Anaximander, answered from the texts and cited to the page.
The apeiron is the divine encompassing principle from which all things come to be and to which all things return. It is boundless (without limit in extension), eternal (without beginning or end in time), ungenerated (because anything generated would be generated from something else, and the apeiron is that-from-which everything else is generated), indestructible (because nothing more fundamental could destroy it), and divine in the precise sense that it surrounds (periechei) all and steers (kybernai) all.
Aristotle's treatment in Physics 203b6-15 is the most faithful surviving testimony, even where Aristotle himself misreads my doctrine through his own categories. The apeiron is not the indefinite primal stuff between the elements that Aristotle's Theophrastean tradition reconstructs by analogy with Anaximenes's aer and Heraclitus's pyr; that reading is the cost of trying to slot my principle into the four-element scheme of later Greek physics, where the principle of the cosmos must be a materia prima in the technical sense.
The apeiron does not have the place of materia prima in my system; it has the place of the divine source-and-encompasser. The opposites (hot/cold, wet/dry) separate out from the apeiron in the process of cosmogony; the apeiron itself is not one of them and is not between them.123
Ἀναξίμανδρος [... = P5] ἀρχήν τε καὶ στοιχεῖον εἴρηκε τῶν ὄντων τὸ ἄπειρον, πρῶτος τοῦτο τοὔνομα κομίσας τῆς ἀρχῆς. λέγει δ' αὐτὴν μήτε ὕδωρ μήτε ἄλλο τι τῶν καλουμένων εἶναι στοιχείων, ἀλλ' ἑτέραν τινὰ φύσιν ἄπειρον, ἐξ ἧς ἅπαντας γίνεσθαι τοὺς οὐρανοὺς καὶ τοὺς ἐν αὐτοῖς κόσμους· ἐξ ὧν δὲ ἡ γένεσίς αὐτὸ coni.Early Greek Philosophy Vol II, Anaximander chapter, pp. 13–14
When this was torn away and enclosed within certain circles, the sun, the moon, and the stars were formed. He also says that at the beginning human beings were born from animals of different species, because of the fact that the other animals nourish themselves quickly by themselves, while only human beings are in need of a long period of nursing; that is why, being of this sort, they could not have survived at the…Early Greek Philosophy Vol II, Anaximander chapter, pp. 19–20
Diels suggests that this sentence is lacunose and supplemented, "The wheel of the sun is twenty-seven times that of <the earth, nineteen times that of> the moon; and the sun occupies the highest position, <and after it the moon,> and the circles of the fixed stars <and of the planets> the lowest one" (cf. D22, D24). D8 (< A10) Ps.-Plut. Strom. 2 (= Eus. PE 1.8.2) μεθ ̓ ὃν Ἀναξίμανδρον [..Early Greek Philosophy Vol II, Anaximander chapter, pp. 18–19
The interpretation of the apeiron is the central contested question in Anaximander scholarship. Aristotle's report at Physics 203b6-15 has been the starting point for every modern reconstruction; the question is how much of Aristotle's framing reflects Anaximander's own thought and how much is Aristotle's retrospective categorization within the arche- and-stoicheion schema of his own physics. The "indefinite primal stuff" reading dominated the older scholarship (Burnet, Zeller). Werner Jaeger's Theology of the Early Greek Philosophers (1947) emphasized the divine character of the apeiron. Kahn's Appendix II (1960) gave the modern definitive reading of the apeiron as the divine encompassing principle, not the indefinite material substrate. KRS (1957) takes a compatible position with characteristic philological caution. The strongly-boundless-in-extension reading has its defenders (Heidel, Cornford in some moods) but is not the consensus view.