On the contrary,_ This is how "to believe" is defined by Augustine
(De Praedest. Sanct. ii).

_I answer that,_ "To think" can be taken in three ways. First, in a
general way for any kind of actual consideration of the intellect, as
Augustine observes (De Trin. xiv, 7): "By understanding I mean now
the faculty whereby we understand when thinking." Secondly, "to
think" is more strictly taken for that consideration of the
intellect, which is accompanied by some kind of inquiry, and which
precedes the intellect's arrival at the stage of perfection that
comes with the certitude of sight. In this sense Augustine says (De
Trin. xv, 16) that "the Son of God is not called the Thought, but the
Word of God. When our thought realizes what we know and takes form
therefrom, it becomes our word. Hence the Word of God must be
understood without any thinking on the part of God, for there is
nothing there that can take form, or be unformed." In this way
thought is, properly speaking, the movement of the mind while yet
deliberating, and not yet perfected by the clear sight of truth.
Since, however, such a movement of the mind may be one of
deliberation either about universal notions, which belongs to the
intellectual faculty, or about particular matters, which belongs to
the sensitive part, hence it is that "to think" is taken secondly for
an act of the deliberating intellect, and thirdly for an act of the
cogitative power.

Accordingly, if "to think" be understood broadly according to the
first sense, then "to think with assent," does not express completely
what is meant by "to believe": since, in this way, a man thinks with
assent even when he considers what he knows by science [*Science is
certain knowledge of a demonstrated conclusion through its
demonstration.], or understands. If, on the other hand, "to think" be
understood in the second way, then this expresses completely the
nature of the act of believing. For among the acts belonging to the
intellect, some have a firm assent without any such kind of thinking,
as when a man considers the things that he knows by science, or
understands, for this consideration is already formed. But some acts
of the intellect have unformed thought devoid of a firm assent,
whether they incline to neither side, as in one who "doubts"; or
incline to one side rather than the other, but on account of some
slight motive, as in one who "suspects"; or incline to one side yet
with fear of the other, as in