... Epitome troporum ac schematum et grammaticorum & rhetorum, ad authores tum prophanos tum sacros intelligendos non minus utilis quam necessaria

You see in this place, more chaste than Hippolytus, the Irony is against those who offer everything to the impious as examples of impiety, and joins that to the impious gods, to sacrifice the unwilling mother.

the people care, forsooth Cicero in Verrem Act. 7. What do you say, good guardian and defender of the province? He prefers Hippolytus in chastity, concerning an adulterer. He acts as Aeneas in the thing itself, concerning him who violated his father. Amos 4. Come to Bethel and do impiously, to Gilgal and multiply prevarication. Go now and trust too much in successful things. Go now and place your hope in your fortune, Verg. Aeneid 7.
Go now, offer yourself to ungrateful dangers, O mocked one,
Lay low the Tyrrhenian ranks, cover the Latins with peace.
Go and do it more. And other figurative commands or permissions of this flour, which have the force of prohibiting. Furthermore, forsooth and truly, particles seem especially apt for irony.

The word Σαρκάζειν signifies as a man who is an angry dog; this transfer is for exprobration, as if one mocks with a certain angry meaning. Hence Sarcasm is when an enemy mocks an enemy with calamity.

4 Sarcasm Σαρκασμὸς, is an expression full of hatred and hostile mockery. Or a joke with bitterness, like a cat playing with a mouse; the cat's jest is the mouse's death.
Mancinellus:
Sarcasm is a derision full of hatred from an enemy.
From σαρκάζω, I laugh bitterly. Verg. Aen. 2.
Pyrrhus to Priam.
You will therefore carry back these things and go as a messenger,
To my father, the son of Peleus, those sad deeds of mine. The same Aen. 12.
Lo, measure the fields and the Hesperia which you sought in war,
O Trojan, lying down. From use and pleasure and the brave, the brave.

5 Asteismus Ἀστεϊσμὸς, Urbanity, is a long-fetched place, and thus unexpected about some absurd thing. Or it is a witty urbanity of a joke lacking rustic simplicity. A facetious and civil sarcasm.
From this gather that the places of Asteismus ought to be pleasant jokes.