Thurificati: Those who had burnt incense on the altar before the statues of the gods. From Latin thurificare – "burn incense"

What do the donatists believe?

Donatism was a Christian sect leading to a schism in the Catholic Church, in the region of the Church of Carthage, from the fourth to the sixth centuries AD. Donatists argued that Christian clergy must be faultless for their ministry to be effective and their prayers and sacraments to be valid.

What does Libellatici mean?

Those who during the Decian persecution (249–51) procured certificates (libelli) by purchase from the civil authorities stating that they had sacrificed to pagan idols, when no such sacrifice had been made. From: libellatici in The Concise Oxford Dictionary of the Christian Church »