Since, then, we have defined in how many ways nature is predicated, let us after this consider in what a mathematician differs from a natural philosopher: for natural bodies have superficies, and solidities, lengths and points about which the mathematician speculates. We must also consider whether astrology (i.e., astronomy), is different from or a part of physics; for if it is the business of the natural philosopher to know what the sun or moon is, but not any of the essential accidents pertaining to these, an absurdity will ensue; especially because those who discourse concerning nature, appear also to speak concerning the figure of the sun and moon, and to inquire whether the earth and the world are spherical or not. The mathematician, therefore, is also employed about these, yet not so far as each of them is the boundary of a natural body. Nor does he contemplate the accidents of these, so far as they happen to things of this kind; and on this account he separates them from their subjects: for they are separable, by intellection, from motion. This, however, is of no consequence; nor is falsehood produced by those who thus separate. But they do not perceive that they do this, who assert that there are ideas: for they separate natural things, which are less separable than such as are mathematical. And this will become manifest, if anyone endeavors to unfold the definitions of each; that is to say, as well of things themselves as their accidents: for the odd and the even, the straight and the curved; and still further, number, line and figure are without motion; but this is not the case with flesh and bone, and man: for these are denominated in the same manner as a flat nose, and not in the same manner as that which is curved. This also is evident from the more physical of mathematical concerns such as optics, music and astrology; for in a certain respect they subsist contrary to geometry: for geometry speculates concerning a physical line, but not so far as it is physical; and optics considers, indeed, a mathematical line, yet not so far as it is mathematical, but so far as it is physical. Since, however, nature is twofold, viz., form and matter, we should contemplate physical things as if we were considering, with respect to flatness of nose what it is. Hence, things of this kind are neither without matter, nor do they subsist according to matter: for some one also may doubt concerning this, since there are two natures, viz. which of these the natural philosopher makes the object of his contemplation, or whether he considers that which consists from both these. But if that which consists from both, he also speculates each of these natures. Whether, therefore, is it the province of the same, or of a different science to know each of these? For if we look to the ancient philosophers, it would seem that matter alone should be regarded by the natural philosopher: for Empedocles and Democritus attended but in a small degree to form, and the very nature or essence of a thing. But if earned imitates nature, and it is the province of the same science to know form and matter to a certain extent; (as, for instance, it is the province of a physician to know health, bile and phlegm; and, in like manner, of an architect to know the form and matter of a house, viz., that the matter consists of tiles and wood, and similarly with respect to other things)—if this be the case, it is also the province of the physical science to have a knowledge of both natures.
Further still, it belongs to the same science to know that for the sake of which a thing subsists, the end, and such things as exist for the sake of these. But nature is an end, and that, for the sake of which a things subsists: for of those things of the motion of which since, it is continued, there is a certain end, this end is the last, and that for the sake of which the motion subsists. Hence the poet was ridiculously led to say:
An end it has, for which it was produced.
For not everything which is last deserves the name of end, but that which is the best. Since, however, the arts produce matter, some of them simply, but others accommodated to the work, and we use all these as if they subsisted for our sake; (for we also in a certain respect are an end, since not for the sake of which I think subsists is considered in a twofold respect, as we have observed in our books concerning Philosophy)—this being the case, there are two arts which rule over and possessive knowledge of matter, viz., the art which uses it, and that which is architectonic of effective arts. Hence, also, that which uses matter is in a certain respect architectonic. They differ, however, so far as the one, viz., the architectonic, has a knowledge of form; but the other is called architectonic as being productive of matter. For the pilot knows what form the rudder of a ship should have, and orders it to be made; but another artist knows from what would and what motions it will be made. In those productions, therefore, which are according to art, we make the matter for the sake of the work; but in natural productions it already exists. Again, matter belongs to the class of relatives: for a different matter pertains to a different form. How far, therefore, ought a natural philosopher to know form and what a thing is? Shall we say, in the same manner as a physician ought to know a nerve, or a brazier brass, to a certain extent? For everything which is produced by nature is for the sake of something; and natural philosophy is conversant with those things which are separable, indeed, in form, but are in matter: for man and the sun generate man. But how that which is separable subsists, and what it is, it is the business of the first philosophy to determine.
