________________
46
THE INDIAN ANTIQUARY.
[FEBRUARY, 1888.
total by the sum of the rates *90 we obtain the manuscript, the number of the dots cor
responding to the number of missing syllables. 1 as the value of a, hence the possessions of
The serpentine lines indicate the fact of lines A, B, C, D are respectively, and ,
being lost at the top and bottom of the leaves of the same as the rates mentioned above).
the manuscript. In the translation the bracketed Fifth Example.
portions supply lost portions of the manuscript. (Its purport is :- A gives plus & certain The latter can, to a great extent, be restored amount; B gives plus 2 times as mnch as A; by a comparison of the several examples. C gives plus 3 times as much as A and B;
Occasionally words are added in brackets to
facilitate the understanding of the passage, D gives plus 4 times as much as A, B and C 2. Satra 18. Problems on progression. The total of their gifts is 222. What was the Two persons advance from the same point. At gift of A ?).
starting B has the advantage over A; but Statement :- A gives + B2 + C 3 afterwards A advances at a quicker rate than + ,D4+; the joint gift is 222.
B. Question :-when will they have made an Solution :-"Having put the number one in
equal distance ? In other words, that period of the empty place," 1 (form), the additions
the two progressions is to be found where and multiplications are made in their proper
their sums coincide. The first example is order. The result is the following series of
taken from the case of two persons travelling.
B makes 3 miles on the first day against 2 rates: 7,5%; the given total is 222.
miles of A; but A makes 3 miles more on each The addition of the rates yields 222, which is
succeeding day against B's 2 miles. The result the same as the given total 222. This practi
is that at the end of the third day they meet, cally finishes the solution.
after each has travelled 15 miles. For A tra(Next follows the fragment of the sixth
vels 2 + (2 + 3) + (2 + 3 + 3) = 15 miles, example, which I again omit).
and B 3+(3+2)+(3+2+2) = 15 miles. Seventh Example.
The second example is taken from the case of (Its purport is :-A has 1} plus a certain
two traders. At starting B has the advantage amount; B has 2 less than 2 times A; C has
of possessing 10 dináras against the 5 of A ; but 3 less than 3 times A; D has 4 less than
in the sequel A gains 6 diráras more on each 4 times A. Their total possessions are day against the 3 of B. The result is that What is the possession of A ?)
after 44 days, they possess an equal amount of (The statement is wanting).
dinaras, viz. 65. Solution :-"Having put the number one in 3. Satra 27. Problems on averages (samathe empty place," the addition is made; bhagata). Certain quantities of gold suffer loss twice the rate of A less five halves is three at different rates. Question :--what is the times the rate of A, less seven halves, is ;
average loss of the whole ? The first problem
is very concisely expressed; the question is four times the rate of A, less nine halves, is
understood; some words, like luto gatá, must The series of these rates is as follows: be supplied to samabháyatdit. The reading
4. The given total is . The sum of the rahita, however, is not certain. rates is 7. Dividing the one by the other,
4. Brahmagupta's version of the forty203 we obtain 1. Multiplying by this, the
ninth satra, referred to above,(MS., No.1, B, 6,
Library, As. Soc. Beng., p. 85) is as follows:same amount is obtained as the gift of A ; viz.
Idânim *). The same is the case with the negative
Yð rašir ishtôno vargô bhavati, sô ch'anyequantities, (ie. BIX [(2 x ) - ] = ishtay tô varga êva bhavati | similarly C D ).
Tat-karana-sútram NOTES
Yair ûnê yais cha yuto rûpair vargas tad1. In the text, the italicised words are con- aikyam ishta-hritam jecturally restored portions. The dots signify Ishtona tad-dala-kritir ûnabhyadhika bhathe syllabies (akshara) which are wanting in! vati raših :