But if it is true that the Reason in which all men participate is universal, that it is infinite, that it is necessary and immutable, then it is certainly not different from God's own reason, for only the infinite and universal being contains in itself an infinite and universal reason....But the reason we consult is not only infinite and universal, it is also independent and necessary, and in one sense, we conceive it as more independent than God Himself. For God can act only according to this reason; He depends on it in a sense--He has to consult and follow it. Now, God consults only Himself and depends on nothing. This reason, therefore, is not different from Himself; it is, therefore, coeternal and consubstantial with Him. (LO 614)
In other words, the most Augustinian of the Cartesians holds that the Divine Word is that whereby the Father is wise. He explicitly states this in a prayer attached to the Christian and Metaphysical Meditations, where he prays eternal Wisdom, "who renders wise creatures and even the Creator, although in a rather different way". In saying this Malebranche deviates considerably from Augustine himself, who expressly considers this topic in the De Trinitate. Augustine considers the following argument used against the Arians:
But among the arguments which those on our side used to hold against them who said that there was a time when the Son was not, some were wont to introduce such an argument as this: If the Son of God is the power and wisdom of God, and God was never without power and wisdom, then the Son is co-eternal with God the Father; but the apostle says, "Christ the power of God, and the wisdom of God;" and a man must be senseless to say that God at any time had not power or wisdom; therefore there was no time when the Son was not. (6.1.1)
Note that this is the argument Malebranche makes in the above passage from the Search. It is in slightly different terms; but in both cases the argument is that since the Son is the wisdom of God, and God cannot not be wise, the Son must be consubstantial and coeternal with God. As Augustine notes, however, this argument requires us to say that the Father is not wise except by begotten wisdom. But the problem with this is explored by Augustine in Book VII. We seem faced with a trilemma: either we deny that Christ is the wisdom and power of God, and thus make the Apostle a liar; or Christ is the wisdom and power of God, but the Father is not the Father of Him; or Christ is the wisdom and power of God, and the Father is not powerful or wise in His own right. His response to this is to point out that on orthodox doctrine, this will not work (7.1.2):
Therefore both the Father Himself is wisdom, and the Son is in such way called the wisdom of the Father, as He is called the light of the Father; that is, that in the same manner as light from light, and yet both one light, so we are to understand wisdom of wisdom, and yet both one wisdom; and therefore also one essence, since, in God, to be, is the same as to be wise. For what to be wise is to wisdom, and to be able is to power, and to be eternal is to eternity, and to be just to justice, and to be great to greatness, that being itself is to essence. And since in the Divine simplicity, to be wise is nothing else than to be, therefore wisdom there is the same as essence.
That is, just as we say that the Son is Light from Light, and yet both are one Light and not two, so we would have to say that He is wisdom from wisdom, and yet both are one wisdom and not two, and thus are consubstantial. The Son does not make the Father wise.
The Apostle does say that Christ is the power and wisdom of God, though, and we have to determine how this should be understood. And Augustine points out that terms like 'wisdom' can be said substantially or relatively. The two are not the same. The Father is wise by His own wisdom, which He shares with the Son; but the Son is called begotten wisdom insofar as He represents the wisdom of the Father by sharing it (7.3.4):
And therefore Christ is the power and wisdom of God, because He Himself, being also power and wisdom, is from the Father, who is power and wisdom; as He is light of the Father, who is light, and the fountain of life with God the Father, who is Himself assuredly the fountain of life. For "with You," He says, "is the fountain of life, and in Your light shall we see light." Because, "as the Father has life in Himself, so has He given to the Son to have life in Himself:" and, "He was the true Light, which lights every man that comes into the world:" and this light, "the Word," was "with God;" but "the Word also was God;" and "God is light, and in Him is no darkness at all:" but a light that is not corporeal, but spiritual; yet not in such way spiritual, that it was wrought by illumination, as it was said to the apostles, "You are the light of the world," but "the light which lights every man," that very supreme wisdom itself who is God, of whom we now treat. The Son therefore is Wisdom of wisdom, namely the Father, as He is Light of light, and God of God; so that both the Father singly is light, and the Son singly is light; and the Father singly is God, and the Son singly is God: therefore the Father also singly is wisdom, and the Son singly is wisdom. And as both together are one light and one God, so both are one wisdom. But the Son is "by God made unto us wisdom, and righteousness, and sanctification;" because we turn ourselves to Him in time, that is, from some particular time, that we may remain with Him for ever. And He Himself from a certain time was "the Word made flesh, and dwelt among us."
Aquinas picks up on exactly this point (ST 1.39.7); it's a key element of the scholastic doctrine of appropriation.
So Malebranche, in thinking of the Divine Wisdom as both the Son and that by which God is wise, is deviating from Augustinian Trinitarian theology. The deviation, I would argue, is actually pretty significant; it makes it possible for him to argue things that someone more rigorously Augustinian in their Trinitarian theology would never argue. In particular, he tends to make no sharp distinction between wisdom, reason, etc., as divine attributes common to the persons and wisdom, reason, etc., as appropriated to one person distinctively. The result is a number of oddities in Malebranche's view.