Concept:
The Natyashastra is an ancient Sanskrit treatise on Indian performing arts written by Bharata Muni. It is regarded as the foundation of Indian classical dance, drama, music, and theatrical traditions. Scholars estimate that this text was composed and compiled over several centuries.
Step 1: Understand the importance of the Natyashastra.
The Natyashastra explains:
• Drama and theatre
• Classical dance techniques
• Music and rhythm
• Facial expressions and emotions
• Stage performance and aesthetics
It is considered one of the earliest and most important texts in Indian performing arts.
Step 2: Identify the period of composition.
Historians generally believe that the Natyashastra was composed between:
\[
\text{Second Century B.C. to Second Century A.D.}
\]
The text evolved gradually and reached its final form during this period.
Step 3: Compare with the given options.
Among the given choices:
• Option (A): Third Century B.C. to Third Century A.D.
• Option (B): Fifth Century A.D. to Eighth Century A.D.
• Option (C): Second Century B.C. to Second Century A.D.
• Option (D): Sixteenth Century A.D. to Eighteenth Century A.D.
The correct period matches:
\[
\boxed{\text{Second Century B.C. to Second Century A.D.}}
\]
Hence, the correct answer is:
\[
\boxed{\mathrm{(C)}}
\]