Show that the symmetric property follows from Euclids Common

Show that the symmetric property follows from Euclid\'s Common Notions 1 and 4. Common Notions Things which are equal to the same thing are also equal to one another. If equals be added to equals, the wholes are equal. If equals be subtracted from equals, the remainders are equal. Things which coincide with one another are equal to one another. The whole is greater than the part.

Solution

ANSWER :-

(1) Things which are equal to the same thing are also equal to one another

If a = b and a = c then b = c.

(2) If equals be added to equals, the wholes are equal

   If a = b and c = d then a + c = b + d

(3) If equals be subtracted friom equals , the remainders are equal

    If a = b and c = d the a - c = b - d

(4) Things which coincide with one another are equal to one another

      X is coincide with X so X = X.