"spint10" - читать интересную книгу автора (Spinoza Baruch)

thence clearly infer that the mind is united [g] to the body,
and that their union is the cause of the given sensation; but
we cannot thence absolutely understand [h] the nature of the
sensation and the union. (2) Or, after I have become acquainted
with the nature of vision, and know that it has the property of
making one and the same thing appear smaller when far off than
when near, I can infer that the sun is larger than it appears,
and can draw other conclusions of the same kind.

[22] (1) Lastly, a thing may be perceived solely through its essence;
when, from the fact of knowing something, I know what it is to know
that thing, or when, from knowing the essence of the mind, I know
that it is united to the body. (2) By the same kind of knowledge
we know that two and three make five, or that two lines each parallel
to a third, are parallel to one another, &c. (3) The things which I
have been able to know by this kind of knowledge are as yet very few.

[23] (1) In order that the whole matter may be put in a clearer
light, I will make use of a single illustration as follows.
(2) Three numbers are given - it is required to find a fourth,
which shall be to the third as the second is to the first.
(23:3) Tradesmen will at once tell us that they know what is required
to find the fourth number, for they have not yet forgotten the rule
which was given to them arbitrarily without proof by their masters;
others construct a universal axiom from their experience with simple
numbers, where the fourth number is self-evident, as in the case of
2, 4, 3, 6; here it is evident that if the second number be
multiplied by the third, and the product divided by the first,
the quotient is 6; when they see that by this process the number
is produced which they knew beforehand to be the proportional,
they infer that the process always holds good for finding a fourth
number proportional.

[24] (1) Mathematicians, however, know by the proof of the nineteenth
proposition of the seventh book of Euclid, what numbers are
proportionals, namely, from the nature and property of proportion
it follows that the product of the first and fourth will be equal
to the product of the second and third: still they do not see the
adequate proportionality of the given numbers, or, if they do see it,
they see it not by virtue of Euclid's proposition, but intuitively,
without going through any process.

[25] (1) In order that from these modes of perception the best may
be selected, it is well that we should briefly enumerate the means
necessary for attaining our end.

I. (2) To have an exact knowledge of our nature which we desire to
perfect, and to know as much as is needful of nature in general.

II. To collect in this way the differences, the agreements, and the