The above page is from the 1823 Korean text Haedong Yeoksa sok (海東繹史續), which translates as "History of Korea - Supplement." It is also called Haedong Yeoksa Jirigo (海東繹史地理考) since it was the geography supplement to the Haedong Yeoksa (海東繹史). The text is stored in the National Library of Korea.
Korean historican Han Chi-yun (韓致奫) had spent about ten years writting seventy volumes of the Haedong Yeoksa (海東繹史), but he died in 1814 before he completed the geography portion (地理考) of the text. Han Chi-yun's nephew, Han Jin-seo, took over his uncle's work and completed the 15-volume geography section in 1823.
The document seems to be saying that Songdo (松島) and Usando (于山島) were just different names Ulleungdo (鬱陵島), which may help explain why Lee Gyu-won told King Kojong in 1882 that Usando was just another name for Ulleungdo. The following is a translation of the above text:
松島 于山島 鬱陵島UPDATE:
[兩朝平攘錄] 萬歷二十五年倭分屯松島蔚山釜山鎭書 謹案文獻備考于山島卽倭所謂松島也 輿地勝覽 于山鬱陵本一島地方百里新羅智證王時討服其國在今蔚珍縣正東海中水道提綱 蔚珍東隔海曰千山島曰 菀陵島千山卽于山之誤菀陵卽鬱陵也. 拾遺記 蓬萊山 高二萬里有鬱夷國王維送日本晁監序扶桑 若薺鬱島如萍鬱夷鬱島似指鬱陵島也.
Songdo, Usando, Ulleungdo
In the Yangjo Pyeongyang Rok (兩朝平攘錄), in 1597, the Japanese set up bases at Songdo (松島), Ulsan (蔚山), and Busan (釜山). I, Jinseo (鎭書), think that in the Munheon Bigo (文獻備考), Usando (于山島) is what the Japanese call Songdo (松島). In the Yeoji Seungram (輿地勝覽), Usan/Ulleungdo were originally one island with an area of 100 ri. During the time of King Jijeung of Silla (新羅智證王), that country was conquered and subjugated and was due east of what is now Uljin-hyeon (蔚珍縣). In the Sudo Jegang (水道提綱), east of Uljin is "千山島" (Cheonsando) and "菀陵島" (Wanleungdo). The 千山 (Cheonsan) was just a mistake for 于山 (Usan), and 菀陵 was just 鬱陵.
In the Seupyugi (拾遺記), Mount Bongrae (蓬萊山) is 20,000 ri high. There is Uliguk (鬱夷國). In Wang Yu's "Sending a forward to Japan's Nakamaro" (送日本晁監序), Japan (扶桑) is like shepherd's purse (薺). Uldo (鬱島) is like duckweed (萍). Uli (鬱夷) and Uldo (鬱島) seem to refer to Ulleungdo (鬱陵島).
Later, in the same text is the following:
The Cheonsando (千山島) being referred to in the above passage is the one that appears just offshore of Pyeonghae (平海) on Chinese and many old Western maps of Korea. It seems that Wanreungdo (莞陵島), for which coordinates are given, may be considered a separate island. You can read the original below or go HERE, where you can find it on the third page.
蔚珍城東其東南隔海曰千山島謹案 千當作于 曰菀陵島. 東三十度極三十六度八分. 又西南數十里經平海城東南有小水口 水西出奉化城東大山. 合兩源流百里入海匕口正爲千山島.
On the east side of Uljin Fort (蔚珍城), in the sea to the southeast, are "Cheonsando" (千山島), of which I think 千 (천) should be corrected to 于 (우), and "Wanreungdo" (菀陵島), which is east 30 degrees, north 36 degrees 8 minutes. Also, some tens of ri to the southeast is the east side of Pyeonghae Fort (平海城). To the southeast of there is the mouth of a small river. The water flows from the west, from a big mountain east of the Bonghwa Fort (奉化城). Two sources merge and flow 100 ri to the sea. Just at the mouth of the river is Cheonsando (口正爲千山島).