Which of the following is not a Euclid's axiom?

Options

A. The whole is greater than the part
B. Things which are double of the same things are equal to one another.
C. Thing which are halves of the same things are equal to one another.
D. If two things are equal, then their sum is equal to `(1)/(3)` of the one thing.

Answer

To determine which of the following statements is not a Euclid's axiom, we will analyze each option one by one.

### Step-by-Step Solution:

1. **Option A: The whole is greater than the part.**
- This statement is true and is indeed one of Euclid's axioms. It states that if you have a whole, it must be greater than any of its parts. Therefore, this option is not the answer.

2. **Option B: Things which are double of the same thing are equal to one another.**
- This statement is also true and corresponds to Euclid's axiom. If A and B are both double of C, then A = B. Thus, this option is not the answer.

3. **Option C: Things which are half of the same thing are equal to one another.**
- This statement is true as well. If A and B are both half of C, then A = B. Therefore, this option is also not the answer.

4. **Option D: If two things are equal, then their sum is equal to one third of one thing.**
- This statement is not true. If A = B, then A + B = 2A, not one third of one thing. This does not align with Euclid's axioms, making this option the correct answer.

### Conclusion:
The statement that is not a Euclid's axiom is **Option D**: "If two things are equal, then their sum is equal to one third of one thing."

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