========= E1: PROP. 31:
The intellect in function, whether finite or infinite, as will, desire, love, etc., should be referred to passive nature and not to active nature.

Proof.--By the intellect we do not (obviously) mean absolute thought, but only a certain mode of thinking, differing from other modes, such as love, desire, etc., and therefore (E1D5) requiring to be conceived through absolute thought. It must (by E1P15 and E1D6), through some attribute of God which expresses the eternal and infinite essence of thought, be so conceived, that without such attribute it could neither be nor be conceived. It must therefore [E1P29N] be referred to nature passive rather than to nature active, as must also the other modes of thinking, Q.E.D.

=========Note:
--I do not here, by speaking of intellect in function, admit that there is such a thing as intellect in potentiality: but, wishing to avoid all confusion, I desire to speak only of what is most clearly perceived by us, namely, of the very act of understanding, than which nothing is more clearly perceived. For we cannot perceive anything without adding to our knowledge of the act of understanding.
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    Well, I hope each of us will contribute by possible explanation or question but I'll start off. He has just gone through a number of propositions about conditioned things and now:

    What is the subject here and in the immediately preceding proposition?:

    "Intellect in function" and in addition, what he is proposing he applies to other modes of thought such as will, desire, love, etc. Now this "Intellect in function" he says is a mode of the attribute of thought, not the attribute of thought itself and he clarifies in the note that he means by this "the very act of understanding."

    So what does he propose about this "very act of understanding" or "intellect in function"?:

    That it "should be referred to passive nature and not to active nature." He has just called our attention to what he means by "active nature" and "passive nature" in the preceding note:

========== E1: PROP. 29, Note:
...by nature viewed as active we should understand that which is in itself, and is conceived through itself, or those attributes of substance, which express eternal and infinite essence, in other words (E1P14C1, and E1P17C2) God, in so far as he is considered as a free cause.

By nature viewed as passive I understand all that which follows from the necessity of the nature of God, or of any of the attributes of God, that is, all the modes of the attributes of God, in so far as they are considered as things which are in God, and which without God cannot exist or be conceived.
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    He seems to want us to see that what he refers to as intellect --the very act of understanding-- even if infinite, does not constitute the essence of God but rather is a mode of an attribute of God. In other words Intellect is not something which is in itself or can be conceived through itself. As he will show shortly, but which we can perhaps anticipate from what has been offered so far, Intellect is conditioned by God to exist and act in a particular manner.

    Now let me think this over more deeply, beyond the mere words...