Euclid's second axiom states that if equals be added to equals, the wholes are equal.
x + y = 15
Adding z to both sides, we get
x + y + z = 15 + z
Thus, Euclid's second axiom illustrates the statement that when x + y = 15, then x + y + z = 15 + z.
Hence, the correct answer is option (b).