Even though Acts 1:17 is a short verse we'll cover it in two posts, looking at the verb forms κατηριθμημένος and ἔλαχεν in more detail.
ὅτι κατηριθμημένος ἦν ἐν ἡμῖν καὶ ἔλαχεν τὸν κλῆρον τῆς διακονίας ταύτης
for numbered he was among us, and he obtained a share of this ministry
From the previous verses we know that it is Peter speaking, and that the subject here is Judas Iscariot.
Κατηριθμημένος is a hapax legomenon. It is the masculine singular nominative, perfect middle/passive participle, of the verb καταριθμέω - 'I number among'.
The middle / passive makes sense here: it doesn't mean that Judas is numbering something or someone else, but that he is either numbering himself or being numbered (by others) among the disciples.
I wondered about the active form of this verb. It exists, as in this excerpt from Plato's Statesman. (Καταριθμεῖν is the present active participle.)
for dogs are not properly to be counted among gregarious creatures
Note that although the form is active, and the underlying meaning is something like 'people don't count dogs . . . ', the translation still puts it in the passive.
And, yes, I think dogs are gregarious too, but the sense here seems to be more that they are not a herding animal.
There is an English derivative from the root form of κατηριθμημένος - obvious when you see it, but hidden in a vowel change. The verb καταριθμέω is a combination of the preposition κατά and the verb ἀριθμέω - 'I number, I count'. Ἀριθμέω, in turn, gives us 'arithmetic' in English.
Next post - the long history of ἔλαχεν.