in this case a conditional, not a circumstantial, participle.
Zembel: I apologize for not being clearer in my initial post. Conditionals are a type of circumstantial participle.
Circumstantial participles can generally be sub-divided into different (potentially overlapping) types: temporal participles, causal, conditional, concessive, final, and others. A few examples of circumstantial ptcps:
(1) Temporal
ἀφικόμενος ἔπειθε τὸ πλῆθος πολεμῆσαι.
Having arrived, he tried to persuade the people to go to war.
After he arrived, he tried to persuade… [temporal]
The addition of a word like ἅμα or εὐθύς would make the participle clearly temporal: ἅμα ἀφικόμενος ἔπειθε τὸ πλῆθος πολεμῆσαι (As soon as he arrived, he tried…)
(2) Causal
πολλά τε καὶ κακὰ παθὼν ἔπειθε τὸ πλῆθος σπονδὰς ποιήσασθαι.
Having suffered many terrible things, he tried to convince the people to make a truce.
Since/because he had suffered many terrible things, he tried… [causal]
The addition of a word like ὡς, ἅτε, or οἷα would make the ptcp clearly causal: οἷα πολλά τε καὶ κακὰ παθὼν ἔπειθε τὸ πλῆθος σπονδὰς ποιήσασθαι.
(3) The last sentence could also be understood as concessive.
πολλά τε καὶ κακὰ παθὼν ἔπειθε τὸ πλῆθος σπονδὰς ποιήσασθαι.
Having suffered many terrible things, he tried to convince the people to make a truce.
Although he had suffered many terrible things… [concessive]
The addition of a word like καίπερ makes the ptcp clearly concessive:
καίπερ πολλά τε καὶ κακὰ παθὼν ἔπειθε τὸ πλῆθος σπονδὰς ποιήσασθαι
(4) Conditional
πολλά τε καὶ κακὰ πάσχων ἐθελήσεις πολεμῆσαι.
Suffering many and terrible things, you will be willing to go to war.
If you suffer many terrible things… [conditional]
Most of these could be understood in multiple ways. Context usually makes it clear.
Those are circumstantial ptcps. There are also non-circumstantial ptcps, like attributive ptcps or supplementary ptcps. Your book will introduce these too. They are very common.
I hope that’s a little clearer.