पाटीगणित (श्रीधराचार्य - प्राचीन संस्कृत टीका एवं प्रो. कृपाशंकर शुक्ल सविस्तार व्याख्या)

INVERSE RULE OF THREE 25
(24) Inverse rule of three (vyasta-trairāśika)
Inverse rule of three :
44(ii). When there is change in the unit of measure-
ment, the middle quantity multiplied by the first quantity and
divided by the last quantity gives the result.¹
Ex. 34. When (a given quantity of pearls is) measured
at 8 pearls a necklace, the number of necklaces is twenty ;
say, mathematician, what the number of necklaces would be
(when the same quantity of pearls is measured) at 6 pearls a
necklace.²
Ex. 35. Being measured by the māṣa of 5 raktikās, a
quantity of gold amounts to 300 suvarṇas. Say how much
would that (quantity of gold) amount to, when measured by
the māṣa of 6 raktikās.³
Raktikā is the same as guñjā.
Ex. 36. How much gold of 11 varṇas can be had in
exchange for 168 suvarṇas of 16 varṇas ?⁴
Ex. 37. Quickly say how many blankets of length 6
(cubits) and breadth 2 (cubits) can be made out of (the yarn
which yields) 200 blankets of length 9 (cubits) and breadth
3 (cubits).⁵
Ex. 38. How much gold of 10½ varṇas will be obtained
in exchange for 100 suvarṇas and 8 māṣas (of gold) of
12½ varṇas ?⁶
(25-27) Rules of five, seven and nine (pañca-sapta-nava-rāśika)
Rule of five, seven, and nine :
45. After transposing the fruit from one side to the
other, and then having transposed the denominators (in like
¹ Cf. BrSpSi, xii. 11(i) ; MSi, xv, 25(ii). Also see L (ASS), p. 74,
vs. 77-78 ; GK, I, p. 49, vs. 61.
² The same example occurs in GT, p. 74, lines 8-9.
³ Cf. L (ASS), p. 76, vs. 81 ; GK, I, p. 50, lines 3-4, 7-8. A similar
example occurs in Bhāskara I's comm. on Ā, ii. 26-27(i).
⁴ Cf. GT, p. 74, vs. 96. Also Cf. GSS, v. 18 (i) ; vi. 173½, 174½;
L (ASS), p. 75, vs. 80. For the meaning of varṇa see infra p. 36.
⁵ Cf. GSS, v. 19. ⁶ Cf. GSS, v. 18(ii).