This is a new printing, the first inexpensive one, of one of the most honored histories of mathematics of all time. When the last revised edition appeared in 1908, it was hailed by mathematicians and laymen alike, and it remains one of the clearest, most authoritative, and most accurate works in the field. Mathematicians welcomed it as a lucid overview of the development of mathematics down through the centuries. Laymen welcomed it as a work which gave them an opportunity to understand the development of one of the most recondite and difficult of all intellectual endeavors, and the individual contributions of its great men.
In this standard work, Dr. Ball treats hundreds of figures and schools that have been instrumental in the development of mathematics from the Egyptians and Phoenicians to such giants of the 19th century as Grassman, Hermite, Galois, Lie, Riemann, and many others who established modern mathematics as we know it today. This semi-biographical approach gives you a real sense of mathematics as a living science, but where Dr. Ball has found that the biographical approach is not sufficient or suited to presenting a mathematical discovery or development, he does not hesitate to depart from his major scheme and treat the mathematics in detail by itself. Thus, while the book is virtually a pocket encyclopedia of the major figures of mathematics and their discoveries, it is also one of the best possible sources for material on such topics as the problems faced by Greek mathematicians, the contributions of the Arab mathematicians, the development of mathematical symbolism, and the invention of the calculus.
While some background in mathematics is desirable to follow the reference in some of the later sections, most of the book can be read without any more preparation than high school algebra. As a history of mathematics to browse through, or as a convenient reference work, it has never been excelled.

Contenu

PREFACE
TABLE OF CONTENTS
CHAPTER I. EGYPTIAN AND PHOENICIAN MATHEMATICS.
The history of mathematics begins with that of the Ionian Greeks
Greek indebtedness to Egyptians and Phoenicians
Knowledge of the science of numbers possessed by the Phoenicians
Knowledge of the science of numbers possessed by the Egyptians
Knowledge of the science of geometry possessed by Egyptians
Note on ignorance of mathematics shewn by the Chinese
First Period. Mathematics under Greek Influence.
CHAPTER II. THE IONIAN AND PYTHAGOREAN SCHOOLS.
Authorities
The Ionian School
"THALES, 640-550 B.C."
His geometrical discoveries
His astronomical teaching
Anaximander. Anaximenes. Mamercus. Mandryatus
The Pythagorean School
"PYTHAGORAS, 569-500 B.C."
The Pythagorean teaching
The Pythagorean geometry
The Pythagorean theory of numbers
Epicharmus. Hippasus. Phiololaus. Archippus. Lysis
"ARCHYTAS, circ. 400 B.C."
His solution of the duplication of a cube
Theodorus. Timaeus. Bryso
Other Greek Mathematical Schools in the Fifth Century B.C.
Oenopides of Chios
Zeno of Elea. Democritus of Abdera
CHAPTER III. THE SCHOOLS OF ATHENS AND CYZICUS.
Authorities
Mathematical teachers at Athens prior to 420 B.C.
Anaxogoras. The Sophists. Hippias (The quadratrix)
Antipho
Three problems in which these schools were specially interested
"HIPPOCRATES of Chios, circ. 420 B.C."
Letters used to describe geometrical diagrams
Introduction in geometry of the method of reduction
The quadrature of certain lunes
The problem of the duplication of the cube
"Plato, 429-348 B.C."
Introduction in geometry of the method of analysis
Theorem on the duplication of the cube
"EUDOXUS, 408-355 B.C."
Theorems on the golden section
Introduction of the method of exhaustions
Pupils of Plato and Eudoxus
"MENAECHMUS, circ. 340 B.C."
Discussion of the conic selections
His two solutions of the duplication of the cube
Aristaeus. Theaetetus
"Aristotle, 384-322 B.C."
Questions on mechanics. Letters used to indicate magnitudes
CHAPTER IV. THE FIRST ALEXANDRIAN SCHOOL
Authorities
Foundation of Alexandria
The Third Century before Christ
"EUCLID, circ. 330-275 B.C."
Euclid's Elements
The Elements as a text-book of geometry
The Elements as a text-book of the theory of numbers
Euclid's other works
"Aristarchus, circ. 310-250 B.C."
Method of determining the distance of the sun
Conon. Dositheus. Zeuxippus. Nicoteles
"ARCHIMEDES, 287-212 B.C."
His works on plane geometry
His works on geometry of three dimensions
"His two papers on arithmetic, and the "cattle problem"
His works on the statistics of solids and fluids
His astronomy
The principles of geometry and that of Archimedes
"APOLLONIUS, circ. 260-200 B.C."
His conic sections
His other works
His solution of the duplication of a cube
Contrast between his geometry and that of Archimedes
"Erathosthenes, 275-194 B.C."
The Sieve of Eratosthenes
The Second Century before Christ
"Hypsicles (Euclid, book XIV). Nicomedes. Diocles"
Perseus. Zejodorus
"HIPPARCHUS, circ. 130 B.C."
Foundation of scientific astronomy
Foundation of trigonometry
"HERO of Alexandria, circ. 125 B.C."
Foundation of scientific engineering and of land-surveying
Area of a triangle determined in terms of its sides
Features of Hero's works
The First Century before Christ
Theodosius
Dionysodorus
End of the First Alexandrian School
Egypt constituted a Roman province
CHAPTER V. THE SECOND ALEXANDRIAN SCHOOL
Authorities
The First Century after Christ
Serenus. Menelaus
Nicomachus
Introduction of the arithmetic current in medieval Europe
The Second Century after Christ
Theon of Smyran. Thymaridas
"PTOLEMY, died in 168"
The Almagest
Ptolemy's astronomy
Ptolemy's geometry
The Third Century after Christ
"Pappus, circ. 280"
"The Suagwg?, a synopsis of Greek mathematics"
The Fourth Century after Christ
Metrodorus. Elementary problems in arithmetic and algebra
Three stages in the development of algebra
"DIOPHANTUS, circ. 320 (?)"
Introduction of syncopated algebra in his Arithmetic
"The notation, methods, and subject-matter of the work"
His Porisms
Subsequent neglect of his discoveries
Iamblichus
Theon of Alexandria. Hypatia
Hostility of the Eastern Church to Greek science
The Athenian School (in the Fifth Century)
"Proclus, 412-485. Damascius. Eutocius"
Roman Mathematics
Nature and extent of the mathematics read at Rome
Contrast between the conditions at Rome and at Alexandria
End of the Second Alexandrian School
"The capture of Alexandria, and end of the Alexandrian Schools"
CHAPTER VI. THE BYZANTINE SCHOOL.
Preservation of works of the great Greek Mathematicians
Hero of Constantinople. Psellus. Planudes. Barlaam. Argyrus
Nicholas Rhabdas. Pachymeres. Moschopulus (Magic Squares)
"Capture of Constantinople, and dispersal of Greek Mathematicians"
CHAPTER VII. SYSTEMS OF NUMERATION AND PRIMITIVE ARITHMETIC.
Authorities
Methods of counting and indicating numbers amoung primitive races
Use of the abacus or swan-pan for practical calculation
Methods of representing nu
The Lilavati or arithmetic ; decimal numeration used
The Bija Ganita or algebra
Development of Mathematics in Arabia
"ALKARISMI or AL-KHWARIZMI, circ. 830"
His Al-gebr we 'l mukabala
His solution of a quadratic equation
Introduction of Arabic or Indian system of numeration
"TABIT IBN KORRA, 836-901 ; solution of a cubic equation"
Alkayami. Alkarki. Development of algebra
Albategni. Albuzjani. Development of trigono…