The idea that O'Sullivan describes in this quotation is A) manifest destiny. Manifest Destiny was an idea that O'Sullivan was responsible for popularizing in the 1800s. This political theory or ideology sought for the United States to expand its borders to the Pacific Coast based upon a god given right to expansion which he called Manifest Destiny.
After defeating China in their first war (1894-1895), Japan forced the Chinese empire to cede the island of Taiwan in 1895. And in 1910, the Japanese empire annexed Korea.