Mathematics in Ancient and Medieval India c5.s10: Numbers and Symbolism
Mathematics in Ancient and Medieval India c5.s10
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Numbers and Symbolism
c5.s10.1
Bhāskara I (600 A. D.) freely used integral and fractional numbers and their operations in his *Āryabhaṭīya-bhāṣya*. He has referred to in this work the names of mathematicians like Maskarī Pūrāṇa, Mudgala Patana and others. In his Āryabhaṭīya-bhāṣya², he has given ample illustrations of these operations as follows :
c5.s10.2
² Shukla, K. S. 'Hindu Mathematics in the seventh century as found in Bhāskara I's, commentary on the *Āryabhaṭīya*', *Gaṇita*, 22, No. 2, p. 61-63, 1971.
c5.s10.3
i) x ± (y/z) = ((xz ± y))/z
c5.s10.4
ii) x/y ± z/u = (xu ± yz)/yu
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iii) x/y × z/u = xz/yu
c5.s10.6
iv) x/y ÷ z/u = xu/yz $v) (x/y)² = (x²)/(y²)$ $vi) (x/y)³ = (x³)/(y³)$ $vii) √(x/y) = (√x)/(√y)$ $viii) [3]x/y = ([3]x)/([3]y)$
c5.s10.7
It is not clearly known to what extent he was indebted to these scholars since their works are lost.
c5.s10.8
Bhāskara I wrote integral numbers within square or circular cells and sometimes without use of any cells The numbers 4, 6 and 7 without circular are written in any one of the following forms.
c5.s10.10
The fractional numbers are sometimes enclosed within rectangular cells or brackets without sticking to any uniform pattern. Thus the number 4 ⅚ was written in any one of the following way.
c5.s10.12
The enclosures were perhaps meant to avoid confusion and mixing up of numbers with the written matter.