History of Hindu Mathematics (Set of 2 Volumes)

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This book at present to historians of mathematics regarding the achievements of the early Hindu mathematicians and our indebtedness to them. Our object in writ- ing the present book has been to make up for this deficiency by giving a comprehen- sive account of the growth and develop- ment of the science of mathematics in India from the earliest known times down to the seventeenth century of the Christian era.

It has been decided to publish the book in two Vols. The first Vol. deals with the history of the numeral notation and of arithmatic. The second Vol. is devoted to algebra, a science in which the ancient Hindus made remarkable progress.

Vol. I contains two chapters. Chapter I gives account of various devices employ- ed by the Hindus for denoting numbers. Chapter II deals with arithmatic in general.

Vol. II of this work devoted to the history of Algebra in India. The use of symbols-letters of the alphabet to denote unknowns-and equations are the founda- tion of thwe of the algebra. The Hindus were the first to make systematic use of the letters of the alphabet to denote un- knowns.

Little is known at present to historians of mathe- matics regarding the achievements of the early Hindu mathematicians and our indebtedness to them. Though generally admitted that the decimal place- it is now gen 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 carliest known times down to the seventeenth century of the Christian cra.

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 termino- logy 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.

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 se- quence 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.

**Contents and Sample Pages**