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

50 DETERMINATIONS
Ex. 96. One-fourth, one-third, and one-sixth of a pillar
are respectively buried under the water, mud, and sand of a
river, and three cubits (of the pillar) are visible. Give out
the measure (of the length) of that (pillar).¹
Here the given fractions (of the pillar) are ¼, ⅓, and ⅙ ; and the
visible quantity (i.e., the visible part of the pillar) is equal to ‘ 3 cubits.’
Hence the length of the pillar
3
= ————————————————— , i.e., 12 cubits.
1 - (¼ + ⅓ + ⅙)
Ex. 97. After giving away one-half of a quantity, then
⅔ of what remains, then ¾ of what remains thereafter, and
then ⅘ of what remains thereafter, the residue left is 3.
(What is that quantity ?)²
Here the fractions (of the whole quantity) given away are
½, ⅔ of (1 - ½), ¾ of (1 - ½) (1 - ⅔) , and
⅘ of (1 - ½) (1 - ⅔) (1 - ¾) ,
i.e., ½, ⅓, ⅛, and ¹/₃₀ ;
and the visible quantity (i.e., the residue left) is 3 .
Hence the required quantity
3
= ——————————————————————— , i.e., 360 .
1 - (½ + ⅓ + ⅛ + ¹/₃₀)
Rule for solving problems involving differences (viśeṣoddeśaka):
74(ii). On subtracting the smaller quantity from the
greater quantity what remains is called the difference
(viśeṣa).³ (This having been done) the procedure (to be adop-
ted is the same as the other one (i.e., the previous one).⁴
Ex. 98. Of a herd of cows, one-half went away towards
the east and one-fourth towards the west, the difference of the

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¹ Cf. GSS, iv. 5; GT, p. 41, vs. 56. For other examples see GSS, iv.
6-22 ;GT, p. 42, vs. 57 ; L (ASS), pp 47-48, vs. 53; GK, I, p. 20, lines 4-7,
10-13, 16-19.
² For other examples, see GSS, iv. 29-30, 31, 32; GT, p. 44, lines
20-23 ; p. 45, lines 16-19; L (ASS), pp. 49-51, vs. 54.
³ Mahāvīra does not differentiate between bhāga-jāti and viśeṣa-jāti
(or viśleṣa-jāti)). So he sets problems on the latter under the bhāga-jāti.
See GSS, iv. Ex. 23-27.
⁴ Cf. GT, p. 46, lines 10-13.