Step 1: Understanding the Concept:
The question asks to identify the primary ancient source text that governs the rules and aesthetics of Indian performing arts.
Step 2: Detailed Explanation:
The Natyashastra is an encyclopedic ancient Indian treatise on the performing arts, attributed to the sage Bharata Muni.
It was likely composed between 200 BCE and 200 CE and covers every aspect of performance, including drama, dance, music, stagecraft, and the emotional theory of Rasa.
Other texts mentioned serve different purposes:
1. Arthashastra: A treatise on statecraft, economic policy, and military strategy by Chanakya.
2. Manusmriti: An ancient legal text among the many Dharmaśāstras of Hinduism.
3. Shilpa Shastra: A collective term for manuals on the mechanical arts, sculpture, and architecture.
Step 3: Final Answer:
The foundational treatise on performing arts is the Natyashastra.