Posted on: 4 August 2012

Digital Rare Book:
On the Bakhshali Manuscript
By August Frederich Rudolf Hoernle
Published by Alfred Holder, Vienna - 1887

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Review: G. R. Kaye, The Bakhshâlî Manuscript— A Study in Mediaeval Mathematics
By Bibhutibhusan Datta

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Dr Hoernle's work above is the first/preliminary analysis of the manuscript, after its discovery in Bakhshali. He continued to work on it & just before his death, passed on his work-papers to G.R.Kaye, for further studies. In his work - ( The Bakhshali Manuscript - A Study of Medieval Mathematics - Published by ASI, Calcutta, 1927 ), Kaye states upfront that the above publication of Dr Hoernle is " an early estimate of the value of the work" and is " inadequate and misleading. One reason for this is, that when the estimate was made, only a comparitively small portion of the contents of the manuscript had been understood, and that was by no means the most interesting portion of the work. The following is a summary list of the contents of the work as far as its present state allows such analysis : Section A - Problems involving systems of linear equations; Section A & K - Indeterminate equations of the second degree; B & C - Arithemtical progressions; C - Quadratic Equations; C - Approximate evaluations of Square Roots; F - Complex Series; G - Problems of the type x (1-a1) (1-a2)..(1-an)=p ; H - The computation of the fineness of gold; L,D & E - Problems of Income & Expenditure, and P&L ; M - Miscellaneous problems; Mensuration " ( Chapter IV - Contents of the Manuscript)....... This ASI book of 1927 has a complete fascimile of the manuscript along with Kaye's translation & interpretation. Of course Kaye's interpretations have subsequently been found to have several errors. However, the fascimile pages of the original parchments in sharda script ( very close to nagari script of today), make this Kaye book very useful for mathematicians/researchers who know sanskrit, nagari script & of course, the aryabhatta system of expressing numbers, today unfortunately taught only to scholars of hindu astrology. Without knowing how a combination of a consonant ( vargas (k,kh,g..etc) for even places & avargas (ya,r,la,v...) for odd places) and vowels (a,aa, e,ee...) generates the unified troika of a unique - sound,musical note (melakarta & its shortcut katapayadi) & number or "hindu numerical" , its not possible to read bakhshali manuscript , despite the ability to read sharda/nagari & the knowledge of sanskrit.

Review: G. R. Kaye, The Bakhshâlî Manuscript— A Study in Mediaeval Mathematics By Bibhutibhusan Datta

Thanks. Apt review by the brilliant Bibhutibhusan Datta. I was however trying to highlight the importance of knowing the ancient numerical system ( to read the Bakhshali manuscript or any treatise of sanskrit maths), whose importance is also highlighted in the first 3 chapters of Bibhutibhushan Datta & AN Singh's " The History of Hindu Maths" ( 2 Volumes). Alphabets doubled up as numbers in such a system. A simple & beautiful primer on the system was written by JF Fleet. I just have a hardcopy of it & cant find a free softcopy access on the web to share with you ( see - )