Which of the following is/are Euclid's postulate?
(i) A terminated line can be produced indefinitely.
(ii) Things which coincide with one another are equal to one another.

Options

A. Only (i)
B. Only (ii)
C. Both (i) and (ii)
D. Neither (i) nor (ii)

Answer

To determine which of the given statements are Euclid's postulates, we need to analyze each statement based on the definitions of Euclid's five postulates.

### Step-by-Step Solution:

1. **Understanding Euclid's Postulates**:
- Euclid's postulates are foundational statements in geometry that are accepted without proof. There are five main postulates.

2. **Analyzing Statement (i)**:
- Statement (i): "A terminated line can be produced indefinitely."
- This statement corresponds to Euclid's second postulate, which states that a line segment can be extended indefinitely in both directions.

3. **Analyzing Statement (ii)**:
- Statement (ii): "Things which coincide with one another are equal to one another."
- This statement is not one of Euclid's five postulates. It is more of a common geometric principle but does not appear explicitly in Euclid's original postulates.

4. **Conclusion**:
- Based on the analysis, statement (i) is a Euclid's postulate, while statement (ii) is not.

5. **Final Answer**:
- The correct answer is that only statement (i) is a Euclid's postulate.