But if, because they happened in a foreign land, you don't know of the exile of Anaxagoras, the poison of Socrates, or the torture of Zeno, still you could have known about Canius, Seneca, Soranus, and others like them -- their memory is neither very old nor very obscure.
Socrates, of course, is obvious, but to refresh my memory, here's some brief background on these.
The Pre-Socratics
Anaxagoras: Anaxagoras taught in Athens for several decades. He famously taught that the sun was just a fiery rock. Apparently he was, for this reason, put on trial for impiety and sentenced to death. He fled to Lampsacus, where he lived until his death.
Zeno: Zeno, the same Zeno famous for the paradoxes, was said to have participated in a revolt against the government of Elea; for which reason he was put on a mortar and pounded to death.
The Stoics
Canius Julius: Canius was a nobleman in the reign of Caligula; Boethius himself tells the story of how Caligula accused him of knowing about a secret conspiracy, to which Canius replied, "If I had known about it, you never would have." He was put to death. Another story about him is that just before he was executed someone asked him what he was thinking about, and he replied, "I'm thinking that I want to see if at the instant of death I can perceive the motion of the soul, and whether it has any feeling at that point." He was put forward by Seneca as an example of tranquillity of soul.
Seneca: Seneca, of course, was Nero's advisor, apparently on good terms for a short while, but this wasn't to last. Nero eventually suspected Seneca of participation in a conspiracy to assassinate him, and ordered him to commit suicide. He slit several veins and, apparently, slowly bled to death, although there are different versions of the story, one famous one in Tacitus, according to which he put himself in a warm bath to speed up the bleeding and suffocated from the steam.
Soranus: Barea Soranus was a Roman senator under Nero who became well known for treating provincial cities fairly; he once refused to punish a city for protecting the statues of its gods from Imperial agents trying to spread the worship of the emperor. Although an old man, he was brought to trial on charges of treason; one of his accusers was one of his old tutors, the Stoic philosopher Publius Egnatius Celer. He was put to death. Under the rule of Vespasian, Musonius Rufus, best known as the teacher of Epictetus, managed to get Egnatius Celer put to death for the deed, and Egnatius Celer passed into history as a standing example of treachery. Soranus's daughter Servilia was also put to death under Nero, allegedly because she consulted the dark arts in order to determine her father's fate.
While Stoics are a good source of philosophical deaths, it's notable that just prior to the passage Philosophy made some very critical comments about Epicureans and Stoics both; it is one's character that she thinks makes one a true philosopher rather than someone violently trying to tear off one little bit of Philosophy's robe. The two last, Seneca and Soranus, are also notable in that Nero comes up several times in the work as a representative symbol of the unjust tyrant.
UPDATE: Just realized I forgot to give the edition for the quote. It's from Relihan's translation, in the Hackett edition (2001).