The Gaṇitatilaka and its Commentary: Two Medieval Sanskrit Mathematical Texts

Description

The Gaṇitatilaka and its Commentary: Two Medieval Sanskrit Mathematical Texts presents the first English annotated translation and analysis of the Gaṇitatilaka by Śrīpati and its Sanskrit commentary by the Jaina monk Siṃhatilakasūri (13th century CE). Siṃhatilakasūri’s commentary upon the Gaṇitatilaka is a key text for the study of Sanskrit mathematical jargon and a precious source of information on mathematical practices of medieval India; this is, in fact, the first known Sanskrit mathematical commentary written by a Jaina monk, about whom we have substantial information, to survive to the present day. In presenting the first annotated translation of these two Sanskrit mathematical texts, this volume focusses on language in mathematics and puts forward a novel, fresh approach to Sanskrit mathematical literature which favours linguistic, literary features and textual data. This key resource makes these important texts available in English for the first time for students of Sanskrit, ancient and medieval mathematics, South Asian history, and philology. Cover Half Title Series Information Title Page Copyright Page Dedication Table of contents Tables Preface Abbreviations Part I Introduction 1 Introducing the Gaṇitatilaka and its commentary 1.1 Sanskrit mathematical writings in medieval India 1.2 Authorship and content of the Gaṇitatilaka 1.3 The Gaṇitatilaka, a work on pāṭīgaṇita 1.4 Siṃhatilakasūri, the commentator of the Gaṇitatilaka 1.5 The genre of mathematical commentaries 1.6 Aspects of style and language in Siṃhatilakasūri’s commentary 1.7 Reading the Gaṇitatilaka and its commentary 2 On the edition of the Gaṇitatilaka and some methodological notes 2.1 The edition 2.2 The Sanskrit manuscript 2.3 Linguistic phenomena and oddities: Between the manuscript and the edition 2.4 Lines of transmission and internal evidence 2.5 Methodological notes: A philological perspective 2.6 Theory and praxis of textual criticism 2.7 A new verse numbering system Part II Translation Some notes on the English translation Editorial conventions 3 Translation of the Gaṇitatilaka and its commentary: The Gaṇitatilaka composed by Śrīpati together with the ... 3.1 Homage to the Jina 3.2 Benedictory verse (maṅgalācaraṇa) [GT 1] 3.3 Section on technical terms (paribhāṣā) [GT 2−12] 3.4 Arithmetical operations with integers [GT 13−34] Addition (saṅkalita) [GT 13] Subtraction (vyavakalita) [GT 15] Multiplication (guṇakāra) [GT 17−18] Division (bhāgahāra) [GT 21] Square (varga)[GT 23–24] Square-root (vargamūla) [GT 26] Cube (ghana) [GT 28–30] Cube-root (ghanamūla) [GT 32–33] 3.5 Arithmetical operations with fractions [GT 35–51] Addition of fractions (bhinnasaṅkalita) [GT 35] Subtraction of fractions (bhinnavyavakalita) [GT38] Multiplication of fractions (bhinnapratyutpanna) [GT 40] Division of fractions (bhinnabhāgahāra) [GT 42] Square of fractions (bhinnavarga) [GT 44] Square-root of fractions (bhinnavargamūla) [GT 46] Cube of fractions (bhinnaghana) [GT48] Cube-root of fractions (bhinnaghanamūla) [GT 50] 3.6 Arithmetic of zero [GT 52] The proper form of zero (śunyasvarūpa) 3.7 Classes of simplification of fractions [GT 53–63] On the simplification of fractions (kalāsavarṇa) The class of simple fractions (bhāgajāti) [GT 53] The multi-part class (prabhāgajāti)[GT 55] The class of fractional increase (bhāgānubandhajāti) [GT 57] The class of fractional decrease (bhāgāpavāhajāti) [GT 60] Chain-simplification class (vallīsavarṇanajāti) [GT 62] 3.8 Type-problems of fractions [GT 64‒92] The visible quantity type-problem (dṛśyajāti) [GT 64] The remainder type-problem ((śeṣajāti) [GT 67] The difference type-problem (viśleṣajāti) [GT 70] The remainder-root type (śeṣamūlajāti) [GT 73] The type-problem of the fraction [executed] with the root and the visible quantity (mūlāgrabhāgajāti)[GT 76] The type-problem of the visible quantity at both tips (ubhayāgradṛśyajāti) [GT 80] The type-problem of the fractions and the visible quantity which is a fraction (bhinnabhāgadṛśyajāti)[GT 84] The type-problem of the [coefficient of the] [square] root of the fraction (bhinnamūlajāti)[GT 87] The type-problem of the subtractive square (hīnavargajāti)[GT 90] 3.9 Inverse operation [GT 93–94] Inverse operation (viparītoddeśaka)[GT 93] 3.10 Rules on proportion [GT 95–117] Rule of three (trairāśika) [GT 95] 3.11 Rule of five (pañcarāśika) [GT 107–117] 3.12 Barter (bhāṇḍapratibhāṇḍa) [GT 112–117] 3.13 The sale of living beings (jīvavikraya) [GT115–117] 3.14 Practices [GT 118–133] Practice of mixture (miśravyavahāra) [GT 118] 3.15 Commission to the moneylender (vyājopajīvivṛtti) [GT 120] 3.16 Rule on interest [GT 122] 3.17 Rule on time and double capital [GT 124] 3.18 Conversion of several bonds into one (ekapatrakaraṇa) [GT 127] 3.19 Equating instalments of capital (samīkaraṇa) [GT 131] Part III Text analysis 4 Text analysis 4.1 Preliminaries 4.2 Benedictory section (maṅgalācaraṇa) [GT 1] 4.3 Section on technical terms (paribhāṣā) [GT 2–12] 4.4 The eight arithmetical operations with integers [GT 13–34] Some remarks Addition (saṅkalita) [GT 13] Subtraction (vyavakalita) [GT 15] Multiplication (guṇakāra) [GT 17–18] Division (bhāgahāra) [GT 21] Square (varga) [GT 23–24] Square-root (vargamūla) [GT 26] Cube (ghana) [GT 28–30] Cube-root (ghanamūla) [GT 32–33] 4.5 The eight arithmetical operations with fractions [GT 35–51] Some remarks Addition of fractions (bhinnasaṅkalita) [GT 35] Subtraction of fractions (bhinnavyavakalita) [GT 38] Multiplication of fractions (bhinnapratyutpanna) [GT 40] Division of fractions (bhinnabhāgahāra) [GT 42] Square of fractions (bhinnavarga) [GT 44] Square-root of fractions (bhinnavargamūla) [GT 46] Cube of fractions (bhinnaghana) [GT 48] Cube-root of fractions (bhinnaghanamūla) [GT 50] Arithmetic of zero [GT 52] 4.6 Classes of simplification of fractions [GT 53–63] Preliminary observations The class of simple fractions (bhāgajāti) [GT 53] Rule corresponding to PG 37 The multi-part class (prabhāgajāti) [GT 55] The class of fractional increase (bhāgānubandhajāti) [GT 57] The class of fractional decrease (bhāgāpavāhajāti) [GT 60] The chain-simplification class (vallīsavarṇanajāti) [GT 62] 4.7 Type-problems of fractions [GT 64–92] Preliminary remarks The visible quantity type-problem (dṛśyajāti) [GT 64] The remainder type-problem (śeṣajāti) [GT 67] The difference type-problem (viśleṣajāti) [GT 70] The remainder-root type-problem (śeṣamūlajāti) [GT 73] The type-problem of the fraction [executed] with the root and the visible quantity (mūlāgrabhāgajāti) [GT 76] The type-problem of the visible quantity at both tips (ubhayāgradṛśyajāti) [GT 80] The type-problem of the fractions and the visible quantity which is a fraction (bhinnabhāgadṛśyajāti) [GT 84] The type-problem of the [coefficient of the] [square] root of the fraction (bhāgamūlajāti) [GT 87] The type-problem of the subtractive square (hīnavargajāti) [GT 90] 4.8 Inverse operation [GT 93–94] Inverse operation (viparītoddeśaka) 4.9 Rules on proportion [GT 95–117] Preliminary observations The rule of three quantities [GT 95] 4.10 The rule of five (pañcarasika) [GT 107] The rules of seven, nine, and eleven 4.11 Barter (bhāṇḍapratibhāṇḍa) [GT 112] 4.12 The rule regarding the sale of living beings (jīvavikraya) [GT 115] 4.13 Practices [GT 118–133] Preliminary observations Practice of mixture (miśravyavahāra) [GT 118] 4.14 Commission to the moneylender (vyājopajīvivṛtti) [GT 120] 4.15 Rule on interest [GT 122] 4.16 Rule on time and double capital [GT 124] 4.17 Conversion of several bonds into one (ekapatrakaraṇa) [GT 127] 4.18 Equating instalments of capital (samīkaraṇa) [GT 131] Appendix 1 List of mathematical rules and sample problems supplied by the SGT and found in other works Appendix 2 Rules and sample problems of the GT occurring in other works Appendix 3 Glossaries Bibliography Primary Sources Secondary Sources Index