Sambodhi 2000 Vol 23

Author(s): Jitendra B Shah, N M Kansara
Publisher: L D Indology Ahmedabad

Page 30

Vol. XXIII, 2000
VEDIC SOURCES OF THE "VEDIC MATHEMATICS
VM Terminology vis-a-vis that of the Medieval Mathematicians :
The medieval mathematicians like Aryabhata I (A.D. 476), Brahmagupta (A.D. 598), Bhāskara I (A.D. 600), Mahāvīrācārya (A.D. 850), Aryabhata II (A.D. 950), Śrīdharācārya (A.D. 991), Śrīpati (A.D. 1000), Bhāskara II (A.D. 1114), Nārāyana (A.D. 1350), and their commentators, have composed works like the Aryabhatiya, Brāhmasphuta-siddhānta, Mahābhāskariya and Laghubhāskariya, Ganita-sāra-samgraha, Mahāsiddhānta, Patiganita and Trisatikā, Ganita-tilaka, Siddhāntasiromani along with Lilāvati and Bijaganita, and Ganitakaumudi, respectively. In these works they have utilized various technical terms for indicating various mathematical operations. Some of these terms they might have inherited traditionally, while some they might have newly coined.
The most important of the Hindu numberal notations is the decimal placevalue notation. In this system there are only ten symbols, those called anka (= mark) for the numbers one to nine, and the zero symbol, ordinarily called śünya (= empty).54 There is further a system called Katapayādi in which the consonants of the Sanskrit aplhabet have been used in the place of the numbers 1 to 9 and zero to express numbers; the conjoint vowels used in the formation have no numerical significance. It gives brief chronograms, which are generally pleasant sounding words. Scholars and scientists have tried to bring out astonishing data of scientific value from the application of this system to various Vedic texts.55 BKTM has treated this topic in one full chapter in his VM.56 The Hindu name for addition is Saṁkalita, with other equivalent terms like Sarnkalana, Misrana, Sammelana, Prakṣepana, Ekikarana, Yukti, Yoga and Abhyāsa. The word Samkalita has been used by some writers in the general sense of a series. 56 The terms Vyutkalita, Vyutkalana, Sodhana, Pātana, Viyoga, etc., have been used for subtraction, while Sesa, Antara denote the remainder. The minuend is called Sarvadhana of Viyojya and the subtrahend Viyojaka 57 The common Hindu name for multiplication is Gunana, which appears to be the oldest as it occurs in the Vedic literature. The terms Hanana, Vedha, Ksaya, etc. are also used for multiplication. The multiplicator is Gunya, multiplier is Gunaka or Gunakāra, and product is Gunana-phala or Pratyutpanna.59
Division seems to have been regarded as the inverse of multiplication; and the common Hindu names for the operation are Bhāgahāra, Bhājana, Harana,