§5.1ἀρχὴ λέγεται ἡ μὲν ὅθεν ἄν τις τοῦ πράγματος κινηθείη πρῶτον, οἷον τοῦ μήκους καὶ ὁδοῦ ἐντεῦθεν μὲν αὕτη ἀρχή, ἐξ ἐναντίας δὲ ἑτέρα· ἡ δὲ ὅθεν ἂν κάλλιστα ἕκαστον γένοιτο, οἷον καὶ μαθήσεως οὐκ ἀπὸ τοῦ πρώτου καὶ τῆς τοῦ πράγματος ἀρχῆς ἐνίοτε ἀρκτέον ἀλλʼ ὅθεν ῥᾷστʼ ἂν μάθοι· ἡ δὲ ὅθεν πρῶτον γίγνεται ἐνυπάρχοντος, οἷον ὡς πλοίου τρόπις καὶ οἰκίας θεμέλιος, καὶ τῶν ζῴων οἱ μὲν καρδίαν οἱ δὲ ἐγκέφαλον οἱ δʼ ὅ τι ἂν τύχωσι τοιοῦτον ὑπολαμβάνουσιν· ἡ δὲ ὅθεν γίγνεται πρῶτον μὴ ἐνυπάρχοντος καὶ ὅθεν πρῶτον ἡ κίνησις πέφυκεν ἄρχεσθαι καὶ ἡ μεταβολή, οἷον τὸ τέκνον ἐκ τοῦ πατρὸς καὶ τῆς μητρὸς καὶ ἡ μάχη ἐκ τῆς λοιδορίας· ἡ δὲ οὗ κατὰ προαίρεσιν κινεῖται τὰ κινούμενα καὶ μεταβάλλει τὰ μεταβάλλοντα, ὥσπερ αἵ τε κατὰ πόλεις ἀρχαὶ καὶ αἱ δυναστεῖαι καὶ αἱ βασιλεῖαι καὶ τυραννίδες ἀρχαὶ λέγονται καὶ αἱ τέχναι, καὶ τούτων αἱ ἀρχιτεκτονικαὶ μάλιστα.
"Beginning" (or "principle") means: (1) that part of a thing from which one would first move, for example, of a line or a road, this is the beginning from this end, but from the opposite end it is another; (2) that from which each thing would best come to be, for example, in learning, sometimes we must not begin from the first principle of the thing, but from where one would learn most easily; (3) that from which a thing first comes to be, while being inherent in it, for example, the keel of a ship and the foundation of a house, and in animals some suppose it to be the heart, others the brain, and others whatever other such part they may happen to choose; (4) that from which a thing first comes to be, while not being inherent in it, and from which motion and change naturally first begin, for example, the child from the father and the mother, and the fight from the insult; (5) that by whose choice the things that are moved are moved and the things that change change, just as the offices in cities, and oligarchies, and kingships, and tyrannies are called "beginnings" (or "authorities"), and so are the arts, and of these especially the architectonic ones.
ἔτι ὅθεν γνωστὸν τὸ πρᾶγμα πρῶτον, καὶ αὕτη ἀρχὴ λέγεται τοῦ πράγματος, οἷον τῶν ἀποδείξεων αἱ ὑποθέσεις.
Further, (6) that from which a thing is first known, this too is called the "beginning" of the thing, for example, the hypotheses of demonstrations.
ἰσαχῶς δὲ καὶ τὰ αἴτια λέγεται· πάντα γὰρ τὰ αἴτια ἀρχαί.
And "causes" are spoken of in as many ways, for all causes are principles.
πασῶν μὲν οὖν κοινὸν τῶν ἀρχῶν τὸ πρῶτον εἶναι ὅθεν ἢ ἔστιν ἢ γίγνεται ἢ γιγνώσκεται· τούτων δὲ αἱ μὲν ἐνυπάρχουσαί εἰσιν αἱ δὲ ἐκτός.
Therefore, what is common to all principles is to be the first point from which a thing either is, or comes to be, or is known; and of these, some are inherent, while others are external.
διὸ ἥ τε φύσις ἀρχὴ καὶ τὸ στοιχεῖον καὶ ἡ διάνοια καὶ ἡ προαίρεσις καὶ οὐσία καὶ τὸ οὗ ἕνεκα· πολλῶν γὰρ καὶ τοῦ γνῶναι καὶ τῆς κινήσεως ἀρχὴ τἀγαθὸν καὶ τὸ καλόν.
For this reason, nature is a principle, and so are the element, thought, choice, substance, and that for the sake of which; for the good and the beautiful are the principle of knowledge and of motion for many things.