Really, at least throw in some words to maintain a pretense that "the common good" isn't just being tossed in as a complete non sequitur.
In any case, it was recognized by the Founders that the common good is not a prerequisite for liberty -- hence the phrase "the pursuit of happiness" rather than simply "happiness". You can fail to catch up to happiness, in which case "the common good" would not be satisfied but you would nevertheless be free.
Implicit in the statement that the first principle of the State is preservation of individual liberties is that this represents the good for society.