पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२८४

एतत् पृष्ठम् परिष्कृतम् अस्ति
88
GAŅIITASĀRASAŃGRAHA

thereof hows down, (to the bottom) a crystal-clear stream of water having 1 aṅgula for the diameter of its circular section, and the well becomes quite filled with water within. What is the height of the hill, and (what) the numerical value (of the liquid-measure) of water ?

17.[17]A king gave, on (the occasion of) the saṅkrāti, to 6 Brahmins, 2 daōṇas of kidney-bean, 9 kuḍabas of ghee, 6 drōṇas if ruce, 8 pairs of cloths, 6 cows with calves and 8 svarṇas. Give out quickly, O friend, what (the measure) is (of) the kidney-bean and the other things given by him (at that rate) to 336 Brahmins.

Here ends the (direct) rule-of-three .

Examples on rule-of-three as explained in the fourth pāda[*]
(of the rule given above)

18.[18]How much is the gold of 9 varṇas for 90 of pure gold, as also for 100 gold (Dharaṇas) along with a guṅjā thereof made up of gold of ${\displaystyle 10{\tfrac {1}{8}}}$varṇas?

19. There are 300 pieces of China silk of 6 hastas in breadth as well as in length; give out, O you who know the method of inverse proportion, how many pieces (of that same silk) there are (in them, each) measuring 5 by 3 hastas.

Here ends the inverse rule-of-three.

An example on inverse double rule-of-three.

20. Say how many pieces of that famous clothing, each measuring 2 hastas in breadth and 3 hastas in length, are to be found in 70(pieces) of China Silk, (each) measuring 5 hastas in breadth and 9 hastas in length.

An example on inverse treble rule-of-three.

21.Say how many images of Tirthaṅkaras, (each) measuring 2 by 6 by 1 hastas, there may be in a big gem, which is 4 hastas in breadth, 9 hastas in length and 8 hastas in height.

17.^ Saṇkranti is the passage of the sun from one zodiacal sign to another.

18.^  Pure gold is here taken to be of 16 varṇas,

^* The reference here is to the fourth quarter of the second stanya in this clhapter