The Complete Aristotle (eng.)

commensurate
universal as its middle term approaches nearer to the basic truth,
and nothing is so near as the immediate premiss which is itself the
basic truth. If, then, proof from the basic truth is more accurate
than proof not so derived, demonstration which depends more closely
on it is more accurate than demonstration which is less closely
dependent. But commensurately universal demonstration is
characterized by this closer dependence, and is therefore superior.
Thus, if A had to be proved to inhere in D, and the middles were B
and C, B being the higher term would render the demonstration which
it mediated the more universal.
    Some of these arguments, however, are dialectical. The clearest
indication of the precedence of commensurately universal
demonstration is as follows: if of two propositions, a prior and a
posterior, we have a grasp of the prior, we have a kind of
knowledge-a potential grasp-of the posterior as well. For example,
if one knows that the angles of all triangles are equal to two
right angles, one knows in a sense-potentially-that the isosceles’
angles also are equal to two right angles, even if one does not
know that the isosceles is a triangle; but to grasp this posterior
proposition is by no means to know the commensurate universal
either potentially or actually. Moreover, commensurately universal
demonstration is through and through intelligible; particular
demonstration issues in sense-perception.
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    The preceding arguments constitute our defence of the
superiority of commensurately universal to particular
demonstration. That affirmative demonstration excels negative may
be shown as follows.
    (1) We may assume the superiority ceteris paribus of the
demonstration which derives from fewer postulates or hypotheses-in
short from fewer premisses; for, given that all these are equally
well known, where they are fewer knowledge will be more speedily
acquired, and that is a desideratum. The argument implied in our
contention that demonstration from fewer assumptions is superior
may be set out in universal form as follows. Assuming that in both
cases alike the middle terms are known, and that middles which are
prior are better known than such as are posterior, we may suppose
two demonstrations of the inherence of A in E, the one proving it
through the middles B, C and D, the other through F and G. Then A-D
is known to the same degree as A-E (in the second proof), but A-D
is better known than and prior to A-E (in the first proof); since
A-E is proved through A-D, and the ground is more certain than the
conclusion.
    Hence demonstration by fewer premisses is ceteris paribus
superior. Now both affirmative and negative demonstration operate
through three terms and two premisses, but whereas the former
assumes only that something is, the latter assumes both that
something is and that something else is not, and thus operating
through more kinds of premiss is inferior.
    (2) It has been proved that no conclusion follows if both
premisses are negative, but that one must be negative, the other
affirmative. So we are compelled to lay down the following
additional rule: as the demonstration expands, the affirmative
premisses must increase in number, but there cannot be more than
one negative premiss in each complete proof. Thus, suppose no B is
A, and all C is B. Then if both the premisses are to be again
expanded, a middle must be interposed. Let us interpose D between A
and B, and E between B and C. Then clearly E is affirmatively
related to B and C, while D is affirmatively related to B but
negatively to A; for all B is D, but there must be no D which is A.
Thus there proves to be a single negative premiss, A-D. In the
further prosyllogisms too it is the same, because in the terms of
an affirmative syllogism the middle is always related affirmatively
to both extremes; in a negative syllogism it must be negatively
related only to one of them, and so this negation comes to be a
single negative premiss, the other premisses being affirmative. If,
then, that through which a truth is proved is a better known and
more certain truth, and if the negative proposition is proved
through the affirmative and not vice versa, affirmative
demonstration, being prior and better known and more certain, will
be superior.
    (3) The basic truth of demonstrative syllogism is the universal
immediate premiss, and the universal premiss asserts in affirmative
demonstration and in negative denies: and the affirmative
proposition is