Geometry in Ancient and Medieval India c5: Contents
Geometry in Ancient and Medieval India c5
- Language
- English
Contents
c5.1
| FOREWORD | V. Raghvàn | v |
| PREFACE | | vii |
c5.2
Chapter I. Introduction* 1
c5.3
Geometry as the branch of Indian mathematics with the earliest recorded development — the change from constructional character to circle-orientedness — lack of proofs explained — utilitarian character of Indian mathematics — general survey of the history of geometry and mathematics in India.
c5.4
Chapter II. Śulbasūtra Geometry* 14
c5.5
The number of *Śulbasūtras* — their date — the term *śulba* — analysis of the contents of the *Śulbasūtras* — the theorem of the square of the diagonal — determining the east-west line — to draw the perpendicular bisector of a given line — construction of squares, rectangles and trapezia — transformation of figures — combination and subtraction of areas — geometrical truths implied in the constructions — properties of similar figures — areas — rational right triangles — early geometrical terminology — the *Śulbasūtras* and later ages.
c5.6
Chapter III. Early Jaina Geometry* 61
c5.7
The impetus for the study of geometry — the very early works — the value √10 for π — solid figures — the trapezium and the trapezoidal solid.
c5.8
Chapter IV. The Trapezium* 70
c5.9
The treatment in early Jaina literature, by Āryabhaṭa I, by Brahmagupta, by Śrīdhara, by Mahāvīra, by later Jaina authors, by Āryabhaṭa II, by Śrīpati, by Bhāskara II, by Nārāyaṇa Paṇḍita.
c5.10
Chapter V. The Quadrilateral
c5.11
The cyclic quadrilateral versus the non-cyclic — *Sūcīkṣetras* — non-cyclic quadrilaterals — Brahmagupta's treatment of the cyclic quadrilateral — Nārāyaṇa Paṇḍita's treatment of the cyclic quadrilateral — Parameśvara's expression for the circumradius and the *Kriyākramakarī* proof for it — the *Yukti-bhāṣā* proof for trigonometrical identities and for Brahmagupta's expressions for the diagonals and area of a cyclic quadrilateral.
c5.12
Chapter VI. The Triangle
c5.13
Early mention of — treatment by Āryabhaṭa, by Brahmagupta etc. — Nīlakaṇṭha's logical demonstration for the concurrence of the perpendicular bisectors of a triangle — the theorem of the square on the hypotenuse and its proof :— rational rectilinear figures — the rational cyclic quadrilateral — Nārāyaṇa's treatment of the rational trapezium — the rational right triangle in the Āryabhaṭa school.
c5.14
Chapter VII. The Circle
c5.15
The circle in early works --- Āryabhaṭa I's value of π — derivation of the value of π by the method of exhaustion — series for π and close approximations to the value of π — finding the area of a circle — the segment and the chord — Mādhava's discovery of Gregory's series --- the common chord and its arrows — inscribed polygons — mutually touching circles.
c5.16
Chapter VIII. Volumes and Surfaces of Solids
c5.17
Volume in early works --- the pyramid — Āryabhaṭa I's rule for the volume of a tetrahedron -- pyramid-frustum and cone-frustum --- the sphere -- the surface-area and volume of a sphere by integration.
c5.18
| *Chapter IX. Geometrical Algebra* | 218 |
c5.19
In the Śulbasūtras — in the commentaries of Bhāskara II's works — in the Āryabhaṭa School Citrabhānu's geometrical demonstrations of algebraical identities — *śreḍhīkṣetras*.
c5.20
| *Chapter X. Shadow problems and other problems* | 251 |
| Glossary of Geometrical Terms | 261 |
| Bibliography | 267 |
| Index | 273 |