It depends on the position of αὐτός.
When it's in attributive position, it means 'same': ὁ αὐτὸς δοῦλος (also, more rarely, δοῦλος ὁ αὐτός or ὁ δοῦλος ὁ αὐτός), 'the same slave.'
Example: Antiphon 5.50 ('On the murder of Herodes'):
ποτέρῳ οὖν εἰκός ἐστι πιστεῦσαι, τῷ διὰ τέλους τὸν αὐτὸν ἀεὶ λόγον λέγοντι, ἢ τῷ τοτὲ μὲν φάσκοντι τοτὲ δ᾽ οὔ;
Which, then, ...
You are confusing gĕnu, -ūs ("knee") and gĕnus, -ĕris ("origin, lineage, stock").
The latter is a 3rd declension neuter noun, so the accusative singular is the same as the nominative singular. Hence, to fill in the blank:
Augustus affirmed that his lineage had arisen from Jupiter.
It's for emphasis, and older than the use of ipse as an intensifier. From Allen & Greenough §143.d:
Emphatic forms of tu are tute and tutemet (tutimet). The other cases of the personal pronouns, excepting the genitive plural, are made emphatic by adding -met: as, egomet, vosmet.
NOTE.—Early emphatic forms are mepte and tepte.
Wiktionary has a list ...
ἑαυτοῦ: this is reflexive because it's referring all the way back to the subject of the verb of speech that introduced this whole passage of indirect discourse. It's an "indirect reflexive": see the discussion in Smyth 1225ff.
οἱ: this is not the nom. pl. of the definite article, but the enclitic dat. sg. of the third-person pronoun, "(to) him". The way to ...
Are there cases where the reflexive pronoun is not used, even though it is referring to the subject of the sentence?
Smyth, at § 1228.a, notes: “instead of the indirect ἑαυτοῦ etc., there may be used the oblique cases of αὐτός.” As an example, he gives:
ἐπειρᾶτο τοὺς Ἀθηναίους τῆς ἐς αὐτὸν ὀργῆς παραλύειν
he tried to divert the Athenians from ...
In the 1929 Loeb edition of Critias (trans. R. G. Bury, p. 266), there is a rough breathing on the second pronoun of your question:
which indicates that it is a contracted reflexive pronoun and, therefore, indeed referring to the gods' disposition.
EDIT Of course, this isn't the definitive argument for a reflexive pronoun - it could be a typo or even an ...
Tacere means "to be quiet", not "to make quiet".
Unless you want to do something like "make it so that your mind is quiet", tacere is not an option.
One possibility in this direction is cura ut mens tua taceat, "take care that your mind becomes silent".
The verb tacere does work for "quiet yourself".
The simple order tace means "be quiet".
If you want to ...
The verb extendere is transitive, meaning it expects a direct object. The verb means to prolong, spread out, or extend something. So, the se here makes the verb reflexive. The scientia Dei isn't spreading something else out; but rather it is itself spread out so that it extends over a (metaphorical) area.
We could translate the last portion this way: the ...