on something else, will form
another common image of men, describing man, for instance, as an animal
capable of laughter, a biped without feathers, a rational animal, and so
on; each person forming universal images of things according to the
temperament of his own body. It is not therefore to be wondered at that
so many controversies have arisen amongst those philosophers who have
endeavored to explain natural objects by the images of things alone.

_The Three Kinds of Knowledge_

From what has been already said, it clearly appears that we perceive
many things and form universal ideas:

1. From individual things, represented by the senses to us in a
mutilated and confused manner, and without order to the intellect. These
perceptions I have therefore been in the habit of calling knowledge
from vague experience.

2. From signs; as, for example, when we hear or read certain words, we
recollect things and form certain ideas of them similar to them, through
which ideas we imagine things. These two ways of looking at things I
shall hereafter call knowledge of the first kind, opinion or
imagination.

3. From our possessing common notions and adequate ideas of the
properties of things. This I shall call reason and knowledge of the
second kind.

Besides these two kinds of knowledge, there is a third, as I shall
hereafter show, which we shall call intuitive science. This kind of
knowing advances from an adequate idea of the formal essence of certain
attributes of God to the adequate knowledge of the essence of things.
All this I will explain by one example. Let there be three numbers given
through which it is required to discover a fourth which shall be to the
third as the second is to the first. A merchant does not hesitate to
multiply the second and third together and divide the product by the
first, either because he has not yet forgotten the things which he heard
without any demonstration from his school-master, or because he has seen
the truth of the rule with the more simple numbers, or because from the
19th Prop. in the 7th book of Euclid he understands the common property
of all proportionals.

But with the simplest numbers there is no need of all this. If the
numbers 1, 2, 3, for instance, be given, every one can see that the
fourth proportional is 6 much more clearly than by any demonstration,
because from the ratio in which we see by one intuition that the first
stands to the second we conclude the fourth.