The adverb form of "particular," the word particularly means "in a focused, precise manner." You looked for stones that had the proper qualities, particularly rounded edges and elongated shapes. Careful near the windows.
The idea of particularly hails from the Lower Latin particularis, which meant "a particle," and in English took on the idea of something "pertaining to a single thing or person." Later, the word was refined to take on the idea of an exactness of detail. Journalist Ambrose Bierce applied the word as emphasis to his definition of incompatibility: "In matrimony a similarity of tastes, particularly the taste for domination."