[1] This is part of a Stoic doxography, reproduced with small variations from Diogenes Laertius 7.134 (see SVF 2.299 and 2.300).
[2] Or "that which acts".
[3] "That which is acted upon".
[4] This is the Stoic theory according to which the cosmic order is not everlasting but recurrently passes away. However, this destruction should not be understood as a destruction in the strict sense. Death is thought to be the separation of soul from body. But the "world soul" is not separated from the "world body" but it goes on growing until it becomes coextensive with the whole matter. The permanent world restoration is always preceded by a conflagration (ekpurosis), a sort of cosmic burning in which all things, except god (a "principle"), are consumed. For evidence on Stoic conflagration see Stobaeus, Eclogae 1.20, p.171 Wachsmuth; Eusebius, Evangelical Preparation 15.18.3; Nemesius, On the nature of man chapter 38; Plutarch, On common conceptions 1075D.
[5] In Diogenes Laertius 7.134, some mss give "bodies" (somata), and this reading is probably better according to the philosophical context. Certainly according to the Stoic orthodoxy, the incorporeals (time, void, "sayables" and place) are inexistent (or rather "subsistent"), and for this reason they have no real causal power. If something is a cause in the strict sense (and indeed "the active" is the cause), it must be bodily. As frequently noted, the Stoic principles should be bodies precisely because they are active and passive (see Mansfeld [1978], 169). In an example, presumably Stoic, quoted by Sextus Empiricus at Adversus Mathematicos 9.211, it is said that both the cause (the sun) and the caused object (a stone) are bodies. The cause is a body acting upon another body. For discussion on this philological issue see Long & Sedley (1987) vol. 1, 273-274 and vol. 2, 266 and Mansfeld (1978) 162-63 & 169.