Index Āryabhaṭa, xi, xiii, xvi xix, xxi, xxvii, xxxii, xxxiii, xxxv, xxxix, xl, xlii xlviii, li, liii, 1, 2, 6, 9, 17, 18, 39, 58, 71, 86, 108, 121, 133, 137, 150, 152 altitude, xxxix, 73, 74, 118 arc, xxix, xxx, 54, 57 66, 92 area, xii, xx, xxiii, xxviii, xxxiii, xxxiv, xxxvii, xxxviii, xliv, xlv, xlvii, xlviii, 8, 13 16, 18, 24 30, 33 49, 52 54 arithmetics, xiv, xix, xx, xxiv xxvi, xxxiii xxxviii, xlviii arrow, xxix, xxxi, xxxix, xlix, 54, 59, 61 64, 84 86, 88, 90, 92, 93 astronomy, xii xiv, xix, xxxi, xxxviii, xxxix, xli, 115, 159 base, xi, xxv, xxviii, xxxiii, xliv, xlvii, xlix, 24 31, 39, 46, 58 64, 68, 71, 73 85, 92 bead, 121 124 Bhāskara, viii, ix, xi xvi, xviii, xix, xxi liii, 1 4, 7, 9, 11 13, 15, 17, 24, 33, 35, 36, 41, 55, 57, 59, 60, 64, 66, 74, 81, 85, 93, 119, 122, 132, 135, 136, 140, 145, 157 159, 162 bow-field, xxix, xxxi xxxiii, xxxix, xlix, 50, 52 55, 84, 85 Brahmagupta, xiii, xxv, 119 breadth, xxviii, 8, 15 calculation, xxxii, 7, 21, 27, 54, 83 capital, xix, 105, 106, 111 characterize, xxviii, xliii, liii, 14, 70, 71, 82 chord, half-chord, xx, xxix xxxii, xxxix, xlix, 50, 53 55, 57 67, 84 86, 88 90 circle, xx, xxii, xxv, xxvi, xxix xxxiii, xxxviii, xxxix, xlix, l, 33 37, 45, 50 52, 54, 56 59, 67, 69 75, 82, 84, 85, 92, 93 circumference, xx, xxix, l, 33 36, 50 52, 54 59, 82, 85 coin, 121 123 commentary, viii, ix, xi xix, xxi xxvi, xxviii xxx, xxxii xliv, xlvi liii, 1, 3, 4, 6, 7, 11, 20, 25, 33, 50, 52, 55, 57, 59, 66, 81, 109, 128, 130, 135, 136, 143, 159, 161, 166 compasses, 59, 67 computation, xix xxi, xxiii, xxv, xxxiii, xxxvii, xxxix, xlv, l lii, 1, 2, 7, 19, 25, 28, 29, 31, 32, 34 36, 38 40, 42 45, 54, 56, 57, 59, 66, 75, 77, 79 83, 86, 95, 96, 99, 107, 109, 112, 113, 115, 116, 118 120, 125 129, 131, 135, 136, 141, 143, 144, 150, 151, 153 156, 158, 160 163, 165 cube, xvii, xx, xxi, xxiv, xxxii xxxv, xxxviii, xlv, xlvi, 7, 18, 19, 22, 23 day, xxxiv, xxxix, xli, 73 75, 81, 82,
168 Index 111, 118, 125 128, 135 149, 151 162, 164 166 denominator, xxii, xxv, 17, 21, 23, 107 110, 112 114, 116, 117, 151, 152 diagonal, xxvii, xxviii, xliv, 13 15, 38, 39, 52, 59 61, 63, 67 69, 84, 90 diagram, xv, xviii, xxx, xxxiii, xxxv, xl, lii, liii, 49, 50, 57, 58, 65, 66, 84 difference, 24, 28, 29, 31, 39, 41, 55, 59 64, 66, 67, 73, 75, 76, 78 80, 82, 86, 88, 93 99, 104, 105 digit, see rūpa distance, xxxix, 73 83, 86, 87, 118, 124 128 divisor, xxv, xlii, 78, 107 110, 113, 115, 116, 118, 119, 128 138, 142, 145, 146, 150, 155 166 ear, viii, xi xiii, xv, xix, xxi xxviii, xxxii xxxviii, xl, xli, xlvi xlix, liii, 3, 4, 6, 8, 10, 19, 22, 25 35, 37 42, 45, 48, 51, 52, 54 56, 58, 70, 80, 96 earth, xxvii, xxviii, 9, 37 42, 57, 73, 79, 81, 82, 118 eclipse, xxxix, 93 edge, xiii, xiv, xxvii, xxviii, xxxvi, xl, xli, xlv, li, 18, 19, 30, 33 equi-quadrilateral, xxvii, xliv, 13 16, 18, 40, 60, 61, 63, 102 equilateral, xix, xx, xxviii, xxxii, xxxiii, xxxvii, xliv, xlv, xlvii, xlviii, li establish, xxiii, xlvi, li, 11, 14, 22, 25, 31, 39, 43, 52, 58, 59, 70, 71, 73, 81, 83, 108, 120, 135, 136, 153 even, xvi, xvii, xxi, xxii, xxix, xxxvi xxxviii, xlvii, l, li, 2, 8, 10, 11, 13, 16, 20, 23, 26, 28, 29, 33 35, 40, 43, 48, 50, 52, 56 59, 61, 63, 67, 71, 76, 77, 80 83, 94, 95, 97, 98, 101, 103, 104, 108, 111 114, 117 124, 129 133, 135, 138, 143 145, 147, 153, 154, 156, 158, 160, 161, 165, 166 example, ix, xiii, xvi, xviii, xxi, xxii, xxiv, xxv, xxxv, xli, xlii, xlv, xlviii l, lii, liii, 3, 4, 16, 17, 19, 21, 23, 26 29, 31, 32, 34, 36, 39, 40, 42, 44, 45, 48, 53 56, 59, 66, 72 78, 80, 84 91, 93 99, 101 123, 127, 130 135, 137, 138, 140, 141, 143, 145, 146, 148 150, 152 156, 158, 161 166 face, xviii, xxi, xxiv xxvii, xxxiii, xxxv, 37 42, 48, 172 field, xvi, xix, xxvii xxxiv, xlix, 7, 8, 13 16, 18, 24 31, 33 36, 38 50, 52 60, 62, 63, 67, 69, 71, 73, 74, 82, 84 86, 92 flank, xxvii fraction, xx xxvi, xlviii, xlix, 17, 19, 21, 23, 51, 65, 66, 112, 116, 130, 154, 168 fraction fractional number, xlix fractionary number, xxii, xxiii, xxv gaṇita, xi, xix, xxxiii, xxxiv, xxxvii xxxix, 6, 8, 10, 20, 21, 25, 27, 31, 34, 36, 38 40, 45, 56, 93, 107, 112, 119, 120, 127 129, 135 geometry, xiv, xix, xxvi, xxviii, xxx, xxxiii xxxviii gnomon, xx, xxxviii, xxxix, xlviii, 70 83 height, xxvii, xxviii, xxxiii, xliv, xlvii, xlix, li, 2, 18, 24, 27, 30, 37
Index 169 39, 42, 48, 71, 74 83, 85 88, 114, 115 Hindu, xii, xiii hypotenuse, 25, 27, 31, 59 64, 73, 82 86, 92 integer, see rūpa investment, 107, 111 114 irrational, see kāraṇī isoceles, 24 27, 38, 41 Jain, xiii, xviii, xliii Jupiter, 9, 147, 150, 151, 165 karaṇī, xxiii, xxxv xxxvii, 8, 13, 27, 31, 32, 35, 37, 46, 52 55 length, xx, xxiii, xxvii, xxviii, xxxii, xxxvii, xlvii, xlix, 7, 8, 15, 34, 43, 44, 46 49, 52, 71, 72, 76, 79, 80 longitude, xxxix, 9, 136 138, 142 152, 159, 160, 162, 163 master, 6, 9, 57, 58, 66, 108, 165 mathematics, xi xiv, xvi, xviii, xix, xxiv, xxvi, xxxiv, xxxvi, xxxviii xl, lii, liii, 6 8, 25, 34, 40, 41, 44, 64, 66, 112, 121, 133, 135, 137 mean, ix, xiii, xv, xxi, xxii, xxvi xxviii, xxxi, xxxvi, xxxix, xli xlvii, xlix, li, lii, 1 3, 6, 8, 9, 65, 66, 93 95, 97, 99, 101, 104, 105, 107 109, 113, 120, 121, 124, 125, 129, 132, 133, 135, 136, 140, 142 144, 148 154, 156 160, 162, 163 measure, xiii, xvi, xxiii, xxiv, xxxvii, xxxviii, l, 15, 24, 31, 34, 39 41, 52, 54, 75, 76, 79, 85, 90, 91, 101, 107 110, 113, 116, 120, 145, 154, 170 method, xxiii, xxxvi, xxxix, xlv xlvii, li, liii, 30, 33, 34, 47, 52 55, 64, 66, 74, 81 83, 90, 96, 97, 103, 112, 116, 119, 120, 125, 126, 135, 137, 139, 142, 146, 148 151, 155, 156, 158, 160 month, 106, 107, 112 114 moon, xxi, 2, 9, 10, 146 149, 158 165 number, ix, xiii xv, xvii xix, xxi xxvi, xxxiv xxxix, xliii, xliv, xlvi xlix, liii, 1 4, 10 12, 16, 17, 19, 21, 23, 40, 51, 52, 55, 57, 58, 60 64, 72, 73, 83, 93 103, 119 121, 129 162, 164 166, 168 numerator, xxii, xxv, 17, 21, 112 object, xii, xvi, xvii, xix, xxxiii, xxxv, xxxvi, xxxviii, xxxix, xlii, xliv, xlv, xlvii, xlviii, liii, 2, 98 operation, xxi, xxiv, xxv, xxviii, xxxiv, xxxv, xxxvii, xxxix, xlii, xlvi, xlviii, l, 2, 6, 8, 10, 11, 13, 14, 17, 18, 20, 21, 57, 77, 118 120, 126, 129, 133, 150, 158, 165, 166 orbit, xxxix, 158 161, 164 166 part, ix, xv, xvi, xviii xx, xxii, xxiv, xxvi, xxxiv xxxvi, xl, xlii, xlvii, xlviii, lii, liii, 3, 6, 7, 11, 12, 14, 16, 19, 20, 22, 25, 34, 37, 38, 43, 50 53, 55 60, 62 67, 70, 72 74, 86 88, 92, 99, 101, 110, 112, 114, 116, 118, 122, 127, 128, 133, 135 138, 154, 156, 159 perpendicular, xxviii, 24 27, 29 31, 37 41, 46, 59, 60, 68, 71, 74 pile, xxxii, xxxv, xxxviii, 99 103 place-value, xxvi planet, xxxix, 6, 9, 125, 126, 135, 143, 145 151, 156, 157, 160, 161 Prabhākara, 57, 65, 66 prakṛt, 123
170 Index procedure, xvii xxv, xxxii xxxiv, xxxvi xliv, xlvii liii, 2, 4, 7, 17, 21, 22, 27 32, 35, 36, 39 41, 44, 48, 49, 53, 55, 57 59, 66, 73, 77, 78, 80, 84 86, 88 91, 93, 95 98, 100, 101, 103 107, 109, 111 113, 117 120, 122 124, 127 131, 133, 134, 137 139, 142 148, 150 152, 154, 156 158, 160, 162, 164 166 profit, 111, 112 proof, xli, li, lii, 31, 52 proportion, xxiv, xxxiv, xxxvi, xxxvii, xxxix, 8, 108, 111 pulverizer, xiv, xx, xxiv, xxxiv, xxxix, xlix, 128, 130, 132 158, 160, 162 166 Pythagoras Theorem, xii, xx, xxviii, xxxii, xxxvii, xxxix, xlix, l quadrilateral, xxvii xxviii, 7, 15, 41, 47, 57, 58, 60, 62, 63, 67, 69, 101, 102 elongated quadrilateral, see rectangle uneven quadrilateral, 40 41 quantity, xxii xxv, xxxiv, xxxvi, xxxvii, xlix, l, 8, 17, 21 23, 31, 35, 37, 39, 54, 72, 78, 93, 108, 109, 112, 116 120, 128 134, 138, 142, 146, 152, 155 158, 160, 161, 165, 166 quotient, xvii, 20, 22, 28, 29, 39, 66, 89, 90, 92, 93, 119, 123 125, 127 132, 134 142, 145, 146, 149 151, 153 156, 158, 159, 161, 163, 164 rāśi, xix, xxii xxiv, xxix, xxxiii, xxxiv, l, 8, 21, 22, 50, 59, 60, 62 64, 107, 115, 116, 138, 148 rūpa, xxi, 11, 16, 19, 23, 39, 53, 106, 107, 109, 110, 113, 114, 116, 117, 121 124, 166 reason, xiv xvi, xxviii, xxxv, lii rectangle, xxviii, xxx, 8, 15, 39, 43 48, 54, 59, 90 reduce, xxii, xlviii, 54, 55, 132 138, 140, 142 152, 154 156, 158 163, 165, 166 refutation, xxxiv, xlii, lii, 7, 8, 73 remainder, xliii, 27, 32, 35, 36, 59, 61 64, 90, 104, 124, 128 137, 139 147, 149, 153, 155 162, 164 166 result, xxi xxiii, xxv, xxxii, xxxiv, 6, 7, 13, 16, 17, 21, 31, 32, 37, 39, 44, 54, 55, 59, 78, 79, 86 88, 90, 91, 93, 98 100, 104, 106, 107, 109, 110, 118, 119, 121 125, 128 134, 136 142, 145 152, 154 156, 158, 160, 166 revolution, 135 142, 144 159, 161 165 root, 18, 20 23, 30, 35, 37, 38, 43, 53, 54, 59 64, 105, 106, 133 rule, xvii xix, xxi xxvii, xxxiii, xxxvi, xxxviii xlii, xliv liii, 3, 11, 12, 16, 17, 19, 21, 23, 25, 38, 39, 43 45, 51 54, 56, 65, 66, 72, 73, 78, 79, 88, 92, 94, 106 109, 111 113, 115, 120, 121, 125, 126, 128, 131 133, 136, 138, 139, 142, 150, 153, 156, 157, 159, 161, 165 Rule of Three, xv, xx, xxii, xxiv, xxxv, xxxvi, xxxix, xl, xlviii lii, 30, 31, 34, 36, 38, 50, 56, 74, 77, 136, 137, 139 142, 145, 149, 151, 153 155 desire quantity, xxiv, l, 107 109, 113 fruit quantity, l, 107 109, 113, 116 measure quantity, 109, 110, 116 measure quantity, xxiv, l Rule of Five, xxv, 108, 112, 113 Rule of Seven, 114
Index 171 Rule of Nine, 108, 115 Sanskrit, ix, xi, xiii xvi, xviii, xix, xxi, xxiii, xxiv, xxvi, xxxiv, xxxv, xl, xliii, xlv, xlvii, xlix, li, liii, 1 4, 6, 7, 9, 10, 20, 52, 53, 109, 123 scalene, xxviii, xlv, xlviii, 37 seed, xli, xlvii, xlviii, liii, 6, 8, 86, 91, 108, 111 semi-diameter, xx, xxix, xxxi, xxxii, xlix, l, 33 36, 47, 50 64, 70 75, 81 83, 85, 86, 92, 93 series, xiv, xix, xx, xxxii, xxxiv xxxvi, xxxviii, xlvi, 7, 8, 93 96, 98, 99, 120 setting down, xxiv, liii, 12, 16, 17, 19, 21, 23, 26, 28, 29, 31, 32, 34, 36, 39, 40, 42, 44 49, 53, 56, 73, 75 78, 80, 84 91, 93, 95 98, 100 104, 106, 107, 110, 112, 113, 115 117, 119 123, 127, 128, 130 132, 134 141, 145, 147 149, 151 153, 155 159, 162, 165 shadow, xxxiv, xxxix, xlviii, 8, 70 83 side, xii xiv, xix, xxiii, xxvii xxxv, xxxvii xli, xliii, xliv, xlvi xlix, li, 3, 8, 11, 13 16, 18, 23 32, 37 39, 41 44, 46, 48 50, 57, 60 64, 69 71, 78 87, 90 93, 96, 100, 101, 109, 132 134, 136, 137, 139, 140, 152 154, 156 159, 162, 164, 166 upright-side, xxviii, xlix, 25, 27, 30, 31, 60 64, 70, 78 85, 92 sign, xvii, xxi, xxiii, xliv, xlv, lii, 135 146, 148 153, 163, 164 sine, see chord, half-chord, xx, xxvi, xxx xxxiii, xxxix, lii, 67, 73 75 size, xix, xxxix, 24, 28 30, 37, 38, 41, 51, 52, 59, 67, 70, 72, 73, 77, 78, 82, 84, 86, 88 90, 93, 111, 115 solid, xxxii, xxxiii, xxxv, xlv, 18, 30, 35, 36, 99 103 sphere, xx, xxxi xxxiii, xxxvii xxxix, xli, 6, 8, 36, 73, 74, 81, 82 square, xvii, xxi, xxvii, xxxiii xxxviii, xliv, xlv, 7, 8, 13 22, 27 29, 31, 34, 35, 37, 41, 52, 54, 55, 59 64, 70, 72, 73, 83 86, 88 90, 92, 97, 98, 100, 101, 103 106, 120, 143, 145, 158, 161 string, xii, 67 69, 71 Śulbasūtra, xii, xxviii sum, xii, xiii, xviii xx, xxiii xxv, xxxv, xxxvii, xxxviii, xliii, xlix, lii, 9 11, 27 29, 37 39, 47 49, 51, 52, 54, 59 66, 70, 72, 73, 78, 80, 82, 84, 85, 90, 92 94, 98 101, 103, 104, 112, 116, 117, 119 122, 124 127, 148, 149, 152 sun, 9, 70, 71, 73 75, 81 83, 127, 135 165 terms; first term, last term, number of terms, 93 101, 103, 119, 120, 122 time, xiii xvi, xx, xxi, xxiii xxv, xxxi, xxxiii, xxxvi, xxxviii xlii, xliv xlvi, xlviii, l liii, 1 3, 6, 8, 10, 71, 74, 83, 118, 119, 122, 124 127, 135, 136, 142 146, 149 154, 156, 157 to explain, xviii, xxi, xxiii, xxiv, xxxii, xxxvi xxxviii, xli, xlii, xliv, xlviii, l liii, 2, 8, 12, 18, 22, 24, 25, 38, 39, 41, 50, 53, 60 64, 66, 72, 86, 94, 107 109, 116, 129, 130, 132, 133, 135, 138, 145, 151, 157, 158, 161 to show, 12, 18, 30, 31, 38, 45, 46, 50, 59, 71, 85, 119 121
172 Index tradition, xii xiv, xvi, xviii, xxi, xxvi, xl, xlv xlvii, li, 10, 12, 35, 52, 83, 129, 133 trapezium, xx, xxvii, xxxviii, 37, 39, 41 treatise, ix, xi xvii, xix, xxiv, xxv, xxxii, xxxviii, xl xlii, xlv, li, liii, 3, 7, 9, 10, 12, 23, 30, 40, 41, 57, 66, 114, 118, 133, 135 triangle, see trilateral trigonometry, xiv, xxix, xxxii trilateral, xxviii, xxxiii, xxxvii, xliv, xlv, 13, 15, 24 31, 38, 39, 45 47, 50, 57 61, 63, 67, 68, 84, 86, 88 width, 37 39, 43, 44, 46 49, 52 working surface, xxi, xxiv, xxvi, xxxiii zenith, xxxix, 73 75, 118, 153 zero, xv, xxv, xxvi, xxxv, 56, 82, 95, 136, 142, 146, 150 153, 156, 158 161, 164 166 understand, xi, xvi, xvii, xxiii, xxxii, xxxiii, xxxv xxxvii, xxxix xlvi, xlviii, li, lii, 1, 2, 7, 11 13, 15, 33, 35 39, 43, 51, 52, 54, 57, 58, 64, 65, 67, 73, 76, 81, 85, 97, 98, 103, 107 109, 112, 120 122, 124, 129, 133, 152, 158 uneven, xliv, 24, 25, 28, 29, 38, 40, 41, 46, 47, 58, 60 64, 129, 170 unit, see rūpa value, xvii, xx xxvi, xxxi, xxxv, xxxvii, xxxviii, xl, xliv, li, 11, 12, 14, 16, 28, 32, 41, 51, 52, 55, 73 75, 81, 93 98, 103, 106, 109, 117, 119 124, 132, 135, 136, 138 140, 147, 148, 153, 154, 158, 160, 162, 163 Vedas, xii verification, xviii, xxviii, lii, 42 46, 106 volume, xi xiii, xvii, xix xxxviii, xl lii, 1, 14, 18, 30 32, 35 37 wealth, xxiii