Not a lot of new information for these two chapters, but it rounds-out participles.
Remember that a Participle is a “Verbal Adjective” so it is based on the same root/stems as a Verb, but it modifies a Noun (head noun).
However, a Participle can function as a “Substantive” (just like an Adjective can), in which case there would not be a noun to modify, you have to supply it when making your English translation.
You will almost always, however, have a definite article that doesn’t go with anything else in the sentence as a clue.
To translate a Participle, start by adding an “-ing” to the end of the meaning of the verb on which it is based.
From there, if it’s present try adding “while” in front or “after” if it’s aorist or perfect.
For the Perfect Participle, it is “completed action” meaning it will be in the past, but the effects are still true (exactly like a perfect verb)
A Perfect ACTIVE Participle has -κ- added to it (remember the -κα- for Perfect Active Verbs) and then an -οτ- added as well. (-ντ- is usually the sign of the Active Participle, but in this case, the ν drops out, leaving the connecting vowel ο and τ to form -οτ-).
Just like verbs, there is reduplication at the start of the word, and then the usual case endings are on the end.
example: λελυκοτες (reduplication + stem + κ + οτ + case ending: λε+λυ+κ+οτ+ες)
For the Perfect Participle, it is translated “after having…” so λελυκοτες is “after having destroyed” – but you’ll want to smooth that out in your second pass into English.
See the master participle chart on page 283 in the book. This will tell you what you need to know for Participles.