This is called knowing the root.

This is called the perfecting of knowledge.

The above fifth chapter of the commentary explained the meaning of "investigating things and carrying knowledge to the utmost extent," but it is now lost. I have ventured to take the views of the scholar Cheng to supply it, as follows: The meaning of the expression, "The perfecting of knowledge depends on the investigation of things, is this:—If we wish to carry our knowledge to the utmost, we must investigate the principles of all things we come into contact with, for the intelligent mind of man is certainly formed to know, and there is not a single thing in which its principles do not inhere. But so long as all principles are not investigated, man's knowledge is incomplete. On this account, the Learning for Adults, at the outset of its lessons, instructs the learner, in regard to all things in the world, to proceed from what knowledge he has of their principles, and pursue his investigaton of them, till he reaches the extreme point. After exerting himself in this way for a long time, he will suddenly find himself possessed of a wide and far-reaching penetration. Then, the qualities of all things, whether external or internal, the subtle or the coarse, will all be apprehended, and the mind, in its entire substance and its relations to things, will be perfectly intelligent. This is called the investigation of things. This is called the perfection of knowledge.