Ancient Hindu Geometry: The Science of the Sulba

Title page......Page 1
Preface......Page 5
Contents......Page 7
Abbréviations......Page 14
Orthodox texts on the Sulba......Page 15
Baudhayana Sulba......Page 16
Apastamba Sulba......Page 17
Katyayana Sulba......Page 18
Manava Sulba......Page 19
Varaha Sulba......Page 20
Hindu names for geometry......Page 21
Their significance......Page 22
Influence......Page 23
Uncertainty about their dates......Page 24
Rama Vajapeyi......Page 25
Sivadasa and Sankara......Page 26
Kapardisvami......Page 27
KaravindasvamI......Page 28
Sundararaja......Page 31
Dvarakanatha Yajva......Page 32
Earlier commentaries lost......Page 33
Vedic Sacrifices......Page 34
Propositions of the Sulba: a brief resume......Page 35
Their earlier origin......Page 40
References in the Rg-veda......Page 41
Taittiriya Samhita......Page 44
Satapatha Brahmana......Page 47
Dimensions of the Caturasra-éyena.citi......Page 48
Measurement by rod......Page 50
Measurement by cord......Page 51
Number of bricks to be used in the construction......Page 53
Number of layers of the Vedi......Page 54
Division of finite straight lines......Page 55
Division of circles......Page 56
Division of rectangles......Page 62
Simple oases of congruence theorems......Page 58
Division of triangles......Page 60
Maximum square within a circle......Page 63
Oldest method of constructing a square......Page 74
Drawing of perpendioulars......Page 66
Method I......Page 69
Method II......Page 70
Method III......Page 71
Method IV......Page 72
Method V......Page 73
Construction of rectangles......Page 76
Construction of isosceles trapeziums......Page 77
Method I......Page 78
Method III......Page 79
Method IV......Page 80
Construction of parallelograms:......Page 81
First Method......Page 82
Alternative Method......Page 83
Two cases of it......Page 84
CHAPTER VI: COMBINATION OF AREAS......Page 85
Multiple of a square......Page 86
Katyuyana's method......Page 87
Submultiple of a square......Page 88
Two methods of it......Page 89
Addition of unequal squares......Page 90
Subtraction of squares......Page 92
Combination of pentagons......Page 94
Transformation of a rectangle into a square......Page 97
Transformation of a square into a rectangle......Page 99
Transformation into an isosceles trapezium......Page 104
Transformation of a triangle into a square......Page 106
Transformation into a rhombus......Page 107
Area of a square......Page 109
Trapeziums......Page 110
Construction of a square having a given area......Page 112
Construction of an isosceles trapezium having agiven area......Page 113
Approximate formula for the frustum of a pyramid......Page 115
Theorem of the Square of the Diagonal......Page 118
Converse Theorem......Page 119
Did ancient Hindus know a proof......Page 120
Hypotheses as regards particular proofs......Page 122
General proofs......Page 129
Early history of the theorem......Page 133
Rational rectangles found in the Sulba......Page 137
Method of their discovery......Page 138
Calculation of the gnomon......Page 141
Interpretation of two Sanskrit words......Page 142
First formula......Page 147
Second formula......Page 148
Third formula......Page 149
Rectangle (15,36,39)......Page 150
Circling the square......Page 154
Squaring the circle......Page 158
Alternative Method......Page 160
Values of Pi......Page 162
Early history......Page 163
Similar Figures......Page 166
Similar isosceles trapeziums......Page 167
Methods of Baudhayana and Apastamba......Page 168
Methods ot Katyayana......Page 170
Early methods of enlargement......Page 172
Two methods of enlargement of the Fire-altar......Page 174
Principle of similarity......Page 175
Application of areas......Page 176
Geometrical solution of pure quadratic equation......Page 179
Solution of complete quadratic equation......Page 180
Solution of simple equation......Page 191
Katyayana's solution......Page 192
Rational right triangles having a given leg......Page 184
Simultaneous Indeterminate Equations......Page 194
Baudhayana's solutions......Page 196
Apastamba's solutions......Page 199
Other Indeterminate Problems......Page 200
Simple operations with surds......Page 201
Approximate value of sqrt(2)......Page 202
Various hypotheses about its origin......Page 203
Approximate value of sqrt(3)......Page 208
Irrationality of sqrt(2)......Page 204
Other approximate values of sqrt(2)......Page 216
Approximations to the value of sqrt(5)......Page 217
Evaluation of other surds......Page 219
Approximate Formula......Page 220
Terminology of fractions......Page 226
Operations with fractions......Page 227
Progessive Series......Page 231
Factorisation......Page 232
APPENDIX.-Some tecbnical terms of the Sulba......Page 235
BIBLIOGRAPHY OF THE SULBA......Page 241
INDEX......Page 247