hōsautōs

This is a pointing word, not a word with content of its own. It is built from the ordinary "as" (ὡς) joined to an old form meaning "in this very way," so it says something close to "just so." Everything it means is borrowed from whatever it points back to: name an action, a fate, or a standard, and this word claims that the next case matches it.

Two settings account for nearly every use.

• In stories and parables it works as a refrain: a landowner goes out again and does the same, tenants seize a second group of servants and treat them the same, one brother after another marries the widow and dies the same way.
• In the letters to Timothy and Titus it opens a new paragraph of instruction: older men, then older women, then younger men, each group brought under the same seriousness of life as the group before.

In both settings the word is doing real work rather than filling space. In a story it lets the writer skip the repetition and still insist that the second episode is a true copy of the first. In a list of instructions it refuses to let the next group off lightly: whatever was just required is required again here.

It overlaps almost entirely with the more common word for "likewise" (ὁμοίως), and the two can stand in parallel sayings without any change of meaning. This one is the heavier, more formal of the pair, and it presses sameness a little harder. It should not be confused with the plain "thus, in this way" (οὕτως), which describes how something is done without necessarily comparing it to anything.