History of Hindu Mathematics: A Source Book v1.c4: Contents
History of Hindu Mathematics: A Source Book v1.c4
- Language
- English
Contents
v1.c4.1
CHAPTER I
v1.c4.2
NUMERAL NOTATION
v1.c4.3
| | PAGE |
| 1. A GLIMPSE OF ANCIENT INDIA | 1 |
| 2. HINDUS AND MATHEMATICS | 3 |
| Appreciation of Mathematics—Mathematics in Hindu Education. | |
| 3. SCOPE AND DEVELOPMENT OF HINDU MATHEMATICS | 7 |
| 4. NUMERAL TERMINOLOGY | 9 |
| Scale of Notation—Numerals in Spoken Language. | |
| 5. THE DEVELOPMENT OF NUMERICAL SYMBOLISM | 16 |
| Writing in Ancient India—Earliest Numerals. | |
| 6. KHAROṢṬHÎ NUMERALS | 21 |
| Early Occurrence—Forms and their Origin. | |
| 7. BRÂHMÎ NUMERALS | 25 |
| Early Occurrence and Forms—Difference from other Notations—Theories about their Origin—Relation with Letter Forms—Indraji's Theory—Period of Invention—Résumé. | |
| 8. THE DECIMAL PLACE-VALUE SYSTEM | 38 |
| Important Features—Forms—Nâgarî Forms—Epigraphic Instances—Their Supposed Unreliability—Place of Invention of the New System—Inventor Unknown—Time of Invention. | |
| 9. PERSISTENCE OF THE OLD SYSTEM | 52 |
v1.c4.4
| | | PAGE |
| 10. | WORD NUMERALS | 53 |
| | Explanation of the System—List of Words—Word Numerals without Place-value—Word Numerals with Place-value—Word Numerals in Inscriptions—Origin and Early History—Date of Invention. | |
| 11. | ALPHABETIC NOTATIONS | 63 |
| | Alphabetic System of Âryabhaṭa I—Explanation—*Kaṭapayâdi* Systems—*Akṣarpallî*—Other Letter Systems. | |
| 12. | THE ZERO SYMBOL | 75 |
| | Earliest use—Form of the Symbol—Other uses of the Symbol. | |
| 13. | THE PLACE-VALUE NOTATION IN HINDU LITERATURE | 83 |
| | Jaina Canonical Works—Purâṇas—Works on Philosophy—Literary Works. | |
| 14. | DATE OF INVENTION OF THE PLACE-VALUE NOTATION | 86 |
| 15. | HINDU NUMERALS IN ARABIA | 88 |
| 16. | HINDU NUMERALS IN EUROPE | 92 |
| | Boethius Question—Definite Evidence. | |
| 17. | MISCELLANEOUS REFERENCES TO THE HINDU NUMERALS | 95 |
| | Syrian Reference—Arabic References—The Terms *Hindasi*, etc.—European References. | |
| 18. | TABLES | 105 |
v1.c4.5
CHAPTER II
v1.c4.6
ARITHMETIC
v1.c4.7
| 1. | GENERAL SURVEY | 123 |
| | Terminology and Scope—Sources—Exposition and Teaching—Decay of Mathematics—The Fundamental Operations. | |
v1.c4.8
2. ADDITION 130 Terminology—The Operation—Direct Process—Inverse Process.
v1.c4.9
3. SUBTRACTION 132 Terminology—The Operation—Direct Process—Inverse Process.
v1.c4.10
4. MULTIPLICATION 134 Terminology—Methods of Multiplication—Doorjunction Method—Transmission to the West—Gelosia Method—Cross Multiplication Method—Multiplication by Separation of Places—Zigzag Method—Parts Multiplication Method—Algebraic Method.
v1.c4.11
5. DIVISION 150 Terminology—The Operation—The Method of Long Division.
v1.c4.12
6. SQUARE 155 Terminology—The Operation—Minor Methods of Squaring.
v1.c4.13
7. CUBE 162 Terminology—The Operation—Minor Methods of Cubing.
v1.c4.14
8. SQUARE-ROOT 169 Terminology—The Operation.
v1.c4.15
9. CUBE-ROOT 175 Terminology—The Operation.
v1.c4.16
10. CHECKS ON OPERATIONS 180
v1.c4.17
11. FRACTIONS 185 Early Use—Weights and Measures—Terminology—Writing of Fractions—Reduction to Lowest Terms—Reduction to Common Denominator—Fraction in Combination—Lowest Common Multiple—The Eight Operations—Addition and Subtraction—Multiplication—Division—Square and Square-root—Cube and Cube-root—Unit Fractions.
v1.c4.18
| 12. | THE RULE OF THREE | 203 |
| | Terminology—The Method—Inverse Rule of Three—Appreciation of the Rule of Three—Proportion in the West—Compound Proportion—The Method—Illustration—The Rule of Three as a Particular Case. | |
| 13. | COMMERCIAL PROBLEMS | 218 |
| | Interest in Ancient India—Interest in Hindu *Gaṇita* Problem involving a Quadratic Equation—Other Problems—Miscellaneous Problems on Interest—Barter and Exchange—Other types of Commercial Problems. | |
| 14. | MISCELLANEOUS PROBLEMS | 230 |
| | *Regula Falsi*—The Method of Inversion—Problems on Mixture—Problems involving Solution of Quadratic Equations. | |
| 15. | THE MATHEMATICS OF ZERO | 238 |
| | Zero in Arithmetic—Zero in Algebra—Zero as an Infinitesimal—Infinity—Indeterminate Forms. | |
| | BIBLIOGRAPHY | 247 |
| | INDEX | 251 |
| | *Transliteration* | xvii |
| | *List of abbreviations* | xix |