Aristotelis Opera (Bekker Edition, Vol. 2): Metaphysica, Ethica, Politica, Rhetorica, Poetica

corresponds to the tetrad; for astronomy deals with heavenly bodies, and every body is three-dimensionally extended; for it has length, depth, or breadth. Each of these is contained by two boundaries, since it has two endpoints from which it is contained (the length is contained from here or there, the breadth likewise, and the depth), which comes together from the boundaries, that is, endpoints. From these six, four result; for the one part is common to two; for the boundary of the breadth is found to be the beginning of the length and of the depth.

It must be known that the Phoenicians discovered arithmetic, being merchants and needing numbers for accounts. The Thracians discovered music; for Orpheus was from there, who is said to have discovered music, for Orpheus was a Thracian. He devised marching songs that excite the spirit, as they were extremely warlike; for cold, by enclosing heat in the depths, makes it sharper, whence they are spirited and warlike by the force of heat, and dancers because of the readiness of fleeing arrows. For there is the Pyrrhic dance among them, which is a dance under arms, and the saying of the poet note: Homer, Iliad 16.617, "Mnemosyne, perhaps even now your dance will profit you." The Egyptians discovered geometry out of necessity; for as the Nile was constantly rising and flooding Egypt, there was a confusion of boundaries, and the Egyptians would enter into battle and kill one another. Hence, they devised a measure by which they measured the land, and each person's own property was preserved, which measure they also called a "rod" original: "ἄκαιναν" to prevent "killing" original: "καίνειν", which means murder, since through it they were prevented from killing and murdering. Thus, the usefulness of geometry appeared out of necessity. The Chaldeans discovered astronomy; for in the climate where they are, the sky is clear and cloudless, so they easily devised from there the teaching about heavenly bodies, that is, astronomy.

It must be known that logistics is adjacent to arithmetic, material music to music, and surveying original: "γεωδαισία" to geometry; surveying is so named from the distribution or division of land. Spherical geometry is adjacent to astronomy. But astronomy deals only with heavenly bodies, while spherical geometry deals with every sphere; for it states the properties of each sphere, whether it be of wax, wood, or stone, considering what pertains to every sphere, not only the celestial, as Theodosius in his Sphericals deals with the sphere contemplated by reason. Note that Olympiodorus says that while the remains of other mathematical types are preserved to this day, such as those of arithmetic, geometry, and astronomy, regarding music he says,

"We hear only the rumor, and we know nothing." note: This refers to the loss of ancient theoretical music treatises.
When he speaks of silence, he means the remains of music. Note, however, that there are musical books until this day. It contributes to the souls of irrational animals; sheep following the shepherd's pipe show this, as if delighted by the sound. That it contributes to the soul of rational animals is shown by the trumpet in war, which excites the soul, and theater instruments, which soothe the soul by delighting it through striking.

Section 21.

It must be known that some say there are eight modes of division... but it can be said that there are not strictly eight modes of division, but three.

Section 23.

Let us come and describe the division of the practical. It must be known that the Aristotelians divide the practical differently than the Platonists. The Aristotelians divide it into three: the ethical, the economical, and the political.

It must be known that Aristotle and Plato have one purpose in their writings on politics; for both say how a city must be managed. But the one on the Republic original: "Πολιτεία" differs in purpose or title. As for the title, Plato wrote it in the singular as Republic, while Aristotle wrote it in the plural as Politics. The purpose is different, because Aristotle says how the ancients governed, such as the Argives and the Boeotians, while Plato says how one must govern or how it is necessary to govern. So much for that. But the Platonists object to the division, saying that the current division is faulty; for a genus is never divided into three species, but always into two.

Section 24.

The Platonists, taking up the Aristotelian division of the practical, come and divide the practical into two: the legislative and the judiciary.
The poet hints at this very thing, I say the legislative and the judiciary, by saying that Minos and Rhadamanthus were brothers (for both had Zeus as their father); Minos was a legislator and Rhadamanthus a judge. He hints that the legislative and the judiciary were born from one practical philosophy. He says again that Minos was older in time, and Rhadamanthus was younger.
Having learned, therefore, through the preceding, what philosophy is, let us come to what sort of thing it is.
Having learned what sort of thing philosophy is, let us come and learn why it exists.
So much for these things, in which, with God's help, are the Prelegomena to philosophy.

PRELEGOMENA WITH GOD TO PORPHYRY'S INTRODUCTION, FROM THE VOICE OF DAVID, THE MOST DIVINE AND GOD-MINDED PHILOSOPHER.

Intending, with God's help, to begin the present book, we shall investigate eight questions. These chapters are said to be the authority of what is customarily investigated by the commentators, as they hold the number of the entire discourse; for just as the head is the authority of all...