Aristotle holds both that everything in motion is moved by another and nature is an intrinsic source of motion. Belcher argues that this is contradictory (pp. 28-32 here), or at least that we have to choose between how Aristotle ultimately understands the first claim and the truth of the second, since he takes the “moved by another” claim to mean that anything in motion is moved by another individual, even while he says that some things are moved by themselves, i.e. not by another individual.
But just as every whole depends on the motion of its parts to move, we can also consider the way in which some parts cause the whole to move. Here again there is a division between the organic and the inorganic: in the first the parts move the whole in the sense that a system carries out various processes for the whole living being: the circulatory system controls all the circulation for the animal; the nervous system carries out all of its information processing; the respiratory system governs its oxygenation, etc. To the extent that this system-part moves the whole, the whole is called “self-moving”. Even among the non-living, it’s still true that the parts of the thing are necessary to move the whole, and, since the parts of some whole count as its own, even the inanimate can be considered as a source of its own motion.
And so in any natural motion we must take the whole-part composition as given, and so the principles of a natural motion have to be partless. On the most basic level, this partlessness in the material order is just the most homogeneous part. Such a part is not the smallest part, since this is only a relative designation, it is the most undifferentiated part, which Aristotle called an element. But though such things in some sense count as the first principles, they cannot be such absolutely, since they still fall under the sort of whole-part analysis given above. On a higher level, there are partless principles like soul in animals and plants. Here there is a higher sort of partlessness, but it is not entirely separated from being a part. Something only counts as a first principle of motion or nature altogether if it is entirely partless or incomposite: it acts upon nature without interacting with it; it exercises power over nature without this exercise being able to render it either more virtuous or more wicked; and all of nature is at once the unfolding of its moving act (since all its motions are just developments of this aboriginal motion) and is nevertheless entirely separate from it (since this absolutely partless reality cannot enter into composition with nature and remain what it is).