"Why tarriest thou?..."See in text(Rappaccini's Daughter)
“Tarriest” comes from the verb “tarry,” which means to delay, wait, or postpone. “Thou” is a second-person subject pronoun, an archaic form of “you.” Beatrice is telling Giovanni to hurry up and join her in the garden.
"You are a connoisseur in flowers, signor..."See in text(Rappaccini's Daughter)
A “connoisseur” is someone who has expertise or highly developed taste in a given area. Beatrice says that Giovanni is an expert of flowers. As this is based on the fact that he merely purchased a bouquet, the sincerity of this statement is unclear. Either she is naive and truly charmed by him, or she is flattering him in order to manipulate him.
“Delusory” is an adjective and means the same thing as “delusive.” When something is delusive it is false or misleading. Generally, Giovanni is progressing onward in his relationship with Beatrice without thinking, but, occasionally, he wonders if those feelings are false or misleading.
"the arcana of medical science..."See in text(Rappaccini's Daughter)
“Arcana” is a noun and means “secrets” or “mysteries.” Baglioni vows to use the secrets and mysteries of medical science to preserve him from any harm. This develops a similarity between Baglioni and Rappaccini: they are both experimenting with medical sciences. It also suggests that medical science is a mysterious, secretive field, and thus perhaps dangerous or foreboding.
"the imperturbable professor..."See in text(Rappaccini's Daughter)
The adjective “imperturbable” indicates that Baglioni is reliably calm; he doesn’t get upset. This contrasts with Giovanni, who is prone to volatility and getting swept away by his emotions.
"the professor's sagacity..."See in text(Rappaccini's Daughter)
The noun “sagacity” refers to intelligence or good judgement. Giovanni has been avoiding Baglioni because he knows Baglioni is clever enough to guess his secrets, such as his continued relationship with Beatrice.
"the vicissitudes..."See in text(Rappaccini's Daughter)
The noun “vicissitudes” refers to sudden, dramatic changes in fortune or circumstance. Giovanni sees the water in the fountain as immortal, whereas other elements of the garden alternate between abundance and decay.
"the armorial bearings of a family long since extinct...."See in text(Rappaccini's Daughter)
The adjective “armorial” refers to heraldry, the practice of landed, wealthy families bearing a coat of arms during the Middle Ages. The mansion in which Giovanni resides has its family’s coat of arms displayed above the door. This reveals the greatness of the house itself, as well as a sense of decay that comes from a formerly powerful family that is “long since extinct.”