The Complete Aristotle (eng.)

his who knows the subject as possessing its attribute qua that
in virtue of which it actually does possess it. Since, then,
triangle is the wider term, and there is one identical definition
of triangle-i.e. the term is not equivocal-and since equality to
two right angles belongs to all triangles, it is isosceles qua
triangle and not triangle qua isosceles which has its angles so
related. It follows that he who knows a connexion universally has
greater knowledge of it as it in fact is than he who knows the
particular; and the inference is that commensurate and universal is
superior to particular demonstration.
    (2) If there is a single identical definition i.e. if the
commensurate universal is unequivocal-then the universal will
possess being not less but more than some of the particulars,
inasmuch as it is universals which comprise the imperishable,
particulars that tend to perish.
    (3) Because the universal has a single meaning, we are not
therefore compelled to suppose that in these examples it has being
as a substance apart from its particulars-any more than we need
make a similar supposition in the other cases of unequivocal
universal predication, viz. where the predicate signifies not
substance but quality, essential relatedness, or action. If such a
supposition is entertained, the blame rests not with the
demonstration but with the hearer.
    (4) Demonstration is syllogism that proves the cause, i.e. the
reasoned fact, and it is rather the commensurate universal than the
particular which is causative (as may be shown thus: that which
possesses an attribute through its own essential nature is itself
the cause of the inherence, and the commensurate universal is
primary; hence the commensurate universal is the cause).
Consequently commensurately universal demonstration is superior as
more especially proving the cause, that is the reasoned fact.
    (5) Our search for the reason ceases, and we think that we know,
when the coming to be or existence of the fact before us is not due
to the coming to be or existence of some other fact, for the last
step of a search thus conducted is eo ipso the end and limit of the
problem. Thus: ‘Why did he come?’ ‘To get the money-wherewith to
pay a debt-that he might thereby do what was right.’ When in this
regress we can no longer find an efficient or final cause, we
regard the last step of it as the end of the coming-or being or
coming to be-and we regard ourselves as then only having full
knowledge of the reason why he came.
    If, then, all causes and reasons are alike in this respect, and
if this is the means to full knowledge in the case of final causes
such as we have exemplified, it follows that in the case of the
other causes also full knowledge is attained when an attribute no
longer inheres because of something else. Thus, when we learn that
exterior angles are equal to four right angles because they are the
exterior angles of an isosceles, there still remains the question
‘Why has isosceles this attribute?’ and its answer ‘Because it is a
triangle, and a triangle has it because a triangle is a rectilinear
figure.’ If rectilinear figure possesses the property for no
further reason, at this point we have full knowledge-but at this
point our knowledge has become commensurately universal, and so we
conclude that commensurately universal demonstration is
superior.
    (6) The more demonstration becomes particular the more it sinks
into an indeterminate manifold, while universal demonstration tends
to the simple and determinate. But objects so far as they are an
indeterminate manifold are unintelligible, so far as they are
determinate, intelligible: they are therefore intelligible rather
in so far as they are universal than in so far as they are
particular. From this it follows that universals are more
demonstrable: but since relative and correlative increase
concomitantly, of the more demonstrable there will be fuller
demonstration. Hence the commensurate and universal form, being
more truly demonstration, is the superior.
    (7) Demonstration which teaches two things is preferable to
demonstration which teaches only one. He who possesses
commensurately universal demonstration knows the particular as
well, but he who possesses particular demonstration does not know
the universal. So that this is an additional reason for preferring
commensurately universal demonstration. And there is yet this
further argument:
    (8) Proof becomes more and more proof of the