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

8 LOGISTICS
equal to the additive (kṣepa) ; when cipher is added to or
subtracted from a number, the number remains unchanged.
In multiplication and other operations on cipher, the result is
cipher. Multiplication (of a number) by cipher also yields
cipher.¹
That is, 0 + a = a,
a ± 0 = a,
0 × a or 0 ÷ a = 0,
a × 0 = 0.
(4) Division (bhāgahāra)
Rule for division :
22. Having removed the common factor, if any, from
the divisor and the dividend, divide (by the divisor the digits
of the dividend) one after another in the inverse order : this
is the method of division. ²
Âryabhaṭa II (c. 950 A.D.) gives more details of the process :
“Having placed the divisor underneath the (last digits) of the
dividend, subtract the proper multiple of the divisor from the (last digits
of the) dividend ; the multiple (thus obtained) is the (partial) quotient
Next having moved the divisor (one place to the right) divide what
remains. (Continue this process until all the digits of the dividend have
been taken).”³
(5) Squaring (varga)
Rule for squaring :
23. To obtain the square of a number (proceed suc-
cessively as follows) : Having squared the last digit (antya-
pada) (i.e., having written the square of the last digit over the
last digit), multiply the remaining digits by twice the last,
moving it from place to place (towards the right, and set down
the resulting products over the respective digits); then (rub
out the last digit and) move the remaining digits (one place
to the right).⁴
¹ Cf. GSS, i. 49 ; MSi, xv. 10(ii)-11(i) ; GK, I, p. 13, vs. 30.
² Cf. GSS, ii. 19 ; GT, p. 6, lines 21-24 ; L (ASS), I, vs. 18(ii) ;
GK, I, p. 5, vs. 16(ii).
³ MSi, xv. 4. Also see SiŚe, xiii. 3 ; L (ASS), I, vs. 18(i) ; GK, I,
p. 5, vs. 16(i).
⁴ Cf. GSS, ii. 31 ; GT, p. 7, lines 24-25 ; L (ASS) I, 19 ; GK, p. 6,
vs. 17.