Place Values Of Digits in Līlāvatī
Introduction
Here we will know the names used to denote the place value of digits as mentioned in Līlāvatī.
Verse 11 & 12
एकदशशतसहस्रायुतलक्षप्रयुतकोटयः क्रमशः ।
अर्बुदमब्जं खर्वनिखर्वमहापद्मशंकवस्तस्मात् ॥ ११ ॥
जलधिश्चान्त्यं मध्यं परार्धमिति दशगुणोत्तरं संज्ञा: ।
संख्यायाः स्थानानां व्यवहारार्थं कृताः पूर्वैः ॥ १२ ॥
Translation
For the purposes (of convenient representation of numbers) the predecessors (in the field of mathematics) defined (made or coined) for mathematical operations the following terms of the places of numbers in that order : eka , daśa , śata , sahasra , ayuta , lakṣa , prayuta , koṭi , arbuda , abja , kharva , nikharva , mahāpadma , śaṅku , jaladhi , antya , madhya , parārdha , each succeeding (term) being ten times (of the preceeding one).[1]
| Name | Indian Notation | Power
Notation |
|---|---|---|
| एक (eka) | 1 | 100 |
| दश (daśa) | 10 eka | 101 |
| शत (śata) | 10 daśa | 102 |
| सहस्र (sahasra) | 10 śata | 103 |
| अयुत (ayuta) | 10 sahasra | 104 |
| लक्ष (lakṣa) | 10 ayuta | 105 |
| प्रयुत (prayuta) | 10 lakṣa | 106 |
| कोटि (koṭi) | 10 prayuta | 107 |
| अर्बुद (arbuda) | 10 koṭi | 108 |
| अब्ज (abja) | 10 arbuda | 109 |
| खर्व (kharva) | 10 abja | 1010 |
| निखर्व (nikharva) | 10 kharva | 1011 |
| महापद्म (mahāpadma) | 10 nikharva | 1012 |
| शङ्कु (śaṅku) | 10 mahāpadma | 1013 |
| जलधि (jaladhi) | 10 śaṅku | 1014 |
| अन्त्य (antya) | 10 jaladhi | 1015 |
| मध्य (madhya) | 10 antya | 1016 |
| परार्ध (parārdha) | 10 madhya | 1017 |
Comment
Indian mathematicians discovered the decimal system in which place values are assigned to digits wherein values increase in powers of ten[2] The Greeks and Romans used letters to represent numbers with the result that the progress of Arithmetic was very slow in Eastern Europe. In India the use of the decimal system and the use of ten symbols (for 0, 1, 9) to represent any given number, made mathematical operations (addition, subtraction, etc.) easy. What Europeans call “Arabic numerals" were discovered in India and only recently some authors have started calling them "Hindu-Arabic numerals". These numerals were invented some time before 200 B.C. The current Devanāgarī numerals have been in use in various parts of India since A.D. 400 and the English numerals are their modified forms. Although this verse goes up to parārdha (1017), there are terms for numbers up to 10140 in Sanskrit.'
See Also
लीलावती में 'अंकों का स्थानीय मान'
References
- ↑ Pandit, M.D. Līlāvatī Of Bhaskarācārya Part I. Pune. pp. 34–37.
- ↑ Līlāvatī Of Bhāskarācārya - A Treatise of Mathematics of Vedic Tradition. New Delhi: Motilal Banarsidass Publishers. 2001. p. 10. ISBN 81-208-1420-7.
