पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३७६

180

GAŅITASĀRASAŃGRAHA.

Examples in illustration thereof.

331${\tfrac {1}{2}}$${\tfrac {1}{2}}$. There is constructed an equilateral quadrilateral structure consisting of 5 layers. The topmost layer is made up of 1 brick. O you who know the calculation of mixed problems, tell me how many bricks there are (here in all).

332${\tfrac {1}{2}}$. There is a structure built up of successive layers of bricks, which is in the form of the nandyāvarta. There are 4 layers built symmetrically with 60 (as the numerical measure of the top‑bricks in single row). Tell me how many are all the bricks (here).

Rules regarding the six things to be known in the science of prosody:-

333-336${\tfrac {1}{2}}$. (The number of syllables in a given syllabic metre or chandas is caused to be markel in a separate column) by zero and

 

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332${\tfrac {1}{2}}$. The nandyāvarta figure referred to in the stanza is 卐;

333${\tfrac {1}{2}}$-336${\tfrac {1}{2}}$. As each syllable found in a line forming a quarter of a stanza may be short or long, there arises a number of varieties corresponding to the different arrangements of long and short syllables. In arranging these varieties, a certain order is followed. The rules given here enable us to find out (1) the number of varieties possible in a metre consisting of a specified number of syllables, (2) the number of arrangement of the syllables in these varieties, (3) the arrangement of the syllables in a variety specified by its ordinal position (4) the or ordinal position of a specified arrangement of syllables, (5) the number of varieties containing a specified number of long or short syllables, and (6) the amount of vertical space required for exhibiting the varieties of a particular metre.

The rules will become clear from the following working of the problems given in stanza 337${\tfrac {1}{2}}$.:-

(1) There are 3 syllable in a metre; now we proceed thus:

	3 - 1		1
2	2		0
	1 - 1		1
	0

Now, multiplying by 2 the figures in the right-hand chain, we obtain ${\begin{aligned}2\\0\\2\end{aligned}}$. By the process of multiplication and squaring, as explained in the note to stanza 94, Ch. II, we get 8; and this is the number of varieties.

(2) The manner of arrangement of the syllable each variety is arrived at thus:-

1st variety: 1. being odd, denotes a long syllable; so the first syllable is long. Add 1 to this 1, and divide the sum by 2; the quotient is old. and denotes another long syllable. Again, 1 is added to this quotient 1, and divided by 2; the result.