A post from 2012:
The Borgias may well have poisoned Cardinal Orsini. But it didn't happen until years after the Showtime series shows it, and certainly not in the manner shown.
Here is the real story of Cardinal Orsini's alleged poisoning: in 1503, Alexander had him thrown in the Castel Sant'Angelo, where he died abruptly without a mark on him. The pope had his body displayed publicly, to quell rumors of poison. It didn't work.
Pope Alexander VI already had a reputation as a poisoner because he imprisoned many powerful Italians when he confiscated their land, which had once belonged to the papacy. Many of his prisoners died abruptly and mysteriously.The Italian aristocracy, who hated the land seizures and Alexander, screamed "poison," as well as accusing the Borgias of many other nasty things, some of which are likely true. But rumors that would have died abruptly in previous generations were preserved and "went viral," Renaissance style, because of a new invention: the printing press. Libel became fact, without careful examination.
The sheer number of prisoners who died while in Pope Alexander's custody is powerful support for the theory that they were poisoned. Modern criminal defense lawyers, however, would quickly shred the case against the pope. There is nothing to prove that Alexander ordered the poisonings, assuming they occurred. Why not suspect Cesare Borgia or his hired assassin Michelotto, who were known killers? Or some underling who assumed he would be rewarded for eliminating the Borgias' enemies? Were prisoners forced to drink the prison well water, and was it somehow contaminated? The Castel Sant'Angelo is not more than 100 feet from the Tiber, which had been a sewer for centuries. Cardinal Orsini was middle aged, debauched and outraged at his imprisonment–might he have suffered a heart attack? Or died from one of the many natural causes that constantly caused premature deaths in this unhealthy era? It is all speculation.
Lucrezia Borgia's reputation as a poisoner is largely derived from a 19th century opera by Donizetti, whose libretto is pure fantasy (as opera usually is). Though some contemporaries labeled Lucrezia a poisoner along with the rest of her family, no one ever identified her supposed victim(s), much less a motive. Unquestionably, Lucrezia suffered guilt by assocation with her infamous father and brothers. She was no angel, but it's unlikely she was a killer.
For a fun and accurate history of the Borgias read my mystery, A Borgia Daughter Dies, which you can get here: https://www.amazon.com/Borgia-Daughter-Dies-history-Machiavelli-ebook/dp/B007WONQV2/ref=sr_1_1?ie=UTF8&qid=1501519534&sr=8-1&keywords=A+Borgia+Daughter+Dies or on Smashwords. Also available in paperback.