When Shakespeare wrote this line, he was telling Brutus that he shouldn't blame the fault on his stars, but on himself. It was his fault that he couldn't find love or that it didn't work out. the Stars are not to blame for problems that he can not handle. However, in "The Fault in Our Stars'" Gus and Hazel both have cancer and they did nothing to themselves to get this. It was just destiny. But on the bright side, this situation they both faced brought them together and brings them closer. That is why I think John Greene titled the book "The Fault in Our Stars," because it was destiny or the aliment in their stars that brought them together.
In Shakespeare Play "Julius Caesar" Cassius tells Brutus that they need to rebel and take down Caesar. Cassius says that every man was born the same, so why would they nee to bow down to one man? Brutus knows he needs to help take a stand for the republic, although he is friends with Caesar. Cassius reminds his friend that the blame is not on the stars, its not on fate, the decision they make is based upon their human drive and condition.
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Now that we realized Shakespeare's meaning for the fault in our stars, we can look at the title of this book and see how they relate. In John Green's book "The Fault in Our Stars" Hazel and Gus both have cancer. This is not something they wanted, this is not a decision they made, This is their fate. This is something they had no control on, that they had to deal with and suffer with. However, Because of this, they were able to meet and get to know each other and fall in love. That was their fate. That was the fault in their stars.