did-you-know? rent-now

Amazon no longer offers textbook rentals. We do!

did-you-know? rent-now

Amazon no longer offers textbook rentals. We do!

We're the #1 textbook rental company. Let us show you why.

9780486432311

A Manual of Greek Mathematics

by
  • ISBN13:

    9780486432311

  • ISBN10:

    0486432319

  • Format: Paperback
  • Copyright: 2003-12-29
  • Publisher: Dover Publications

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

Purchase Benefits

  • Free Shipping Icon Free Shipping On Orders Over $35!
    Your order must be $35 or more to qualify for free economy shipping. Bulk sales, PO's, Marketplace items, eBooks and apparel do not qualify for this offer.
  • eCampus.com Logo Get Rewarded for Ordering Your Textbooks! Enroll Now
List Price: $29.95 Save up to $11.45
  • Rent Book $18.50
    Add to Cart Free Shipping Icon Free Shipping

    TERM
    PRICE
    DUE
    USUALLY SHIPS IN 24-48 HOURS
    *This item is part of an exclusive publisher rental program and requires an additional convenience fee. This fee will be reflected in the shopping cart.

Supplemental Materials

What is included with this book?

Summary

This concise but thorough history encompasses the enduring contributions of the ancient Greek mathematicians whose works form the basis of most modern mathematics. Written by a distinguished scholar and mathematician, the well-written, nontechnical text is geared toward high school, college, and graduate students, teachers, and those seeking a historical perspective on mathematics. Topics include Pythagorean arithmetic, Plato's use and philosophy of mathematics, an in-depth analysis of Euclid's "Elements," the beginnings of Greek algebra and trigonometry, and other mathematical milestones. 1931 ed.

Author Biography

Thomas Little Heath: Bringing the Past to Life
Thomas Little Heath (1861–1940) was unusual for an authority on many esoteric, and many less esoteric, subjects in the history of mathematics in that he was never a university professor. The son of an English farmer from Lincolnshire, Heath demonstrated his academic gifts at a young age; studied at Trinity College, Cambridge, from 1879 to 1882; came away with numerous awards; and obtained the top grade in the 1884 English Civil Service examination. From that foundation, he went to work in the English Treasury, rose through the ranks, and by 1913, was permanent secretary to the Treasury, effectively the head of its operations. He left that post in 1919 at the end of the first World War, worked several years at the National Debt office, and retired in 1926.

During all of that time, however, he became independently one of the world's leading authorities on the history of mathematics, especially on the history of ancient Greek mathematics. Heath's three-volume edition of Euclid is still the standard, it is generally accepted that it is primarily through Heath's great work on Archimedes that the accomplishments of Archimedes are known as well as they are.

Dover has reprinted these and other books by Heath, preserving over several decades a unique legacy in the history of mathematical scholarship.

In the Author's Own Words:
"The works of Archimedes are without exception, monuments of mathematical exposition; the gradual revelation of the plan of attack, the masterly ordering of the propositions, the stern elimination of everything not immediately relevant to the purpose, the finish of the whole, are so impressive in their perfection as to create a feeling akin to awe in the mind of the reader." — Thomas L. Heath

Table of Contents

I. INTRODUCTORY 1(10)
Classification of mathematical subjects
5(2)
Mathematics in Greek education
7(4)
II. NUMERICAL NOTATION AND PRACTICAL CALCULATION 11(25)
The decimal system
11(1)
Egyptian numerical notation
11(1)
Babylonian systems
12(2)
Greek numerical notation
14(6)
(a) The 'Herodianic' or 'Attic' system
14(1)
(b) The ordinary alphabetic numerals
15(3)
(c) Notation for large numbers
18(1)
(d) Archimedes' system for large numbers ('octads')
19(1)
Fractions
20(4)
Sexagesimal fractions
23(1)
Practical calculation
24(12)
(α) The abacus
24(4)
(β) Addition and subtraction
28(1)
(γ) Multiplication
29(2)
(δ) Division
31(1)
(epsilon) Extraction of square root
32(4)
III. PYTHAGOREAN ARITHMETIC 36(37)
Definitions of the unit and of number
38(1)
Classification of numbers
39(2)
'Perfect' and 'Friendly' numbers
41(2)
Figured numbers
43(8)
(a) Triangular numbers
43(1)
(b) Square numbers and gnomons
44(1)
(c) Gnomons of the polygonal numbers
45(1)
(d) Right-angled triangles with sides in rational numbers
46(2)
(e) Oblong numbers
48(3)
The theory of proportion and means
51(3)
Geometric Means
53(1)
The irrational
54(1)
Algebraic equations
55(6)
(α) Indeterminate equations of the second degree 2x2 - y2 = ±1
55(2)
(β) Epanthema of Thymaridas
57(3)
(γ) Equation xy = 2(x+y)
60(1)
Manuals of 'Arithmetic'
61(12)
Nicomachus of Gerasa
61(9)
Sum of series of cube numbers
68(2)
Theon of Smyrna
70(1)
Iamblichus
71(2)
IV. THE EARLIEST GREEK GEOMETRY. THALES 73(19)
The 'Summary' of Proclus
73(2)
Egyptian geometry (mensuration)
75(6)
Thales
81(9)
(a) Measurement of height of pyramid
82(1)
(b) Geometrical theorems
83(6)
(c) Thales as astronomer
89(1)
From Thales to Pythagoras
90(1)
Anaximander
90(2)
V. PYTHAGOREAN GEOMETRY 92(20)
(α) Sum of angles of any triangle equal to two right angles
93(2)
(β) The 'Theorem of Pythagoras'
95(5)
(γ) Application of areas and geometrical algebra
100(5)
(δ) The irrational
105(1)
(ε) The five regular solids
106(3)
(ζ) Pythagorean astronomy
109(1)
Summary
110(2)
VI. PROGRESS IN THE ELEMENTS DOWN TO PLATO'S TIME 112(27)
Anaxagoras
113(1)
Oenopides of Chios
114(1)
Democritus
115(5)
Hippias of Elis
120(1)
Hippocrates of Chios
121(11)
(a) Quadratures of lunes
122(9)
(b) Reduction of the problem of doubling the cube
131(1)
(c) The Elements as known to Hippocrates
131(1)
Theodorus of Cyrene
132(1)
Theaetetus
133(1)
Archytas of Taras
134(5)
VII. SPECIAL PROBLEMS 139(32)
THE SQUARING OF THE CIRCLE
139(8)
(a) The quadratrix of Hippias
143(1)
(b) The spiral of Archimedes
144(1)
(c) Solutions by Apollonus and Carpus
145(1)
(d) Ancient approximations to π
146(1)
THE TRISECTION OF ANY ANGLE
147(7)
(a) Reduction to a νευσιs solved by conics
148(2)
(b) The conchoids of Nicomedes
150(1)
(c) Another reduction to a νευσιs
151(1)
(d) Solution by means of conics
152(2)
THE DUPLICATION OF THE CUBE, OR THE PROBLEM OF THE TWO MEAN PROPORTIONALS
154(17)
Archytas
155(2)
Eudoxus
157(1)
Menaechmus
158(3)
Solution attributed to Plato
161(1)
Eratosthenes
162(2)
Nicomedes
164(2)
Apollonus, Heron, Philon of Byzantium
166(1)
Diodes and the cissoid
167(2)
Sporos and Pappus
169(2)
VIII. FROM PLATO TO EUCLID 171(31)
Plato and the philosophy of mathematics
172(3)
The hypotheses of mathematics
173(1)
Definitions
174(1)
Summary of the mathematics in Plato
175(7)
The five regular solids
175(3)
Geometric means
178(1)
The two geometrical passages in the Meno
178(2)
Solution in integers of x2 + y2 = z2
180(1)
Incommensurables
180(2)
Plato's astronomy
182(1)
Successors of Plato
183(3)
Heraclides of Pontus
186(1)
EUDOXUS of Cuidos
187(1)
Hypothesis of concentric spheres
188(2)
Theory of proportion
190(1)
The Method of Exhaustion
191(1)
Zeno's paradoxes
192(2)
Aristotle
194(6)
Sphaeric. Autolycus of Pitane
200(2)
IX. EUCLID 202(68)
THE ELEMENTS
204(51)
EUCLID'S OTHER WORKS
255(15)
The Data
255(3)
On Divisions (of Figures)
258(4)
Pseudaria. Porisms
262(3)
Conics. Surface-Loci
265(1)
Phaenomena. Optics
266(1)
Catoptrics
267(1)
Musical treatises
268(1)
Supposed mechanical works
269(1)
X. ARISTARCHUS OF SAMOS 270(7)
Anticipation of Copernicus
270(2)
On the sizes and distances of the Sun and Moon
272(5)
XI. ARCHIMEDES 277(70)
Extant works
283(2)
Other reputed works
285(1)
Text and editions
286(57)
The Method
287(6)
On the Sphere and Cylinder
293(12)
Measurement of a Circle
305(5)
On Conoids and Spheroids
310(7)
On Spirals
317(6)
Plane Eguilibriums
323(4)
The Sand-reckoner
327(3)
Quadrature of a Parabola
330(2)
On Floating Bodies
332(4)
The Cattle-Problem
336(1)
On semi-regular solids
337(1)
'Liber assumptorum'
338(2)
On the regular heptagon in a circle
340(3)
ERATOSTHENES
343(4)
Measurement of the earth
343(4)
XII. CONIC SECTIONS 347(30)
Discovery of conics by Menaechmus
347(2)
Euclid and Aristaeus
349(2)
Archimedes
351(1)
APOLLONIUS of Perga
352(25)
The Conics
352(11)
Sectio Rationis
363(2)
Sectio Spatil
365(1)
On Determinate Section
366(1)
Contacts or Tangencies
366(5)
Circle touching three circles
367(4)
Plane Loci
371(1)
Νευσειs, Inclinationes
372(3)
Other works
375(2)
XIII. THE SUCCESSORS OF THE GREAT GEOMETERS 377(16)
Nicomedes
378(1)
Diodes
378(1)
The Fragmentum mathematicum Bobiene
379(1)
Persen and 'spirit sections'
380(2)
Zenodorus
382(1)
Hypsicles
383(2)
Dionysodorus
385(1)
Posidonius
385(2)
Geminus
387(6)
XIV. TRIGONOMETRY: HIPPARCHUS, MENELAUS, PTOLEMY 393(22)
Theodosius' Sphaerica
393(2)
HIPPARCHUS
395(4)
Discovery of precession
396(1)
On the Length of the Year
396(2)
Trigonometry
398(1)
MENELAUS of Alexandria
399(3)
Sphaerica
400(2)
PTOLEMY
402(13)
The Syntaxis
403(9)
Preparation of Table of Chords
405(7)
Other works
412(3)
XV. MENSURATION: HERON OF ALEXANDRIA 415(19)
Heron's date
415(2)
List of works
417(1)
Commentary on Euclid
417(1)
Mensuration
418(13)
The Metrica
419(16)
Area of triangle in terms of sides
420(2)
Approximations to surds
422(2)
Areas of regular polygons
424(2)
Measurement of solids
426(2)
On divisions of figures
428(2)
Quadratic equations
430(1)
On the Dioptra
431(1)
Mechanics
431(1)
Catoptrics
432(2)
XVI. PAPPUS OF ALEXANDRIA 434(32)
Date and works
434(1)
The Collection
435(31)
Editions
436(1)
Books I, II
437(1)
Book III
437(3)
On problem of two mean proportionals
437(1)
On Means
438(1)
'Paradoxes' of Erycinus
439(1)
On five regular solids
440(1)
Book IV
440(8)
Extension of Pythagoras' Theorem
441(1)
Problems on the αρβηλοs
442(1)
On spirals, conchoids, and the quadratrix
443(2)
A spiral on a sphere
445(1)
On the trisection of any angle
446(2)
Book V
448(2)
On isoperimetry: digression on bees and honeycombs
448(1)
On the sphere and cylinder
449(1)
Comparison of five regular solids
450(1)
Book VI
450(1)
On astronomical treatises
450(1)
Book VII
451(9)
On works forming 'Treasury of Analysis'
451(2)
Extension of notion of locus with respect to three or four lines (Pappus' Problem)
453(1)
'Theorem of Guldin' anticipated
454(1)
Lemmas to treatises of Apollonus and Euclid
455(5)
Book VIII
460(16)
Mechanics: historical preface
460(1)
On centre of gravity
461(1)
Construction of conic through five points
462(1)
Problem of seven equal hexagons in a circle
463(3)
XVII. ALGEBRA: DIOPHANTUS OF ALEXANDRIA 466(44)
Egyptian anticipations of algebra
466(2)
Problems in Anthology
468(1)
Indeterminate problems, first degree
469(1)
Indeterminate problems from MS. of Heron's Metrica
470(2)
DIOPHANTUS
472(1)
Date and works
472(1)
The Arithmetica
473(1)
Lost Books. 'Porisms'
474(1)
Commentaries and editions
474(2)
Notation: sign for unknown and its powers
476(6)
sign for minus
479(3)
I. Diophantus' treatment of equations
482(11)
A. Determinate Equations
482(2)
(1) 'Pure' equations
482(1)
(2) 'Mixed' quadratics
482(1)
(3) Simultaneous equations involving quadratics
483(1)
B. Indeterminate equations
484(9)
(a) Equations of second degree
484(7)
(1) Single equation
484(3)
(2) Double equation
487(1)
(a) of first degree
487(3)
(b) of second degree
490(1)
(b) Equations of degree higher than second
491(5)
(1) Single equations
491(1)
(i) Expressions to be made squares
491(1)
(ii) Expressions to be made cubes
492(1)
(2) Double equations
493(1)
II. Method of approximation to limits
493(1)
III. Porisms and propositions in the theory of numbers
494(13)
Numbers as the sum of two, three, or four squares
496(3)
Characteristic examples and solutions
499(6)
Rational right-angled triangles
505(2)
Treatise on Polygonal Numbers
507(3)
XVIII. COMMENTATORS AND MINOR WRITERS 510(10)
Cleomedes
510(2)
Theon of Smyrna
512(3)
Serenus of Antinoeia
515(1)
Theon of Alexandria
516(1)
Hypatia
516(1)
Proclus
516(1)
Domninus of Larissa
517(1)
Simplicius
517(1)
Eutocius
518(1)
Anthemius of Tralles
519(1)
APPENDIX ADDITION NOTES:
1. Egyptian mathematics
520(2)
2. Ancient Babylonian mathematics
522(8)
3. Hipparchus and Chaldaean astronomy
530(2)
INDICES
Greek
532(5)
English
537

Supplemental Materials

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

Rewards Program