numbers
• (?) Triangular numbers
• (ß) Square numbers and gnomons
• (?) History of the term gnomon’
• (?) Gnomons of the polygonal numbers
• (?) Right-angled triangles with sides in rational numbers
• (?) Oblong numbers
• The theory of proportion and means
• (?) Arithmetic, geometric and harmonic means
• (ß) Seven other means distinguished
• (?) Plato on geometric means between two squares or two cubes
• (?) A theorem of Archytas
• The irrational’
• Algebraic equations
• (?) Side-’ and diameter-’ numbers, giving successive approximations to ?2 (solutions of 2x2 - y2 = 1)
• (ß) The ??????µ? (bloom’) of Thymaridas
• (?) Area of rectangles in relation to perimeter (equation xy = 2x+y)
• Systematic treatises on arithmetic (theory of numbers)
• Nicomachus, Introductio Arithmetica
• Sum of series of cube numbers
• Theon of Smyrna
• Iamblichus, Commentary on Nicomachus
• The pythmen and the rule of nine or seven
• IV. The Earliest Greek Geometry. Thales
• The Summary’ of Proclus
• Tradition as to the origin of geometry
• Egyptian geometry, i.e. mensuration
• The beginnings of Greek geometry. Thales
• (?) Measurement of height of pyramid
• (ß) Geometrical theorems attributed to Thales
• (?) Thales as astronomer
• From Thales to Pythagoras
• V. Pythagorean Geometry
• Pythagoras
• Discoveries attributed to the Pythagoreans
• (?) Equality of sum of angles of any triangle to two right angles
• (ß) The Theorem of Pythagoras’
• (?) Application of areas and geometrical algebra (solution of quadratic equations)
• (?) The irrational
• (?) The five regular solids
• (?) Pythagorean astronomy
• Recapitulation
• VI. Progress in the Elements Down to Plato’s Time
• Extract from Proclus’s summary
• Anaxagoras
• Oenopides of Chios
• Democritus
• Hippias of Elis
• Hippocrates of Chios
• (?) Hippocrates’s quadrature of lunes
• (ß) Reduction of the problem of doubling the cube to the finding of two mean proportionals
• (?) The Elements as known to Hippocrates
• Theodorus of Cyrene
• Theaetetus
• Archytas
• Summary
• VII. Special Problems
• The squaring of the circle
• Antiphon
• Bryson
• Hippias, Dinostratus, Nicomedes. &c.
• (?) The quadratrix of Hippias
• (ß) The spiral of Archimedes
• (?) Solutions by Apollonius and Carpus
• (?) Approximations to the value of ?
• The trisection of any angle
• (?) Reduction to a certain ??????, solved by conics
• (ß) The ?????? equivalent to a cubic equation
• (?) The conchoids of Nicomedes
• (?) Another reduction to a ?????? (Archimedes)
• (?) Direct solutions by means of conics (Pappus)
• The duplication of the cube, or the problem of the two mean proportionals
• (?) History of the problem
• (ß) Archytas
• (?) Eudoxus
• (?) Menaechmus
• (?) The solution attributed to Plato
• (?) Eratosthenes
• (?) Nicomedes
• (?) Apollonius, Heron, Philon of Byzantium
• (?) Diocles and the cissoid
• (?) Sporus and Pappus
• (?) Approximation to a solution by plane methods only
• VIII. Zeno of Elea
• Zeno’s arguments about motion
• IX. PLATO
• Contributions to the philosophy of mathematics
• (?) The hypotheses of mathematics
• (ß) The two intellectual methods
• (?) Definitions
• Summary of the mathematics in Plato
• (?) Regular and semi-regular solids
• (ß) The construction of the regular solids
• (?) Geometric means between two square numbers or two cubes
• (?) The two geometrical passages in the Meno
• (?) Plato and the doubling of the cube
• (?) Solution of x2 + y2 = z2 in integers
• (?) Incommensurables
• (?) The Geometrical Number
• Mathematical arts’
• (?) Optics
• (ß) Music
• (?) Astronomy
• X. From Plato to Euclid
• Heraclides of Pontus : astronomical discoveries
• Theory of numbers (Speusippus, Xenocrates)
• The Elements. Proclus’s summary (continued)
• Eudoxus
• (?) Theory of proportion
• (ß) The method of exhaustion
• (?) Theory of concentric spheres
• Aristotle
• (?) First principles
• (ß) Indications of proofs differing from Euclid’s
• (?) Propositions not found in Euclid
• (?) Curves and solids known to Aristotle
• (?) The continuous and the infinite
• (?) Mechanics
• The Aristotelian tract on indivisible lines
• Sphaeric
• Autolycus of Pitane
• A lost text-book on Sphaeric
• Autolycus, On the Moving Sphere : relation to Euclid
• Autolycus, On Risings and Settings
• XI. Euclid
• Date and traditions
• Ancient commentaries, criticisms and references
• The text of the Elements
• Latin and Arabic translations
• The first printed editions
• The study of Euclid in the Middle Ages
• The first English editions
• Technical terms
• (?) Terms for the formal divisions of a proposition
• (ß) The ??????µ?? or statement of conditions of possibility
• (?) Analysis, synthesis, reduction, reductio ad absurdum
• (?) Case, objection, porism, lemma
• Analysis of the Elements
• Book I
• ” II
• Book III
• ” IV
• ” V
• ” VI
• ” VII
• ” VIII
• ” IX
• ” X
• ” XI
• ” XII
• ” XIII
• The so-called Books XIV, XV
• The Data
• On divisions (of figures)
• Lost geometrical works
• (?) The Pseudaria
• (ß) The Porisms
• (?) The Conics
• (?) The Surface Loci
• Applied mathematics
• (?) The Phaenomena
• (ß) Optics and Catoptrica
• (?) Music
• (?) Works on mechanics attributed to Euclid

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