Ganitasara Sangraha

SR No.: 020800
Original Sutra Author: N/A
Author: Mahaviracharya, M Rangacharya
Publisher: Government of Madras
Publication Year: 1912
Total Pages: 523
Language: Hindi, Sanskrit
Classification: Book_Devnagari
File Size: 22 MB

Page 378

CHAPTER VI--MIXED PROBLEMS.
181
by one (respectively), corresponding to the even (value) which is halved, and the uneven (value from which one is subtracted, till by continuing these processes sero is ultimately reached. The numbers in the chain of figures so obtained are) all doubled, (and then in the process of continued multiplication from the bottom to the top of the chain, those figures which come to have a xiro above them) are squared. The resulting product (of this continuell multiplication gives the number (of the varieties of stanzas possible in that syllabic metre or chandas).
The arrangement of short and long syllables in all the varieties of stanzas 80 obtained) is shown to be arrived at thus:-- (The natural numbers commencing with one and ending with the measure of the maximum number of possible stanzas in the given metre being noted down), every odd number (therein) has one added to it, and is (then) halved. (Whenever this process is gone through), a long syllable is decidedly indicated. Where
again odd, denotes a third long syllable. Thus the first variety consists of three long syllables, and is indicated
thug . 2nd variety : 2, beiny even, indicates a short syllable; when this 2 is
divided by 2, the quotient is 1, which being udd indicates a long syllable. Add 1 to this l, and divide the sum by 2; the quotient being odd indicates a long syllable; thus we
get 117. Similarly the other six varieties are to be found ont. (3) The fifth variety, for instance, may be found out as above.
(4) To find out, for instance, the ordinal position of the variety, 171 we proceed thus :Below these syllables, write down the terms of a series in geometrical pro
gression, having l as the first term and 2 as the common ratio. Add the 1 figures 4 and 1 ander the the short syllables, and increase the sum by l; 1 2 4 we get 6: and we, therefore, say that this is the sixth variety in the
tri-syllabio metre. 15) Suppose the problem is : How many varieties contain 2 short syllables? Write down the natural numbers in the regular and in the inverse order, one
1 2 3 below the other thus:
8: 32 1 Takmg two te
Taking two terms from right to left, both from above and from below, we divide the product of the former by the product of the latter. And the quotient 3 is the answer required.
(6) It is prescribed that the symbols representing the long and short syllables of any variety of metre should occupy an angula of vertical space, and that the intervening space between any two varieties should also be an angula. The amount, therefore, of vertical space required for the 8 varieties of this metre is 2 x 8-1 or 15 augulas.