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Proteus appears alone on stage and delivers a big speech to the audience (a.k.a. a "soliloquy"), which takes up the entire scene. We'll break it down in a second, but the speech boils down to Proteus deciding to do what's best for Proteus.
At first, Proteus acknowledges that, if he leaves Julia and wrongs Proteus by loving "fair Silvia," then he's a jerk. But then, he suggests that "Love" is the culprit here and love is "tempt[ing]" him to betray his girl and his best pal. (Funny how that works out so Proteus is responsible for any of his actions, isn't it?)
Proteus goes on to say, "At first I did adore a twinkling star,/ But now I worship a celestial sun." Translation: Julia is pretty cute, but Silvia is insanely gorgeous.
Proteus then rationalizes that the only way he can be true to himself is by betraying Valentine and Julia.
Proteus then decides that Valentine will be his "enemy" and Julia will be "dead" to him.
Finally, Proteus resolves to get Valentine in big time trouble with the Duke of Milan – Proteus will tattle to the Duke that Valentine plans to elope with Silvia. The Duke, of course, will be enraged since he's got plans for his daughter to marry Thurio.