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

MULTIPLICATION 7
to the residue left (after the extraction of the square root),
should be declared as the number of terms (of the subtrahend
series).
That is, m = integral part of √2[Sₙ - D] ,
where D ≡ Sₙ - Sₘ .
(3) Multiplication (pratyutpanna)
Four methods of multiplication :
18-19. Having placed the multiplicand (guṇya) below
the multiplier (guṇa-rāśi) as in the junction of two doors,
multiply successively in the inverse or direct order, moving
(the multiplier) each time. This process is known as kavāṭa-
sandhi ("the door-junction method").
When the multiplication ( pratyutpanna ) is performed by
keeping that (i.e., the multiplier) stationary, the process is
called tatstha (i.e., "multiplication at the same place") on that
account.¹
20. The process of multiplication called khaṇḍa (or
khaṇḍa-guṇana, "multiplication by parts") is of two varieties
(called rūpa-vibhāga and sthāna-vibhāga), depending on whether
the multiplicand or multiplier is broken up into two or more
parts whose sum or product is equal to it, or the digits stand-
ing in the different notational places (sthāna) of the multipli-
cand or multiplier are taken separately.
These are the four methods of multiplication.²
For details of these methods, see B. Datta and A. N. Singh, History
of Hindu Mathematics, Part I, pp. 136-143, and 146-149.
Ex. 3. Multiply 1296 by 21, 896 by 37, and 8065 by 60.
Operations with cipher :
21. When something is added to cipher, the sum is

---

¹ See Siṁhatilaka Sūri's comm. on Śrīpati's Gaṇita tilaka, Rule 15-
16(i). The tatstha method of multiplication has been called tatsthāna-guṇana
by Gaṇeśa See L (ASS), p. 17.
² Cf. GSS, ii. 1 ; GT, pp. 4-5, vv. 15-16(i). Also see MSi, xv. 3 ;
SiŚe, xiii. 2 ; GK, I, p. 4, vv. 13-14.