Final answer:
Dupin comes to his conclusions by critiquing the police's one-dimensional investigative approach and devising measures that consider the complete character and anticipated actions of the culprit, D—.
Step-by-step explanation:
In the passages provided, Dupin explains his conclusions by employing a logical and methodical approach to understanding the mind of the criminal and the inherent flaws in the police's investigative techniques.
He advises a thorough re-search of the premises, challenges the Prefect's conventional modes of search that are limited by uniform principles, and contrasts them with the uniqueness of the criminal's cunning.
Dupin underscores that the police fail when they only consider their own ideas of ingenuity and neglect to measure the intellect they are contending with, especially when it diverges from their own.
Dupin also recognizes the individuality and complexity of the culprit, D—, noting his desperation, nerve, and political motivations which influence his actions. Dupin's strategy involves understanding the entirety of D—'s character, including his role as a mathematician, poet, courtier, and bold intrigant.
By accounting for the totality of the circumstances surrounding D—, Dupin devises measures tailored to counteract his anticipations of the police's conventional tactics, ensuring a successful resolution.