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Ophelia tells her father that Hamlet has expressed his love for her "With almost all the holy vows of heaven." Polonius calls Hamlet's words "blazes" and says that they are insincere. By saying that they give more light than heat and are "extinct in both," he means that they are lacking in both light and heat. They are figuratively lacking in honesty and in genuine emotion. Further, Polonius says, "You must not take [these blazes] for fire." The old man is afraid that Hamlet is only using a lot of insincere words in an attempt to seduce his innocent and naive daughter. "Blazes" is the key word here, and evidently Polonius means something like "flashes" or "flares." No doubt the old man would be very happy to have Prince Hamlet fall in love with his daughter if he thought Hamlet was sincere.
Ophelia tries to tell her father, Polonius, that she believes the professions of love that Hamlet has made to her are sincere. However, Polonius believes that these pretty words are essentially just traps to ensnare Ophelia and persuade her to sleep with Hamlet. He does not believe that Hamlet actually loves her, and he tries to caution her against believing him or allowing herself to fall prey to Hamlet's traps. He refers to Hamlet's vows of love as "blazes" that give "more light than heat, extinct in both / Even in their promise as it is a-making, / [She] must not take for fire." He means that Hamlet's loving words, his blazes as Polonius refers to them, cease to provide either light or heat (this is what he means by "both") almost as soon as they appear. They might seem strong and hot, but, ultimately, they provide no benefit to her.
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