Mathematics in Ancient and Medieval India c3: Contents

Mathematics in Ancient and Medieval India c3

Language: English

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| | | | Pages |
| *INTRODUCTION* | ... | ... | iii–vi |
| CHAPTER I—*SCHOLARS OF MATHEMATICS* | | | 1–51 |

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1. *Vedic Period* ( 1500 B. C.–200 B. C. )— Sūtra period—an age of specialisation, Vedic sources in Mathematics, Baudhāyana, Āpastamba, and other Śulba workers and Vedāṅga Jyautiṣa.

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2. *Post-Vedic Period* ( c. 200 B. C.–400 A. D. )— Jaina works, Kusumpura School, Hindu works.

3. *Early Medieval Period* ( c. 400–1200 A. D. )—Bakshāli Ms., Āryabhaṭa I, Varāhamihira, Bhāskara I, Brahmagupta, Lalla, Govindasvāmin, Skandasena, Pṛthudakasvāmī, Mahāvīra, Śrīdhara, Āryabhaṭa II, Śrīpati, Bhāskara II.

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4. *Late Medieval Period* ( c. 1200 A. D.—1800 A. D. )—Nārāyaṇa Paṇḍita, Mādhava, Parameśvara, Karaṇapaddhati, Nīlakaṇṭha Somasutvan, Jñanarāja, Citrabhānu, Śaṅkara Vāriar, Jyeṣṭhadeva, Acyuta Piṣāraṭi, Nārāyaṇa, Muniśvara, Kamalākara, Paṇḍit Jagannāth, Śaṃkaravarman.

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CHAPTER II—*ARITHMETIC* ... 52–102

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Numbers, Classification of Numbers, Indices, Fractions, Numerals, Symbol for zero and Place-value, Eight Fundamental Operations, Rule of Three, Surd Numbers and References.

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CHAPTER III—*GEOMETRY* ... 103–174

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Vedic altars, Instruments, Units and Bricks in the *Śulbasūtras*, Geometrical propositions, Theorem of Square on the Diagonal (Pythagoras' Theorem), Value of √2, Technical terms, *Śulbasūtras* and later mathematics.

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Technical terms in Jaina works, *Āryabhaṭīya* and *Brāhmasphuṭasiddhānta*, Basic Concepts of Nomenclature of the Rectilinear Geometrical Figures occurring in Indian Works, Propositions, Area and Miscellaneous Problems, Some useful Geometrical Deductions from Pythagoras' Theorem, Some Typical Constructions, The Foundation of Solid (Co-ordinate) Geometry, Euclid's Elements in India, Technical Terms connected with Plane Figures in the Rekhāgaṇita, Notes and References.

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CHAPTER IV—*ALGEBRA* ... 175–228

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Symbols of Operations, Equations, Rule of False Positions, Quadratic Equations, Progressive Series, Permutation and Combination, Pascal Triangle and the Binomial Theorem, Indeterminate equations of the first degree, Indeterminate equations of the second degree, Notes and References.

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CHAPTER V—*TRIGONOMETRY* ... 229–285 Formulae, Deductions of the formulae, Sine Table and its Origin, Method of Interpolation, Spherical Trigonometry, Value of π, Trigonometrical Series, π-Series, Convergency of π-Series, Sine and Cosine Series, Tan Series with proofs, Notes and References.