________________
OCTOBER, 1888.]
THE BAKHSHALI MANUSCRIPT.
277
Eleventh Example.
the difference 40 is multiplied, giving or (This example is too fragmentary to be | 80; hence the original quantity was 30, and the translated. Its purport may be inferred from final amount is 70). the solution to have been somewhat as follows:
Thirteenth Example. -Of a certain quantity of goods, a merchant
Of an unknown quantity of lapis lazuli, onehas to pay, as duty, one-third, one-fourth and
third, one-fourth and one-fifth go in loss; the one-fifth on three successive occasions. The
(total) loss of the quantity, accruing in three total amount of duty he thas pays is 24. What was the original quantity of his goods P)
instalmente, is found to be twenty-seven. Say,
O wise man, what is the total, and let me also (The statement is partially wanting, but the
be told the difference between the total and whole of it may be easily restored thus :
the loss, ie, the remainder)? is the series of rates); the total duty taken is 24.
Statement: are the rates of loss; the Solution :-" Having subtracted the series
(total) loss is 27. from one" we get ,,; these multiplied alto
Solution :-" Having subtracted the series gether give; that again, subtracted from one, from one," we get , , , which being malgives; with this, after having been divided, tiplied give; subtracting this from one, we (i.e. inverted, ;), the total daty (24) is multi
get, by this the low is divided; the loss is plied, giving 40 ; that is the original quantity.
27; dividing this by it, we get 45; out of this
the loss is twenty-seven; hence the difference Proof: multiplied with 40 gives 16 as the
(or remainder) is 18. (ultimate) remainder; (to this add the total
Fourteenth Example. duty) 24; hence (the original quantity is) 40. Another proof of it : 40 multiplied with 1-5
Of waste iron there are three instalmente, of
which one-fifth is the last rate." The original and 1 and 1 - ) gives the result 16 (or in nota
amount is not known, nor is the wastage detion): 40 x [(1-1)×(1-1) * (1- -16); clared; but the remainder of the original the deduction is 24 ; hence (the total is) 40. amount is only twenty. Now let the original Twelfth Example.
amount be shown, and tell me what shall be
the wastage. [I cannot venture to translate the example,
Statement is the series of rates of as it is only preserved in a fragmentary state,
Wastago): and all the rest that might have explained it
(The solution and proof are wanting ; but statement, solution and proof-is entirely lost.
after the analogy of those of the preceding The following does not pretend to be more than
examples, the solution would run thus :- Sub* guese at ite parport :- A merchant possesses & quantity of molasses of a certain weight; he
tracting the series from one,' we get , ; makes, on four successive occasions, additions multiplying these, we get dividing with thereto of one-third, one-fourth, one-fifth and this the remainder 20, we get 50 as the origione-sixth; the difference (between these addi- nal amount; hence the wastage is 30). tions and the original quantity) is forty. What
54th Sætrs. was the original quantity, and what is the final total amount ?
*With the sale the purchase should be Solution :-One added severally to
divided; then divide it again (after being)
dinvinished by one; thes multiply it with the à gives , i these instalmente multi
profit; (the result) is then the capital plied together give; subtracting 1 from
Example. we get § ; with divided (or inverted, i.e. ) One who purchases seven for two, sells six
13 This, as the oontext and statement shows, is undoubtedly the meaning of the word whioh in the MS.is written parhchamasakan, and which qualifies tridhantar. The former word seems to be mis-spelling for parcha.
mdmdakah.. parchama nadash Satan) 'baving one-Afth M. (Anal) part. But it may be also suggested to be an orror for pail chamantalah, having one-Afth wita Apal (rate).'
