Explain how Common Notions 1 and 4 may be interpreted as the transitiveand reflexive properties.
Also,show that the symmetric property follows from Euclid’s Common Notions
1 and 4.

1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one another. 5. The whole is greater than the part.