History of Hindu Mathematics: A Source Book v2.c13: Preface
History of Hindu Mathematics: A Source Book v2.c13
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Preface
v2.c13.1
The present work forms Part II of our History of Hindu Mathematics and is devoted to the history of Algebra in India. It is intended to be a source book, and the subject is treated topicwise. Under each topic are collected together and set forth in chronological order translations of relevant Sanskrit texts as found in the Hindu mathematical works. This plan necessitates a certain amount of repetition. But it shows to the reader at a glance the improvements made from century to century
v2.c13.2
To gather materials for the book we have examined all the published mathematical treatises of the Hindus as well as most of the important manuscripts available in Indian libraries, a list of the most important of which has already been included in Part I. We have great pleasure in once more expressing our thanks to the authorities of the libraries at Madras, Bangalore, Trivandrum, Tripunithura, Baroda, Jammu, and Benares, and those of the India Office (London) and the Asiatic Society of Bengal for supplying transcripts of manuscripts or sending them to us 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.
v2.c13.3
In translating Sanskrit texts we have tried to be as literal and faithful as possible without sacrificing the spirit of the original, in order to preserve which we have at a few places used literal translations of Sanskrit technical terms instead of modern terminology. For instance, we have used the term 'pulveriser' for the equation *ax*+*by*=1, and the term 'Square-nature' for the equation *Nx*²+*c*=*y*².
v2.c13.4
The use of symbols—letters of the alphabet to denote unknowns—and equations are the foundations of the science of algebra. The Hindus were the first to make systematic use of the letters of the alphabet to denote unknowns. They were also the first to classify and make a detailed study of equations. Thus they may be said to have given birth to the modern science of algebra.
v2.c13.5
A portion of the subject matter of this book has been available to scholars through papers by various authors and through Colebrooke's *Algebra with Arithmetic and Mensuration from the Sanscrit of Brahmegupta and Bhascara*, but about half of it is being presented here for the first time. For want of space it has not been possible to give a detailed comparison of the Hindu achievements in Algebra with those of other nations. For this the reader is referred to the general works on the history of mathematics by Cantor, Smith, and Tropfke, to Dixon's *History of the Theory of Numbers* and to Neugebauer's *Mathematische Keilschrift-Texte*. A study of this book along with the above standard works will reveal to the reader the remarkable progress in algebra made by the Hindus at an early date. It will also show that we are indebted to the Hindus for the technique and the fundamental results of algebra just as we owe to them the place-value notation and the elements of our arithmetic.
v2.c13.6
We have pleasure in expressing our thanks to Mr. T. N. Singh and Mr. Ahmad Ali for help in correcting proofs and to Mr. R. D. Misra for preparing the index to this volume.
v2.c13.7
<pre> LUCKNOW BIBHUTIBHUSAN DATTA *March, 1938* AVADHESH NARAYAN SINGH </pre>