Charles Haanel wants us to understand that there is nothing happening by chance. It's all law. It's cause and effect. It's the Law of Attraction. Sometimes the chain of causation is a very long one, where we aren't aware of all the details. However, as we have seen with the exercise of part 8, we see a battleship but are hardly aware of all that's going on inside and also how it came about.
So in this part our focus lies on comparing individual cases until we find the common denominator that gave rise to them all. Why is this important? Because that common denominator show the workings of the Law. That's why it's called common and denominator. This way we can say with certainty that one particular cause leads to a particular effect. This takes away the element of uncertainty, as Charles Haanel himself mentions in the MKS. Certainty leads to centeredness; centeredness leads to peace of mind, and peace of mind leads to intelligent decisions. They in turn lead to the best that life has to offer us.
You see why it is so important to look closely, to compare, to identify the common denominator, because then and only we move from belief to knowledge and from there to wisdom.