For example, the former easily learn hydrostatics, where the premises
are few, but the conclusions are so fine that only the greatest
acuteness can reach them.

And in spite of that these persons would perhaps not be great
mathematicians, because mathematics contain a great number of premises,
and there is perhaps a kind of intellect that can search with ease a few
premises to the bottom, and cannot in the least penetrate those matters
in which there are many premises.

There are then two kinds of intellect: the one able to penetrate acutely
and deeply into the conclusions of given premises, and this is the
precise intellect; the other able to comprehend a great number of
premises without confusing them, and this is the mathematical intellect.
The one has force and exactness, the other comprehension. Now the one
quality can exist without the other; the intellect can be strong and
narrow, and can also be comprehensive and weak.


3

Those who are accustomed to judge by feeling do not understand the
process of reasoning, for they would understand at first sight, and are
not used to seek for principles. And others, on the contrary, who are
accustomed to reason from principles, do not at all understand matters
of feeling, seeking principles, and being unable to see at a glance.


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