Vedic literature went through four stages of development: the Samhitas (c. 1000 bc), the Brahmanas (c. 800 bc), the Aranyakas (c 700 bc) and the Upanishads (c. 600-500 bc). The Samhitas were Iyrical collections of hymns, prayers, incantations, and sacrificial and magical formulae. From what must have been a vast corpus of such writings, four great collections have come down to us - the oldest surviving literary efforts of mankind. In order of their age, they are
l Riveda, which contains hymns and prayers to be recited during the perfomance of rituals and sacrafices,
2 Samaveda, which contains melodies to be sung on suitable occasions,
3 Yajurveda, which contains sacrificial formulae for ceremonial occasions, and
4 Atharvaveda, a collection of magical fommulae and spells.
The Brahmanas, the second great division of Vedic literature, have been described as practical handbooks for those conducting sacrifices. As the Brahmana communities gradually dispersed from the north to the eastem and southem parts of the country, there arose a need for a record of ritual procedures and duties for a travelling class of priests, and a means of allocating special tasks among different priests.
For mathematics, a more important source is provided by the 'appendices' to the main Vedas, known as the Vedangas. These were classified into six branches of knowledge: (I) phonetics, the science of articulation and pronunciation, (2) grammar, (3) etymology, (4) metronomy (chandah), the art of prosody, (s) astronomy, and (6) rules for rituals and ceremonials (kalpa). In the last two Vedangas are found the most important sources of mathematics from the Vedic period. The evidence is usually in the form of sutras, a peculiar form of writing which aims at the utmost brevity and often uses a poetic style to capture the essence of an argument or result. By avoiding the use of verbs as far as possible and compounding nouns at great length, a vast body of knowledge was made easier to memorize. Condensation into sutras was also a way of eking out scarce writing materials. This was the form in which the contents of the Brahmanas were preserved, and it was adopted later not only by various philosophical and scientific schools, but also by writers of books on statecraft (arthasastra) and sex manuals (kamasastra).
We have referred to the Kalpasutras as an important source of Vedic mathematics. This ritual literature included Srautasutras, which gave directions for constructing sacrificial fires at different times of the year. Part of this literature dealt with the measurement and construction of sacrificial altars, and came to be known as the Sulbasutras. The term originally meant rules goveming 'sacrificial rites', though later the word sulba came to refer to the cord of rope used in measuring altars. Most of what we know of Vedic geometry comes from these sutras.
€The dating of early Indian texts is hghly uncertain. The dates given here are rough and conservative estimates of when the first versions of the texts were recorded. It is very likely tht before they were written, an earlier oral tradition kept the contents alive. Copying old texts was a common pursuit of the Indian scholars and students, sanctioned by religion and custom. It is therefore important not to depend on evidence of the dates of copies of mathematical texts in assessing the true age of a particular method or technique.