Most of the chapters of the Isagoge are fairly short; this one is an exception, and so we will take it in pieces. In this chapter Porphyry discusses the meaning of the terms genus and species.
Neither genus nor species appear to be simply denominated,…
I believe what he means, here, is that each term has a number of distinct (but analogical) senses.
…for that is called genus which is a collection of certain things, subsisting in a certain respect relatively to one thing, and to each other, according to which signification the genus of the Heraclidae is denominated from the habitude from one, I mean Hercules, and from the multitude of those who have alliance to each other from him, denominated according to separation from other genera.
So the tribe of the Heraclidae is a genus, because it is a distinct group, and all members of the group are related to each other due to their shared relationship to Hercules.
Again, after another manner also, the principle of the generation of every one is called genus, whether from the generator or from the place in which a person is generated, for thus we say that Orestes had his genus from Tantalus, Hyllus from Hercules, and again, that Pindar was by genus a Theban, but Plato an Athenian, for country is a certain principle of each man’s generation, in the same manner as a father. Still, this signification appears to be most ready, for they are called Heraclidae who derive their origin from the genus of Hercules, and Cecropidae who are from Cecrops; also their next of kin. The first genus, moreover, is so called, which is the principle of each man’s generation, but afterwards the number of those who are from one principle, e. g. from Hercules, which defining and separating from others, we call the whole collected multitude the genus of the Heraclidae.
The principle of generation of a thing is called its genus, e.g., that person’s father or country of origin. This sense applies to the prior sense as well, for the Heraclidae are precisely those who are the descendants of Hercules.
As Thomas points at the beginning of De Ente et Essentia, the proper approach to philosophy is to begin with the well-known and familiar and move by analogical steps to the logical and metaphysical, and that’s clearly what Porphyry is doing here. The second paragraph of the chapter, which I expect we’ll get to tomorrow, begins to discuss genus in the terms I’ve become familiar with over the last few months; here, he’s clearly describing the usual, every-day meanings it would have had for his readers.