### 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)–

[Numerals:]

*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–

saṅkhyāmātrārthevartamānāyā viṃśatyadeḥ saṅkhyāyā dvivacanabahuvacane āpi sthaḥ |

ekaśeṣāt dveviṃśatī 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–

yadāhuḥ–

ekadśaśatasahasrāṇyayutaṃ prayutākhyalakṣamathaniyutaṃ |

ārbudakoṭinyarbudapadmaṃ kharvaṃ nikharvamiti daśabhiḥ |

guṇanānmahābdaśaṅkūsamudramadhyāntamatha parārdhaṃ ca |

svahatam parārdhamamitaṃtatsvahataṃ 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”–

## (*c) Guṇitāhata* (III. 1. 89; p. 255)–

[Multiplication:]

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