The Bakhshali Manuscript

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THE BAKHSHALI MANUSCRIPT AN ANCIENT TREATISE OF INDIAN ARITHME[TIC] EDITED BY Svami Satya Prakash SarasvatI and Dr. Usha Jyotishmati, M. Sc., D. Phil. PUBLISHED BY Dr. Ratn Kumari Svadhyaya Sansthana Vijnana Parishad Buildings Maharshi Dayanand Marg Allahabad-211002 Phone : 54413 FIRST EDITION 1979

Contents of the Manuscript

The portions of the manuscript that have been preserved are wholly concerned with mathematics. Dr. Hoernle described the work in 1888 in the following words :-

"The beginning and end of the manuscript being lost, both the name of the work and its author are unknown. The subject of the Contents of the Manuscript 4) work, however, is arithmetic. It contains it great variety of lun hlems relating to daily life. The following are examples :

(i) in a carriage, instead of 10 horses, there are yoked …the distance traversed by the former was one hundred; how much will the other horses be able to accomplish" ?

(ii) The following is more complicated :- 'A certain travels 5 yojanas on the first day, and 3 more on each succerding day ; another who travels 7 yojanas on each day, has it start of 5 days ; in what time will they meet ?'

(iii) The following is still more complicated :--'Of 3 merehnnln, the first possesses 7 horses, the second 9 ponies, the third 10 each of them gives away 3 animals to be equally distributed among themselves. The result is that the value of their respective properties become equal : how much was the value of each animal ?

"The method prescribed in the rules for the solution of these problems is extremely mechanical and reduces the labour of thinking to a minimum".

The following is a summary list of the contents of the work as far as its present state allows of such analysis :-

Problems involving systems of linear equations

Indeterminate equations of the second degree

Arithmetical progressions

Quadratic equations

Approximate evaluations of square-roots C

Complex series

Bakhshali manuscript

The computation of the fineness of gold

Problems of income and expenditure, and profit and loss

Miscellaneous problems

Mensuration

Such is a very rough outline of the work as it now stands.

Perhaps the most interesting sections are C, A and M; and of these C is the most complete and was evidently treated as of cosiderable importance. Section A is also of special interest as it contains examples which may be described as of the epanthcm type. Section M is of interest principally on account of the methods of expressing the numerous measures involved and also because of its literary and social references.