The Bakhshali Manuscript

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Bakhshali manuscript2

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Svami Satya Prakash SarasvatI
Dr. Usha Jyotishmati, M. Sc., D. Phil.

Dr. Ratn Kumari Svadhyaya Sansthana
Vijnana Parishad Buildings
Maharshi Dayanand Marg
Phone : 54413



Chajakputra -The Scribe

While we pay homage to the unknown author of a text w came to be known as the Bakhshali Manuscript, we should express our gratitude to another person of unknown name who scribed the manuscript from a text quite lost to us, and not only that, since that scribe was himself a mathematician of no less repute, being known as a prince amongst calculators, he added illustrations and often added something to the running commentary of this Text. Though we have no independent source to corroborate, it is definite that a Text existed as early as the second or third century A. D. [i.e. a century before the UK scholars’s estimate of 3/4th century] if not earlier; this text was traditionally used by the lovers of calculations (teachers and taughts) in some parts of the country (specially the north-western parts of the Aryavartta), and as it was handed down to us generation after generation, new worked and unworked problems were added to the existing material. At the end of the manu script (or somewhere on Folio 50, recto) we find a colophon mentioning that the work was scribed by a certain Brahmana, a prince of calculators the son of Chajaka [Indpaedia: Chhajak]. Thus we know the name of the father of the scribe only. I would like to call the scribe of the present manuscript himself as Chajaka-Putra, the son of Chajaka. He himself is not an author of the Text; he merely copies it out from some other text already current. Even if the date of copying this text were so late as the tenth or eleventh century and even if some illustrations included in the manuscript were not of at very early origin, the Bakhshali Text has its great importance, this being one of the earliest Texts in history available to us on the science of calculations.

How the Text was Found

In 1881, a mathematical work written on birchbark was found at Bakhshali near Mardan on the north-west frontier of India. This manuscript was supposed to be of great age and its discovery aroused considerable interest. Part of it was examined by Dr. Hoernle, who published a short account of it in 1883, and a fuller account in 1886, which together with the translation of a few of the leaves was republished in 1888. Dr. Hoernle had intended, in due course, to publish a complete edition of the Text, but was unable to do so. The work was later on printed and published in 1927, under the title The Bakhshali Manuscript, Part I and 11, by the Government of India with photographic facsimiles and transliteration of the Text together with a very comprehensive introduction by G. R. Kaye. This was followed by the publication of the Bakhshali Manuscript, Part 111, in 1933 as the Text Rearranged shortly after Kaye's death. Dr. Bibhutibhushan Datta, a distinguished worker in the field of Indian mathematics, also published a critical review on the Bakhshali Manuscripts.

Bakhshali (or Bakhshalai, as it was written in the official maps) is a village of the Yusufzai subdivision of the district of Peshawar of the North-Western Frontier of India ( now Khyber Pakhtunkhwa in Pakistan ). It is situated on, or near, the river Mukham, which eventually joins the Kabul river near Nowshers [sic], some twenty miles further south. Six miles W. N. W. of Bakhshali is Jamalgarhi, twelve miles to the West of Takht-i-Bhai and twenty miles W. S. W. is Charsada [Charsadda], famous for their Indo-Greek art treasures.

Bakhshali is about 150 miles from Kabul, 160 from Srinagar, 50 from Peshawar, 350 from Balkh and 70 from Taxila. It is in the Trans-Indus country and in ancient times was within Persian boundaries -in the Arachosian satrapy of the Achaemenid kings. It is within that part of the country to which the name Gandhara has been given, and was subject to those western influences which are so bountifully illustrated in the so-called Gandhara art. I The authentic record of the discovery of the manuscript appears to be contained in the following letter dated the 5th of July, [illegible: 1881?] from the Assistant Commissioner at Mardan.

"In reply to your No. 1306. dated 20th ultimo, and its enclosures, I have the honour to inform you that the remains of the papyrus MS. referred to were brought to me by the lnspector of police. Mian An-Wan-Udin [sic: Anwar?]. The finder, a tenant of the latter, said he had found the manuscript while digging in a ruined stone enclosure on one of the mounds near Bakhshali. These mounds lie on the west side of the Mardan and Bakhshtlli roads and are evidently the remains of a former village. Close to the same spot the man found a triangular-shaped 'diva', a soap-stone pencil, and it large Iota of baked clay with a perforated bottom. I had it further search made but nothing else was found.

"According to the finder's statement the greater part of the Manuscript had been destroyed in taking it up from the place where It lay between stones. The remains when brought to me were like dry tinder, and there may be about fifty pages left some of which Would be certainly legible to anyone who knew the characters, The letters on some of the pages are very clear and look like some kind of Prakrita, but it is most difficult to separate the pages without injuring them. I had intended to forward the manuscript to the Lahore Museum in the hope that it might be sent on thence to soMe Scholar, but I was unable to have a proper tin box made for it before I left Mardan. I will see to this on my return from leave. The papyrus will require very tender manipulation. The result will be interesting if it enables us to judge the age of the ruins where the manuscript was found."

In the meantime notices of the discovery had found their way into the Indian newspapers. Professor Buhler, who had read of the discovery in the "Bombay Gazette,' communicated the announcement to Professor Weber, who brought it to the notice of the Fifth International Congress of Orientalists then assembled in Berlin. In Professor Buhler's letter to Prof. Weber it was stated that the manuscript had been found "carefully enclosed in a stone chamber" and it was thought that the newly discovered manuscript might prove to be "one of the Tripitakas which Kaniska ordered to be deposited in Stupas".

Kaye, however, says that there is nothing whatever in the record of the find to justify Buhler's statement, which seems to have originated in a rather strange interpretation of the words "while digging in a stone enclosure" that occur in the letter quoted above, and which are themselves of doubtful reliability.

The manuscript was subsequently sent to the Lieutenent-Governor of the Punjab, who, on the advice of General Cunningham, directed it to be transmitted to Dr. Hoernle, then head of the Calcutta Madrasa, for examination and publication. In 1882, Dr. Hoernle gave a short description of the manuscript before the Asiatic Society of Bengal, and this description was published in the Indian Antiquary of 1883. At the Seventh Oriental Conference, held at Vienna in 1886, he gave a fuller account which was published in the proceedings of the Conference, and also with some additions, in the Indian Antiquary of 1888. In 1902 Dr. Hoernle presented the manuscript to the Bodleian Library.

The Script

Old Indian scripts

The Bakhshali text is written in the Sarada script, which flourished on the north-west borders of India from about the Ninth Century until within recent times. Its distribution in space is fairly definitely limited to a comparatively small area lying between longitudes 72 and 78 east of Greenwich and latitudes 32 and 36 north Dr. Vogel distinguishes between Sarada proper, of which the latest examples are of the early Thirteenth Century, and modern Sarada.

The writing of the Bakhshali manuscript is of the earlier period and is generally very good writing indeed, It was written by at least two scribes. Kaye gives a detailed account of it, and has classified the writing styles also (a and B as he denotes them). Style a is divided into four sub-sections which possibly belong to the work of four separate scribes, although it is not easy to point out any fundamental differences between these styles. Folio 65 possibly exhibits the writings of two separate scribes on the two sides, which do not belong to the same original leaf.

The style b is distinguished by its boldness by tails" or flourishes (including very long virama marks), the methods of writing mediale, ai and o, the looped six, etc , etc.

A particular section, which Kaye calls as M, has no example of ai and contains practically all the examples of "o". Sections 1 and G show marked differences in the methods of writing e, while section F is, in this matter, very much like section L. Section C has no example of either the JIHVAMULIYA or UPADHMANIYA, and so on; but it must be borne in mind that these statistics are only of value in the mass.

The Language

The language of the text may be described as an irregular Sanskrit. Nearly all the words used are Sanskrit, and the rules of Sanskrit grammar and prosody are followed with some laxity, The peculiarities of spelling, sandhi, grammar, etc, that occur in the text are exceedingly common in the inscriptions of the Eleventh and Twelfth Centuries found in the north-west of India. Dr. Hoernle however, implies that the language is much older. He states that the text "is written in the socalled Gatha dialect, or in thty literary form the North-Western Prakrita which preceded the employment, in secular composition, of the classical Sanskrit". He also states that this dialect "appears to have been in general use, in North-Western India, for literary purposes, till about the end of the Third Century A. D".

Order and Arrangement of Folios

The Bodleian Library order of the folios, which was definitely fixed by circumstances not within the control of the editor has necessarily been followed by Kaye in his edition, in the arrangement of the facsimiles and the first transliteration of the text (Part I and Part II). The whole material was rearranged in the posthumous publication : The Bakhshali Manuscript, Part Ill.

The leaves were disarranged to some extent before they reached Dr. Hoernle, but unfortunately he did not leave any proper record of the order in which the leaves reached him.

Dr. Hoernle attempted to arrange the leaves on the basis of the numbered sutras; but the numbered sutras were two few and too unevenly distributed to serve this purpose, and in some ways they were even misleading. The chief criterion of order is, of course, the nature of the contents of the leaves, but Kaye made an attempt to utilise all available criteria as help towards the solution of the problem of order. Had all the leaves been extant, even if fragments, the problem could have been completely solved; but some leaves are completely missing and many fragments have disappeared altogether, so that the problem could be only partially soluble Sometimes, even the knots in the birch-bark were of assistance, and besides this natural aid there was the accidental one of the effects of the method of storage. Possibly for some hundreds of years the bundle of leaves was subject to a certain amount of pressure, and was exposed particularly at the edges, to chemical and other disintegrating actions. Some of the leaves stuck together, the edges of all became frayed and certain leaves became so frail as to break up into scraps when handled. On the principle that contiguous leaves would be affected approximately to the same extent, we might, if no disintegrating effects had taken place since the find, rebuild in layers the original bundle. But we know that further disintegration has taken place; however, similarity in size and shape and mechanical makings were of distinct help in rearranging the leaves.

The Manuscript

The manuscript consists of some 70 leaves of birch bark, but some of these are mere scraps. The largest leaf measures about 5.75 by 3.5 inches or 14.5 by 8.9 centimetres. The leaves, which are numbered according to the Bodleian Library arrangement from I to 70, may be classified according to their size and condition as follows

In fair condition but broken at the edges-size, not less than 5 by 3 inches (13 by 8 cms.) …

One folio (19) is entirely blank.

Certain folios consist of two leaves stuck together, namely 7, 31 and 65, and possibly others. It would not be difficult to separate these double leaves without damaging the manuscript.

The leaves are now mounted between sheets of mica and placed within an album. The mica sheets arc about 7.4 by 4.6 inches and are fixed together by strips of gummed paper at the edges leaving it ulcer area of 6 1/8 by 3 ¾ inches,

Possibly the original strip of birchbark from which the leaves of Bakhshali manuscript were taken was roughly of the shape of the annexed diagram and was cut up into the oblongs indicated. If A, B, C, etc., represent the upper layer, and A', B', C', etc. the lower layer, then, according to the evidence of the leaves themselves, they were arranged for purposes of writing upon in the order A, A'; B, B'; C, C' ; etc., or A, A' D' ; etc.

Regarding the format of the Bakhshali manuscript (ratio 1.7) as a criterion of age, Kaye says that he could come to no positive conclusion from the evidence before him. Dr. Hoernle, however, writes as follows :-

"It is noteworthy that the two oldest (Indian paper) manuscript known to us point to their having been made in imitation of such a birch bark prototype as the Bakhshali manuscript."

Kaye, however, does not accept this argument, for it would be quite as reasonable to cocclude that the Bakhshali format was determined by the paper manuscript formats, and that it is of later date than the introduction into India of paper as a writing material; and this, according to Kaye, would place the Bakhshali manuscript about the twelfth century of our era at the earliest.


I. Apparently the manuscript was found in May 1881. General Cunnigham in a private letter to Dr. Hoernle, dated Simla, 5th (?) June, 1882, says : " Bakhshali is 4 miles north of Shahbazgarhi. It is a mound with the village on the top of it The birch-hark manuscript was found in it field near a well without trace of any building near the spot, which Is outside the mound vlllage.......".

3. Kaye has, however, expressed doubts regarding the authenticity of this account, for, he thinks. It was written apparently from memory, a month or so after the discovery of the manuscript

1. This accont appears in the Bombay Gazette of Wednesday, August 13th, 1881 and is as follows :

"The remains of a very ancient papyrus manuscript have been found near Bakhshali, in the Mardan Tahsil, Peshawar District. On the west side of the Mardan and Bakhshali road are some mounds, believed to be the remains of a former village, though nothing is known with any certainty regarding them, and it was while digging in a ruined stone enclosure on one of these mounds the discovery was made. A triangular-shaped stone 'Diwa', and a soap-stone pencil and a large lotah of baked clay, with a perforated bottom, were found at the same place. Much of the manuscript was destroyed by the ignorant finder in taking it up from the spot where it lay between the stones; and the remains are described as being like dry tinder, in some of the pages However, the character, which somewhat resembles 'prakrita' is clear. and it is hoped it may be deciphered when it reaches Lahore, whither we understand it is shortly to be sent".

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


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.

See also


The Bakhshali Manuscript

Indian numerals/ numbers

Zero, a history

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