Upavedas
Knowledge systems which are regarded as the supplementary of the four Vedas are known as Ūpavedas. They are also four in numbers. Viṣṇupurāṇa in its third chapter says that Ayurveda, Dhanurveda, Gandharvaveda and Arthaśāstra are Upavedas. Ayurveda is the science of medicine, dhanurveda the science of warfare or martial arts, Gandharvaveda the science of music or poetry, Arthaśāstra the science of governance economy and administration. Many scholars also define Sthpatyaveda or Vāstuśāstra as one Upaveda. Among this, Ayurveda is considered as the Upaveda of both Rigveda and Atharvaveda. Dhanurveda associated with Yajurveda, Gandharvaveda with Sāmaveda and Arthaśāstra with Atharvaveda.
The Indian system of medicine called Ayurveda is associated with both Rigveda and Atharvaveda. Atharvaveda has many sections dealing with health, hygiene and medical usages. Sages like Atreya, Kaśyapa, Harita, Agnivesa etc. are regarded as the propounders of ancient Ayurvedic science.
Starting from the Vedic period itself, one can see many descriptions about wars. It is also believed that sages like Viśvamitra, Sadaśiva, Śārṅgadatta and Vikramāditya have written books on Archery. But works dealing with Dhanurveda available now are so less. Music as we all know had its origin from Sāmaveda. The laws and rules for chanting Sāmaveda Mantras in musical way was specifically mentioned in the Sāmavedic and related texts. The three Vedic accents or Svaras viz., Udatta, Anudatta and Svarita can be said as the base for later developed Saptasvaras or Seven Svaras.
Arthaśāstra is understood as politics many times. But to say it means science of administration and science of governance. The prosperity of an individual leis and depends on the prosperity of the society which ultimately having a good government. Hence from ancient times itself, Arthaśāstra were associated with Kings, government and politics. We can see many sages such as Bṛhaspati, Bharadvāja, Parāśara and so on as the law makers and mentioned as the authorities of Arthaśāstra.