Lilavati (The Beautiful) of Bhaskaracharya (Unknown) - Page 15

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Table of Contents

Subject	Page	Subject	Page
48. Rule for Mathematical Progressions original: "Sredhi-vyavahara-vidhi"; refers to arithmetic and geometric series	.... 104	72. Description of Special Rules therein	,,
49. Rule for the Sum of Squares and Cubes	.... 106	73. Finding the Area of Regular Quadrilaterals and Rectangles	148
50. Method for Finding the Common Difference	.... 107	74. Knowledge of Area, Perpendicular, and Hypotenuse	154
51. Knowledge of the First Term	.... 109	75. Knowledge of the Perpendicular	.... 155
52. Method for Finding the Sum of a Series	.... 110	76. Knowledge of the Hypotenuse original: "Karna"; also means diagonal in the context of quadrilaterals	.... 156
53. Rule for the Calculation of Circles and Cylinders	.... 114	77. Another Method for Finding the Hypotenuse	,,
54. Practical Geometry Kshetra-vyavahara: The branch of mathematics concerning the measurement of areas and shapes	.... 117	78. Exhaustive Statement on Assuming a Desired Hypotenuse	.... 157
55. Knowledge of the Base, Perpendicular, and Hypotenuse Bhuja-koti-karna: The three sides of a right-angled triangle	.... ,,	79. Calculating the Area of an Irregular Quadrilateral	160
56. Description of Alternative Methods	.... 119	80. Knowledge of Segments in Figures with Equal Perpendiculars Abadha: The segments into which the base of a triangle is divided by the perpendicular	.... 161
57. Means of Finding Approximate Roots	121	81. Short Method for Figures with Equal Perpendiculars	167
58. Description of the Classes of Triangles	.... 122	82. Description of Pyramidal Figures original: "Suchi-kshetra"; literally 'needle-field', refers to cones or pyramids	.... 171
59. Process for finding the Perpendicular from a Desired Hypotenuse	125	83. Finding the Junctions and Related Parts	.... 172
60. Description of Another Method	.... 127	84. Description of the Vertical Segment at the Intersection of Diagonals	.... 174
61. Rule for Deriving the Base, Perpendicular, and Hypotenuse from an Assumed Value	.... 128	85. Knowledge of the Segments and Altitude of a Pyramidal Figure	176
62. Finding the Base from the Hypotenuse and Perpendicular	.... 130	86. Knowledge of the Base	.... ,,
63. Finding the Perpendicular from the Sum of the Base and Hypotenuse	132	87. Circular Figures	.... 179
64. Method for Separating the Perpendicular and Hypotenuse from the Base	.... 133	88. Finding the Area and Volume of Spheres	.... 181
65. Finding the Base, Perpendicular, and Hypotenuse when the Hypotenuse is Combined with a Segment of the Perpendicular	136	89. Another Method	.... 183
66. Method for Separating the Hypotenuse from the Sum of the Base and Perpendicular	137	90. Finding the Arrow and the Chord Shara and Jiva: The sagitta and chord of a circle, fundamental to Indian trigonometry	184
67. Knowledge of the Perpendicular and the Base Segments	.... 138	91. Method for Finding the Sides of Regular Polygons (from Triangle to Nonagon) Inscribed within a Circle	.... 186
68. Characteristics of Geometrical Figures	.... 140	92. Simplified Operation for the Gross Chord	.... 191
69. Description of the Knowledge of Segments	.... 142	93. Rule for Calculating the Arc original: "Dhanusha"; literally 'the bow'	193
70. Finding the Gross and Exact Areas in Quadrilaterals and Triangles	.... 144
71. Explanation of the Gross Area	.... 147