Indian Antiquary Vol 17

Author(s): John Faithfull Fleet, Richard Carnac Temple
Publisher: Swati Publications

Page 49

FEBRUABY, 1888.]
THE BAKHSHALI MANUSCRIPT.
43
Statement :
Second Example. No. 1, init. term 5, increment 6, period 2, There are suvarnas numbering one, two possession a.
three, four. There are thrown out the followNo. 2, init. term 10, increment 3, period , ing mashakas; one-half, one-third, one-fourth, possession 2.
one-fifth. What is the average) wastage in Solution :-"Twice the difference of the two the whole mass of gold)? initial terms," etc.; the initial terms are 5 and Statement:10, their difference is 5. “By the difference of quantities of gold, 1, 2, 3, 4 suvarpa. the (two) increments;" the increments are 6 wastage
, , , $ mashaka. and 3; their difference is 3. The difference of Solution :-"Having multiplied severally the the initial terms 5, being doubled, is 10, and parts of gold with the wastage," the products divided by the difference of the increments 3, may thus be stated, -, , , “Let the 10 and augmented by one is 13. This i.e. total wastage be divided ;" the division being
directed to be made, the total wastage is or 4$) is the period; in that time the two persons become possessed of the same amount
; dividing" by the sum of the parts of of wealth.
gold;" here the sum of the parts of gold is 10 : Proof :--by the rúpôra method the sum of being divided by this, the result is a This is either progression is found to be 65 (i.e. each the wastage of each part of the whole mass of of the two persons earns 65 in 4 days). gold.
Proof may be made by the rule of three :27th satra.
as the sum of the parts of gold 10 is to the Now I shall discass the wastage (in the total wastage of 60 mashaka, so the sum of working) of gold, the rule about which is as
gold 4 is to the wastage of 16 mashaka, etc. follows:--
Third Example. Having multiplied severally the parts of
(The problem in words is only partially gold with the wastage, let the total wastage be divided by the sum of the parts of gold.
preserved, but from its statement in figures The result is the wastage of each part of the
and the subsequent explanation, its purport
may be thus restored) :whole mass) of gold.
Of gold mashakas numbering respectively First Example.
five, six, seven, eight, nine, ten, quantities Suvarnas numbering respectively one, two, three, four, are subject to a wastage of masha
numbering respectively four, five, six, seven, kas numbering respectively one, two, three,
eight, nine, are wasted. Of another metal
numbering in order two mashakas, etc. (ie., four, Irrespective of such wastage they suffer
two, three, four) also quantities numbering in an equal distribution of wastage. (What is
order one, etc. (i.e., one, two, three), are wasted. the latter?)
Mixing the gold with the alloy, 0 best of The statement is as follows:
arithmeticians ! tell me what is the average Wastage - 1, -2, -3, - 4 mashaka.
wastage of the whole mass of mixed gold) ? Gold 1, 2, 3, 4 suvarna.
Statement :Solution :-" Having multiplied severally
wastage: -4,-5,4-6, -7,-8,-9;-1,-2,-3. the parts of gold with the wastage," etc. ; by
gold : 5, 6, 7, 8, 9, 10; 2, 3, 4. multiplying with the wastage, the products 1, 4, 9, 16 are obtained ; "let the total wastage,"
(Solution) :-"Having multiplied severally
the parts of gold with the wastage," the proits sum is 30; the sum of the parts of gold is
ducts are 20, 30, 42, 56, 72, 90, 2, 6, 12; their sum 10; dividing with it, we obtain 3. (This is
is 330; the sum of the parts of gold is 45 : the wastage of each part, or the average wastage, of the whole mass of gold.)
dividing by this we obtain ; this is reduced (Proof by the rule of three is the follow by 15 (i.e.); the result is 7 leaving $ (i.e. ing) :-as the sum of gold 10 is to the total 7}); that is the wastage of each mashaka (of wastage of 30 mashakas, so the sum of gold 4 mixed gold). is to the wastage of 12 mashakas, etc.
Proof :-by the rule of three the total