Final answer:
The question's observations confirm the Law of Definite Proportions, as they demonstrate that magnesium oxide always has a consistent proportion of magnesium to oxygen by mass.
Step-by-step explanation:
The observations given in the question are in agreement with the Law of Definite Proportions. This law states that a chemical compound always contains exactly the same proportion of elements by mass. In the first experiment, burning 1g of Mg with oxygen results in 1.66g of magnesium oxide, showing that the mass of oxygen that combined with magnesium is constant and in a fixed ratio. In the second experiment, magnesium oxide obtained from heating magnesium carbonate contains 60% magnesium regardless of the method of preparation, which also demonstrates a definite proportion of Mg to O in magnesium oxide.