No. Hypostasis and person add the individual principles to the idea of essence because strictly speaking, the essence is what is expressed by the definition: the definition comprises the principles of the species, but not the individual principles (hence in things composed of matter and form, the essence signifies not only the form, nor only the matter, but what is composed of matter and the common form, as the principles of the species; but what is composed of this matter and this form has the nature of hypostasis and person).
According to the Philosopher (Metaph. v), substance is twofold. In one sense it means the quiddity of a thing, signified by its definition, and thus we say that the definition means the substance of a thing; in which sense substance is called by the Greeks ousia, what we may call "essence."
In another sense substance means a subject or "suppositum," which subsists in the genus of substance. To this, taken in a general sense, can be applied a name expressive of an intention; and thus it is called "suppositum."
It is also called by three names signifying a reality--that is, "a thing of nature," "subsistence," and "hypostasis," according to a threefold consideration of the substance thus named. For, as it exists in itself and not in another, it is called "subsistence"; as we say that those things subsist which exist in themselves, and not in another.
As it underlies some common nature, it is called "a thing of nature"; as, for instance, this particular man is a human natural thing.
As it underlies the accidents, it is called "hypostasis," or "substance." What these three names signify in common to the whole genus of substances, this name "person" signifies in the genus of rational substances.