Indian Antiquary Vol 17

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

Page 51

FEBRUARY, 1888.]
THE BAKHSHALI MANUSCRIPT.
45
Tell me now, how much was given by the first, Solution :-"the desired quantity is put in the and what is the amount of each gift.
empty place;" the desired quantity is l; this Statement:-A gives æ, B2, C3, D 4. Total is placed as the first number; then the succes200.
sive multiplications are made, 1, 2, 9, 48. Solution :-Having filled up the empty place Their addition gives the sum of the rates 60; (oro) with one, (we obtain) 1, 2, 3, 4 (as the with this the given total is divided, thus i several rates); by the application of the sum
the result is 5, and this is the possession of A. of the rates we obtain 20, 40, 60, 80, and thence
With this by multiplication the several rates the total 200.
are obtained, thus 5, 10, 45, 240. Thence the This is the statement of the proof :
total of the items is calculated to be 300. Init. term 20, increment 20, period 4.
(Next follows the fragment of a third examBy the rúpõna method the total is found to
ple which I omit. After this must have be 200.
followed a third modification of the same Sutra.
sútra, which is lost; but the first portion of (Only the first portion of this sútra is pre
it, as quoted in the examples, must have run served ; viz. "put into the empty place the
thus:number 1 representing the desired quantity,
The
Súnyastháné rúpan and then make up the series of items."
datvá, yutan chaina
gunan tataḥ purport of this rule will be understood from
1.e., "having put the number one in the empty the following examples). First Example.
place, the (needful) additions and multiplica
tions are then made.") (Its purport is:-B gives 2 times as much as
Fourth Example. A, C gives 3 times as much as B, D gives 4
(Its purport is :--A possesses something and times as much as C. Their total gift is 132.
1 in addition; B has 2 times as much as A What is the gift of AP)
and 2) in addition ; C has 3 times as much as Statement :- A gives t, B2, C3, D 4.
B and 3) in addition ; D has 4 times as much Total 132.
as C and 45 in addition. Their total possesSolution :-"Put 1 in the place of 2; then
sions are one hundred and forty-four and one form the series of items" 1, 2, 3 X 2, 4 X 6,
half. What is the possession of A?). multiplying these several rates, 1, 2, 6, 24,
Statement :-A has + 1}, B 2 + 25, their total is 33 ; with it divide the given
C 3+ 3, D + 41. Total 144. total, thus 18; the resulting item is 4, and
Solution :-"Having put one in the empty this is the gift of A. Hence the series of
the series of place," thus 1+1:"the several additions gifts is as follows :-4, 8, 24, 96, and the total and multiplications are then made:" in making gift is 132. This is calculated from the series
the additions and multiplications, let the proper of items, and hence the total of the items is order of calculation be observed, (hence by one hundred and thirty-two.
addition) ; next comes multiplication; (here) (Here follows what appears to be intended
multiply numerator with numerator and denoas a modification of the same sútra, since it is not specialised as a separate sútra. What
minator with denominator, i.e. i X); two remains of it, runs thus :-“the number 1 is put and one half are now added, thus : now comes into the empty place, and then (the items) are the multiplication with the third number, or successively multiplied." The purport of the three(is multiplied) with seven and one half (i.e. rule will be again understood from the example.)
15 = 7), thus ; three and one half are Second Example. (Its purport is :-B possesses 2 times as much now added, thus ; now multiply the number as A; C bas 3 times as much as A and B four with twenty-six (i.e. -26); the result together; D has 4 times as much as A, B and
is 20$; four and one half are now added, thus C together. Their total possessions are 300. What is the possession of A?)
317. The total of these rates is which is Statement :-A has a, B2, C3 X 3, D the given total of the possessions. All the rest 4 X 12. Total 300.
remains the same; (i.e. dividing the given