Amarakoshodghatana of Kshirasvamin (study)

by A. Yamuna Devi | 2012 | 77,297 words | ISBN-13: 9788193658048

This page relates ‘Education (9): Knowledge in Mathematics’ of the study on the Amarakoshodghatana of Kshirasvamin (in English) which represents a commentary on the Amarakosha of Amarasimha. These ancient texts belong the Kosha or “lexicography” category of Sanskrit literature which deals with the analysis and meaning of technical words from a variety of subjects, such as cosmology, anatomy, medicine, hygiene. The Amarakosa itself is one of the earliest of such text, dating from the 6th century A.D., while the Amarakoshodghatana is the earliest known commentary on that work.

Education (9): Knowledge in Mathematics

Mathematics is represented by numerals and hence form its integral part. Some of the mathematical aspects found in commentary of Kṣīrasvāmin are–terms used for representation of the numerals upto the 18th place value, multiplication and odd numbers.

(a) Saṅkhyā (II. 9. 84; p. 219)–


Amarakośa mentions that the numerals as numbers or adjectives are always in singular; and mentions ten, hundred, and thousand and so on which are respectively multiples of tens.

Kṣīrasvāmin remarks on the same that the numerals above twenty when used as numbers alone can take dual or plural as follows–

saṅkhyāmātrārthe vartamānāyā viṃśatyadeḥ saṅkhyāyā dvivacanabahuvacane āpi sthaḥ |
ekaśeṣāt dve
viṃśatī tisro viṃśatayaḥ gavāṃ viṃśatī gavāṃ viṃśatayaḥ |

Kṣīrasvāmin further adds that the numerals were represented upto the eighteenth place value called parārdha and enumerates them thus citing from an unknown source–

ekadśaśatasahasrāṇyayutaṃ prayutākhyalakṣamatha niyutaṃ |
ārbudakoṭinyarbudapadmaṃ kharvaṃ nikharvamiti daśabhiḥ |
guṇanānmahābdaśaṅkūsamudramadhyāntamatha parārdhaṃ ca |
svahatam parārdhamamitaṃ
tatsvahataṃ pūryate saṅkhyeti |
prayutasaṃjñaṃ lakṣamarbhudasaṃjñā koṭirityarthaḥ ||

S.No Name as given by Kṣīrasvāmin Value According to Medhatithi[1]
1 eka 1 Eka
2 daśa 10 daśa
3 śata 100 śata
4 sahasra 1000 sahasra
5 ayuta 10,000 ayuta
6 prayuta or lakṣa 1,00,000 niyuta
7 niyuta 10,00,000 prayuta
8 arbuda or koṭi 1,00,00,000 arbuda
9 nyarbuda 10,00,00,000 nyarbuda
10 padma 1,00,00,00,000 samudra
11 kharva 10,00,00,00,000 madhya
12 nikharva 1,00,00,00,00,000 anta
13 mahābda 10,00,00,00,00,000 parārdha
14 śaṅkū 1,00,00,00,00,00,000  
15 samudra 10,00,00,00,00,00,000  
16 madhya 1,00,00,00,00,00,00,000  
17 anta 10,00,00,00,00,00,00,000  
18 parārdha 1,00,00,00,00,00,00,00,000  

(b) Oja (III. 3. 233; pp. 328-29)–

[Odd number:]

Amarakośa metions that the homonymous word ojas denotes splendour and strength. Kṣīrasvāmin adds that the word ending in short ‘a’ denotes an odd number and mentions a mathematical operation to illustrate it–

“That an odd number added to another odd number gives an even number”–

viṣamasaṃkhyāvācī tvojo'dantaḥ | ojenaujaḥ samaḥ..... |

(c) Guṇitāhata (III. 1. 89; p. 255)–


This homonymous term denoting multiplication is explained by Kṣīrasvāmin as doubling of numbers–āhanyate sma ekādiraṅko'ṅkāntareṇa ābhyasyate āhatam |

Footnotes and references:


The History of Mathematics and Mathematicians of India, Er. Venugopal D. Heroor, 2006, p. 15.

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