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

80 DETERMINATIONS
Let the initial speeds, etc., of the two travellers be as follows :
Initial speed Acceleration No. of days elapsed since start
at the first at the second
meeting meeting
I v₁ f₁ n n+D
II v₂ f₂ n-d n-d+D
Then s, the distance travelled by the travellers at the first meeting,
and s₁, the distance travelled by them at the second meeting, are given by
s = n/2 [2v₁ + (n - 1) f₁] = (n - d)/2 [2v₂ + (n - d - 1) f₂], (1)
s₁ = (n + D)/2 [2v₁ + (n + D - 1) f₁] = (n - d + D)/2 [2v₂ + (n - d + D - 1) f₂]. (2)
Using (1), (2) can be written as
(n + D)/2 [2s/n + Df₁] = (n - d + D)/2 [2s/(n - d) + Df₂],
whence
D = ((s/(n - d) - s/n) - ½{n f₁ - (n - d) f₂}) / (½ (f₁ - f₂)) .
Ex. 112. After one man had travelled for 6 days with
some (unknown) initial speed (ādi) and acceleration (uttara),
another man went by the same track with (an unknown
initial speed and) acceleration 2 per day per day. Say how
will they meet each other two times (on the way).¹
Rule for finding the amount by which one gambler defeats
his opponent in a play with dice, when the moneys staked at
the successive casts of dice are in an arithmetic progression :
99-101. Diminish the first pada (i.e., the number of
casts of dice won in the beginning by either of the two
persons) by one ; (taking the remainder as the number
of terms) find the sum of the series whose first term (ādi)
and common difference (caya) are each one : this is the vṛddhi
(for the first pada). In regard to the other padas (i.e., the
number of casts of dice won subsequently), take the sum of
the preceding padas for the first term (prabhava), one for the

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¹ Cf. GK, I, p. 111, lines 4-7.