The map shown below is from the 1873 Vienna International Exhibition. It shows "Take I." (Takeshima) and "Matsou I." (Matsushima) as Japanese territory. Notice that the Korean pennisula was only dotted in, and that no Korean placenames were listed. Not even Korean islands were drawn in, including Jeju Island, which suggests that the Korean peninsula was only dotted in for geographic perspective. Only Japanese territory was labeled, which shows that the mapmaker considered Takeshima (Take I.) and Matsushima (Matsou I.) to be Japanese. Mr. Tanaka Kunitaka writes about the map (in Japanese) HERE.
Though the "Take I." (Takeshima) on the map was almost certainly the non-existant island of Argonaut (mismapped Ulleungdo), and "Matsou I." (Matsushima) was almost certainly present-day Ulleungdo, which Japan had conceded to Korea in the 1690s, the map shows that the mapmaker, for whatever reason, associated both names with Japanese territory. It also suggests that other Western nations made the same associations.
The following 1881 Japanese map also shows Takeshima (竹島) and Matsushima (松島) as Japanese territory. The map seems to have been based on the 1873 map mentioned above. Mr. Tanaka Kunitaka talks a little about the following map HERE.
Even though Ulleungdo (Takeshima) had been conceded to Korea in the 1690s, Japanese maps in the 18th and 19th centuries continued to show Takeshima (Ulleungdo), in addition to Liancourt Rocks (Matsushima), as Japanese territory. See HERE. This conflicts with Korean claims that Japanese maps in the 1800s recognized both Ulleungdo (Takeshima) and Liancourt Rocks (Matsushima) as Korean territory.
Even though Japan conceded Ulleungdo (Takeshima) to Korea, Japan never recognized Liancourt Rocks (Matsushima) as Korean territory. In fact, there are no old Korean maps that even show Liancourt Rocks, which suggests that Korea did not even know about the islets before Japan officially incorporated them in 1905.