Latin tragedy: Seneca
If Shakespeare was unlikely to have known much
about Greek tragedy except at second hand, he
would certainly have known about Seneca.
Seneca was a Roman tragedian who was born within a few years of Christ, and died in about A.D. 65. His tragedies, probably written to be read rather than acted, are indebted to their Greek originals, but add to them a depth of horror and revenge which becomes, at times, almost sensational*.
The Elizabethans also admired Seneca for his elevated style. The highest praise Sir Philip Sidney could give the one English play of which he approved--Gorboduc--was that it was "full of stately speeches and well sounding phrases, climbing to the height of Seneca his style."
Footnotes
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Staging violence
The Elizabethan audience was accustomed to violence on stage: in the miracle plays, grimly realistic soldiers nailed Christ to the cross, for example.
(Click here to see more about the audience.)