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पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३४०

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एतत् पृष्ठम् परिष्कृतम् अस्ति
144
GAŅITASĀRASAṄGRAHA.

(weight of all the) sticks, this is to be subtracted. What remains is (the quantity of) the prapūraņikā (that is, the quantity of the baser metal mixed).

An example in illustration thereof.

198-196. (Three) merchants, well acquainted with the varņa of gold, were desirous of making test sticks of gold, and produced (such) golden sticks. The gold of the first (merchant) was of 12 varņas; (that of tho second was of) 14 varņas; and that of the third was of 16 varņas. The (various specimens of the test sticks of) gold in the case of the first (merchant) were (regularly) less by 1 (in varņa); those of the second were less by and ; and those of tho third were (in regular order) lass by . (The specimens of test gold) possessed by the first (merchant) began with that of (his) maximum varņa, and ended with that of 1 varņa; (similarly, those of the second began with that of his maximum varņa and) ended with that of 2 varņas; and those of the third merchant (began with that of his maximum varņa and) ended with that of 3 varņas. Every test stick is 1 māșa in weight. O mathematician, if you indeed know gold calculation, tell me separately and soon what the measure of pure gold here is, and what that of the baser metal mixed.

The rule for arriving at (the different weights of) gold obtained in exchange and characterised by (two given) varņas:--

197.[*] The two differences between, (firstly,) the product of the (given weight of) gold to be exchanged as multiplied by the (given) varņa (thereof) and the product of the weight of gold obtained in exchange as multiplied by the (first of the two specified) varņas (of the exchanged gold)-(and, secondly, between the first product above-mentioned and the product of the weight of

 

 

197.^  This rule will be clear from the following working of the problem given in stanza 198:-

, and are altered in position and written down as 896 and 1120; and these, when divided by 12-10 or 2, give rise to the answers, namely, 448 and 560 in weight of gold of 10 and 12 varņas respectively.