In the great hall of the Capulets, all is a-bustle. The servants work feverishly to make sure all runs smoothly, and they set aside some food to make sure they have some enjoyment of the feast as well. Capulet makes his rounds through groups of guests, joking with them and encouraging all to dance.
From across the room, Romeo sees Juliet and asks a serving-man who she is. The serving-man does not know. Romeo is transfixed; Rosaline vanishes from his mind and he declares that he has never been in love until this moment. Moving through the crowd, Tybalt hears and recognizes Romeo’s voice. Realizing that there is a Montague present, Tybalt sends a servant to fetch his rapier. Capulet overhears Tybalt and reprimands him, telling him that Romeo is well regarded in Verona, and that he will not have the youth harmed at his feast. Tybalt protests, but Capulet scolds him until he agrees to keep the peace. As Capulet moves on, Tybalt vows that he will not let this indignity pass.
A hyperbole is an exaggeration that is not meant to be taken literally. It is usually used to make a persuasive point or to add emphasis. In this case, "opening a door to eternal tyranny" is an example of an exaggeration of this type. While it is likely that tyranny will not be eternal (the country itself will not be eternal), its purpose is to emphasize the risk of keeping the seat of governent vacant.
In this sentence "intensive" is used incorrectly. Intensive means very concentrated or focused on a specific subject. The sentence should say "for all intents and purposes". This does repeat the idea of purposes because someone's intent is their purpose, but that is the correct phrase that is commonly used. It comes from 16th century English law and means "in every practical sense".
