Mathematics in Ancient and Medieval India c5.s7.52

c5.s7.52

We find here the use of word numerals with right to left order and symbolic numerals with a left to right order. The use of word numerals with left to right order has also been found in the *Mahāsiddhanta* of Āryabhaṭa II. These orders were so used for no obvious reason except possibly for emphasizing the idea that the decimal place-value concept remains unchanged in whatever order (right or left) the numerals are arranged when the number is always expressed by reading from higher to lower order in the scale. The symbolic use of zero is found to occur in the *Bakhshālī* Ms. (400 A. D.) of India as well as in number of inscriptions found at Sambor, Malay, Java, used in a decimal place-value system with their dates expressed in Śaka era of Indian origin. Some of these symbols including that of zero found in these inscriptions bear more or less close resemblance with those of the corresponding numbers in the *Bakhshālī* Ms. . The *Dinaya Sanskrit inscription* (see p. 72) found at Java (760 A. D.) however contained both word-numerals and the numeral symbols. This seems to suggest strongly a common origin of all these symbols obviously in India. Moreover, the evidence of the association of decimal scale e. g. *eka*, *daśa*, *śata* etc. with places is found in the works of Āryabhaṭa I (b. 476 A. D.) onwards. He writes that the value of the places are ten times of the preceding (*sthanāt-sthānaṃ daśaguṇaṃ syāt*, *Āryabhaṭīya*, Gaṇita, verse 2) in a numerical notation thereby expressing the idea of decimal place-value. That the decimal place-value concept was current before seventh century A.D., has also been attested by Vyāsa (before 700 A. D.) in his philosophical work, *Yogadarśanabhāṣya* (Ch 3, Sū. 13) thus : *yathaikā rekhā śatasthāne śataṃ daśasthāne daśa ekaṃ caikasthāne* i. e. "a (numerical) sign denotes hundred in the *śata* place, ten in the *daśa* place, and one in the *eka* place." The very similar language is used by Śaṅkarācārya (c. 800 A. D.) in his *bhāṣya* on *Vedānta Sūtra* (II. 2. 17). These illustrations establish without doubt that by the time of compositions of these two works, the decimal place-value concept must have been well established and was generally known. This system has appeared amongst the Arabs in the tenth century A. D. From there it went to Europe and it has now been adopted by all the civilised peoples of the world.