Mathematics in Ancient and Medieval India c4.s1.2

c4.s1.2

The Vedic civilisation has four stages of development viz., ( 1 ) the *Saṃhita* ( the four *Saṃhitas*, namely *Ṛk*, *Sāma*, *Yajus* and *Atharvan* ), ( 2 ) the next stage of the *Brāhmaṇa* ( theological and ritual treatises ), ( 3 ) then the stage of the *Āraṇyakas* ( metaphysical appendices of the *Brāhmaṇas* ) and *Upaniṣads* ( philosophical texts regarding the absolute one ), and ( 4 ) the last stage of the *Vedāṅgas*. Information related to mathematical ideas in the literatures of the first three stages of the Vedic age is meagre. The *Vedāṅga* literatures are of six types namely : (i) *śikṣā* ( the science of the pronunciation of letters, accents ......), ( ii ) *kalpa* ( containing rules for ceremonial and sacrificial ceremony ), ( iii ) *vyākaraṇa* ( grammar ), ( iv ) *nirukta* ( etymology ), ( v ) *chanda* ( the science of metres ) and ( vi ) *jyautiṣa* ( astronomy ). The literatures of the *Vedāṅgas* are known as a whole Sūtra literatures, because they are written in forms of short rule, a peculiar style of composition characterised by utmost brevity and rigid systematization to preserve the cultural heritages of the Brāhmaṇas in a manageable form.