ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

MULTIPLICATION 157
19. Ekādaśa-rāśikam (the rule of eleven)
20. Bhāṇḍa-pratibhāṇḍam (barter and exchange)
(B) Vyavahāra or determinations

1. Miśrakaḥ (mixture)
2. Śreḍhī (progession or series)
3. Kṣetram (plane figures)
4. Khātam (excavation)
5. Citiḥ (stock)
6. . Krākacikaḥ (saw)
7. Rāśiḥ (mound)
8. Chāyā (shadow)
   Of the operations enlisted here, the first eight have been
   considered fundamental by later writers as Mahāvīra. The opera-
   tions of duplation and mediation (doubling and halving) were
   considered fundamental by Arabs, Greeks and Egyptians; since
   they were not familiar with the place-value system.
   Mathematics in this country developed as an aid to astro-
   nomy, and therefore, for the first time we find Āryabhaṭa(499AD.)
   in his Āryabhaṭīya describing as a special section (Gaṇitapāda).
   Brahmagupta (628 A.D.) also followed Āryabhaṭa in this respect
   and gave the science of calculation (gaṇita) a special place in his
   treatise on astronomy. The Siddhānta treatises, earlier than those
   of Āryabhaṭa and Brahmagupta do not contain a chapter exclu-
   sively devoted to gaṇita (the Sūrya-Siddhānta and the Siddhāntas
   of Vasiṣṭha, Pitāmaha and Romaka are thus without gaṇita
   chapetrs). Later on Bhāskara I and Lalla also did not include
   gaṇita as a section or chapter in their treatises. It is said, howe-
   ver, that Lalla wrote a separate treatise on Pāṭīgaṇita.
   It may further be remarked here that Āryabhaṭa I gives
   the rules for finding the square and cube-roots only whilst Bra-
   hmagupta gives the cube-root rule only (BrSPSi. XII. 7).
   Multiplication
   Undoubtedly the common Indian name ‘multiplication’ is
   ‘guṇana’, this term occurs in the Vedic literature also. The other
   terms for this logistics are hanana, vadha, kṣaya etc., which all
   mean ‘killing’ or ‘destroying.’ The synonyms of ‘hanana’ (killing)
   for multiplication have been used by Āryabhaṭa I (499). Brahma-
   gupta (628), Śrīdhara (c.750) and later writers, and these terms