EmergeEmerge means to come out into the open, or to become clear, to materialize. If you emerge from something, you must come out of it, whether literally or figuratively.
EX: As new details on the case emerge and new features are brought to light, public opinion has dramatically changed.
EX: The tennis star, wanting the most options available to him, made sure to emerge from his amateur league and enter the professional world as soon as possible.
The expression emerge victorious means to be successful after some period of a lack of success. If you emerge victorious, others or yourself may have doubted a positive outcome at one point.
EX: Though the trials were difficult, he felt that he would emerge victorious, and the anticipation of success helped him to persevere.
EX: Although the teams were evenly matched and both exhausted, the sports commentator knew who the more determined team was, and therefore who would emerge victorious.
ManifestThe verb manifest means to make visible or to make something seen or understood. In its adjective form, manifest means something that is clear or obvious.
EX: In order for the hard work you have put in in the gym to manifest itself in your actual appearance, you will have to control your diet as well.
EX: The lack of effort on Jim's part throughout the term was made manifest when he received his report. A manifesto is a document that explains the positions and beliefs of an organization or group.
A manifesto is meant to make the positions of the group clear or obvious to those who are reading it.
EX: After reading the Communist Manifesto in her politics class, Jemmica had a better idea of Marx's economic philosophy.
EX: In a manifesto explaining his resistance to the intrusiveness of technology, the recluse condemned the violations he claimed were a matter of habit among data gatherers.