पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३७८

विकिस्रोतः तः
Jump to navigation Jump to search
एतत् पृष्ठम् परिष्कृतम् अस्ति
184
GAṆITASĀRASAṄGRAHA.

the number is even, it is (immediately) halved and this indicates a short syllable. In this manner, the process (of halving with or without the addition of one as tho onse may be, noting down at the same time the corresponding long and short syllables as indicated), is to be regularly carried on (till the actual number of syllables in the metre is arrived at in each case).

(If the number representing in the natural order any given variety of a stanza), the arrangement of the syllables wherein has to be found out, (happens to be even, it) has to be halved, and indicated a short syllable. (If it happens to be however odd), one has to be added to it, and (then) it is to be halved: and this indicates a long syllable. Thus (the long and short syllables have to be put down over and over again (in their respective positions) till the maximum number of syllables in the stanza is arrived at. This gives the arrangement (of long and short syllables in the required variety of the stanza).

Where (a stanza of a particular variety is given, and) its ordinal position (among the varioties of stanzans possible in the metre) is to be found out, the terms (of a series in geometrical progression) commencing with one and having two as the as the conmmon ratio are written dowm, (the number of terms in the series being equal to the number of syllables in the given metre. Above those terms, the corresponding long or short syllables are noted down). Then the terms (immediately) below the position of short syllables are all added; the sum (so obtained) is increased by one. (This gives the required ordinal number.)

Natural numbers commencing with one, and going up to the number (of syllables in the given metre), are written down in the regular and in the inverse (order in two rows) one below the other When the numbers in the row are multiplied (1, 2, 3 or more at a time) from the right to the left, and the products (so obtained in relation to the upper row) are divided by the (corresponding) products (in relation to tho lower row), the quotient represents the result of the operation intended to arrive at (the number of varieties of stanzas in the given metre, with 1, 2, 3 or more) short or long syllables (in the verse)