“Methought that to ascertain the hand who killed my friend was not impossible, and to punish the crime was just.” 

This comes early in Edgar’s letter to Mary—he is trying to discover who killed her brother by returning to the scene of the crime, an elm tree. The “hand” motif that runs throughout the novel appears here; this develops the theme of authorship of crimes. Also, Brown’s distinctive passive voice appears. The subject—the person who is ascertaining and punishing—isn’t stated. It’s implied that Edgar is the investigator, but the grammatical choice intentionally obfuscates him. 

“Knowledge is of value for its own sake, and pleasure is annexed to the acquisition, without regard to anything beyond. It is precious even when disconnected with moral inducements and heartfelt sympathies, but the knowledge I sought by its union with these was calculated to excite the most complex and fiery sentiments in my bosom.” 

Edgar reflects on his motivations for investigating Clithero as a suspect for murder. He is debating whether or not to spy on the elm tree where he saw Clithero. Curiosity does eventually get Edgar into trouble, but he believes the combination of a quest for knowledge and offering sympathy justifies his actions. The gothic genre frequently uses forbidden and dangerous knowledge as a trope.

“It was in the highest degree rugged, picturesque, and wild. This vale, though I had never before viewed it by the glimpses of the moon, suggested the belief that I had visited it before. Such a one I knew belonged to this uncultivated region.” 

This passage occurs when Edgar is following Clithero from the elm to a cave and develops the theme of nature as the site of the early American gothic. Even previously familiar nature—Edgar and Sarsefield would go on walks through this vale—becomes uncanny in the moonlight. Nature is wild, “uncultivated,” which causes fear in the white settlers of Pennsylvania.