The Complete Aristotle (eng.)

e.g. weight and lightness, hardness and its contrary,
and also heat and cold and the other sensible contrarieties, and
leaves only the quantitative and continuous, sometimes in one,
sometimes in two, sometimes in three dimensions, and the attributes
of these qua quantitative and continuous, and does not consider
them in any other respect, and examines the relative positions of
some and the attributes of these, and the commensurabilities and
incommensurabilities of others, and the ratios of others; but yet
we posit one and the same science of all these things—geometry)—the
same is true with regard to being. For the attributes of this in so
far as it is being, and the contrarieties in it qua being, it is
the business of no other science than philosophy to investigate;
for to physics one would assign the study of things not qua being,
but rather qua sharing in movement; while dialectic and sophistic
deal with the attributes of things that are, but not of things qua
being, and not with being itself in so far as it is being;
therefore it remains that it is the philosopher who studies the
things we have named, in so far as they are being. Since all that
is is to ‘be’ in virtue of something single and common, though the
term has many meanings, and contraries are in the same case (for
they are referred to the first contrarieties and differences of
being), and things of this sort can fall under one science, the
difficulty we stated at the beginning appears to be solved,-I mean
the question how there can be a single science of things which are
many and different in genus.
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4
    Since even the mathematician uses the common axioms only in a
special application, it must be the business of first philosophy to
examine the principles of mathematics also. That when equals are
taken from equals the remainders are equal, is common to all
quantities, but mathematics studies a part of its proper matter
which it has detached, e.g. lines or angles or numbers or some
other kind of quantity-not, however, qua being but in so far as
each of them is continuous in one or two or three dimensions; but
philosophy does not inquire about particular subjects in so far as
each of them has some attribute or other, but speculates about
being, in so far as each particular thing is.-Physics is in the
same position as mathematics; for physics studies the attributes
and the principles of the things that are, qua moving and not qua
being (whereas the primary science, we have said, deals with these,
only in so far as the underlying subjects are existent, and not in
virtue of any other character); and so both physics and mathematics
must be classed as parts of Wisdom.
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5
    There is a principle in things, about which we cannot be
deceived, but must always, on the contrary recognize the
truth,-viz. that the same thing cannot at one and the same time be
and not be, or admit any other similar pair of opposites. About
such matters there is no proof in the full sense, though there is
proof ad hominem. For it is not possible to infer this truth itself
from a more certain principle, yet this is necessary if there is to
be completed proof of it in the full sense. But he who wants to
prove to the asserter of opposites that he is wrong must get from
him an admission which shall be identical with the principle that
the same thing cannot be and not be at one and the same time, but
shall not seem to be identical; for thus alone can his thesis be
demonstrated to the man who asserts that opposite statements can be
truly made about the same subject. Those, then, who are to join in
argument with one another must to some extent understand one
another; for if this does not happen how are they to join in
argument with one another? Therefore every word must be
intelligible and indicate something, and not many things but only
one; and if it signifies more than one thing, it must be made plain
to which of these the word is being applied. He, then, who says
‘this is and is not’ denies what he affirms, so that what the word
signifies, he says it does not signify; and this is impossible.
Therefore if ‘this is’ signifies something, one cannot truly assert
its contradictory.
    Further, if the word signifies something and this is asserted
truly, this connexion must be necessary; and it is not possible
that that which necessarily is should ever not be; it is not
possible therefore to