History of Hindu Mathematics: A Source Book v1.c3: Preface
History of Hindu Mathematics: A Source Book v1.c3
- Language
- English
Preface
v1.c3.1
Little is known at present to historians of mathematics regarding the achievements of the early Hindu mathematicians and our indebtedness to them. Though it is now generally admitted that the decimal place-value system of numeral notation was invented and first used by the Hindus, it is not yet fully realized to what extent we are indebted to them for our elementary mathematics. This is due to the lack of a reliable and authentic history of Hindu mathematics. Our object in writing the present book has been to make up for this deficiency by giving a comprehensive account of the growth and development of the science of mathematics in India from the earliest known times down to the seventeenth century of the Christian era.
v1.c3.2
The subject is treated by topics. Under each topic are collected together and set forth in chronological order translations of relevant Sanskrit texts as found in the Hindu works. The texts have been elucidated, wherever necessary, by adding explanatory notes and comments, and also by illustrative examples culled from original sources. We have tried to avoid repetition as far as has been consistent with our aim. However, on several occasions it has been considered desirable to repeat the same rule in the words of different authors in order to emphasize the continuity or rather the gradual evolution of mathematical thought and terminology in India. Comparative study of this kind has helped us to throw light on certain obscure Sanskrit passages and technical terms whose full significance had not been understood before. In translating the texts we have tried to be as literal and faithful as possible without sacrificing the spirit of the original. Sometimes it has not been possible to find exact parallels to Sanskrit words and technical terms in English. In all such cases we have tried to maintain the spirit of the original in the English version.
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The above plan of the book has been adopted in pursuance of our intention to place before those who have no access to the Sanskrit sources all evidence, unfavourable as well as favourable, so that they can judge for themselves the claims of Hindu mathematics, without depending solely on our statements. In order to facilitate comparison with the development of mathematics in other countries the various topics have been arranged generally in accordance with the sequence in Professor D. E. Smith’s *History of Mathematics*, Vol. II. This has sometimes necessitated divergence from the arrangement of topics as found in the Hindu works on mathematics.
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In search of material for the book we had to examine the literature of the Hindus, non-mathematical as well as mathematical, whether in Sanskrit or in Prâkrit (Pâlî and Ardha Mâgadhî). Very few of the Hindu treatises on mathematics have been printed so far, and even these are not generally known. The manuscript works that exist in the various Sanskrit libraries in India and Europe are still less known. We have not spared labour in collecting as many of these as we could. Sanskrit mathematical works mentioned in the bibliography given at the end of this volume have been specially consulted by us. We are thankful to the authorities of the libraries at Madras, Bangalore, Trivandrum, Trippunithura and Benares, and those of the India Office (London) and the Asiatic Society of Bengal (Calcutta) for supplying us transcripts of the manuscripts required or sending us manuscripts for consultation. We are indebted also to Dr. R. P. Paranjpye, Vice-Chancellor of the Lucknow University, for help in securing for our use several manuscripts or their transcripts from the state libraries in India and the India Office, London.
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It would not have been possible to carry our study as far as has been done without the spade work of previous writers. Foremost among these must be mentioned the late Pandit Sudhakar Dvivedi of Benares, whose editions of the *Lîlâvatî*, *Brâmasphuṭa-siddhânta*, *Triśatikâ*, *Mahâsiddhânta*, *Siddhânta-tattva-viveka*, etc., have been of immense help. Colebrooke's translations of the arithmetic and algebra of Brahmagupta and Bhâskara II, Kern's edition of the *Âryabhaṭîya* and Rangacarya's edition (with English translation) of the *Gaṇita-sâra-saṁgraha* of Mahâvîra have also been of much use. The recent work of G. R. Kaye, however, has been found to be extremely unreliable. His translation of the *Gaṇitapâda* of the *Âryabhaṭîya* and his edition of the Bakhshâlî Manuscript are full of mistakes and are misleading.
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It has been decided to publish the book in three parts. The first part deals with the history of the numeral notation and of arithmetic. The second is devoted to algebra, a science in which the ancient Hindus made remarkable progress. The third part contains the history of geometry, trigonometry, calculus and various other topics such as magic squares, theory of series and permutations and combinations. Each part is complete in itself, so that one interested in any particular branch of mathematics need not consult all of them.
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Part I which is now being published contains two chapters. Chapter I gives an account of the various devices employed by the Hindus for denoting numbers. The gradual evolution of the decimal place-value system of notation has been traced and all evidence relating to its use in India collected together for the first time. This evidence shows that the system was in use in India during the earliest centuries of the Christian era, if not earlier. We hope that the facts set forth in this chapter will finally set at rest the controversy about its place of origin. Considerations of space have prevented us from giving details regarding the introduction of the Hindu numerals into Arabia, Northern Africa and Europe. A brief account has, however, been included.
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Chapter II deals with arithmetic in general. We have become so familiar with our methods of performing the fundamental arithmetical operations of addition, subtraction, multiplication, division and the extraction of roots that we seldom pause to think how and when these methods were invented. The problem, however, has deep interest for the teacher and historian of mathematics. And an account of the evolution of these methods in the land of their birth should be welcome. We have given details and illustrations of different methods of performing these operations on a *pāṭī*, ("board"), as followed in India from the fifth century onwards. It has been shown that our present methods are simple variations of those of the ancient Hindus. The rule of three, the rules of supposition and false position, and rules relating to calculations involving interest, exchange of commodities, fineness of gold, etc., are all due to the Hindus. In fact, practically the whole of elementary arithmetic can be traced back to them. Thus the importance of chapter II cannot be over-emphasised.
v1.c3.9
The scheme of transliteration of Sanskrit words and proper names has been indicated in the beginning. Arabic words and proper names that occur in the book have been taken down as found in various secondary sources consulted.
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Acknowledgment has been made in footnotes to the texts of various sources from which we have derived assistance. Of the books which have been found specially helpful, we would mention Bühler's Indian Palæography and Ojha's Prâcîna Lipi Mâlâ (in Hindi). We are indebted to Mr. Ojha for permitting us to reproduce from his book the tables of Brâhmî and Kharoṣṭhî numerals. We have pleasure in expressing our obligation to Mr. T. N. Singh for his help in the revision of proof-sheets. He has caused the removal of many obscurities and has made many valuable suggestions of which we have availed ourselves. Our thanks are also due to Mr. R. D. Misra for preparing the index to this volume.
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In conclusion we express our thanks to the Law Journal Press for their unfailing courtesy and for expediting the work of printing.
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LUCKNOW *September, 1935* BIBHUTIBHUSAN DATTA AVADHESH NARAYAN SINGH