Answer:

Introduction:
Euclid's Elements of Geometry and Napier's work on logarithms are two significant mathematical works. The translation of Euclid's Elements of Geometry into Sanskrit and the study of logarithms in India were both important contributions to the development of mathematics in the country. Among the given options, Sawai Jai Singh is the correct answer as he was known for his translation of Euclid's Elements of Geometry into Sanskrit and his study of logarithms.

Explanation:
Sawai Jai Singh:
- Sawai Jai Singh (1688-1743) was a Rajput king and an avid scholar of mathematics and astronomy.
- He was the ruler of the Kingdom of Amber (present-day Jaipur) in Rajasthan, India.
- Sawai Jai Singh had a keen interest in mathematics and made significant contributions to the field.
- He was known for his translation of Euclid's Elements of Geometry into Sanskrit, which was a significant work in the field of mathematics.
- His translation helped spread the knowledge of Euclidean geometry among scholars in India.

Euclid's Elements of Geometry:
- Euclid's Elements of Geometry is a seminal work in the field of mathematics, particularly in the study of geometry.
- It was written by the Greek mathematician Euclid around 300 BCE.
- The Elements consists of thirteen books that cover various aspects of geometry, including plane geometry, solid geometry, and number theory.
- Euclid's work laid the foundation for the study of geometry and is still widely studied and referenced today.

Napier's work on logarithms:
- John Napier (1550-1617) was a Scottish mathematician and astronomer known for his invention of logarithms.
- Logarithms are mathematical tools used to simplify calculations involving large numbers or complex calculations.
- Napier's work on logarithms revolutionized mathematics and greatly facilitated mathematical calculations.
- The study of logarithms was important in various fields, including astronomy, navigation, and scientific research.
- The development and study of logarithms played a crucial role in the advancement of mathematics.

Conclusion:
Sawai Jai Singh, the ruler of the Kingdom of Amber, translated Euclid's Elements of Geometry into Sanskrit and made significant contributions to the study of logarithms. His work helped spread knowledge in the field of mathematics and played a crucial role in the development of mathematics in India.