How we cite our quotes: (Paragraph)
Quote #1
[…] naval units of the Communist regime in Vietnam, in violation of the principles of the Charter of the United Nations and of international law, have deliberately and repeatedly attacked United States naval vessels lawfully present in international waters, and have thereby created a serious threat to international peace […] (2)
This is kind of like Congress saying, "just to be perfectly clear we're talking about war here." By discussing the military attacks against American ships, the U.S. has a defendable reason for going to war. Typically, when a nation is purposefully attacked by another nation that's grounds for war, and other nations would probably agree. (Think Pearl Harbor.) Therefore, Congress sets the scene for war by focusing on the whole "we were attacked" statement.
Quote #2
[…] the Congress approves and supports the determination of the President, as Commander in Chief, to take all necessary measures to repel any armed attack against the forces of the United States and to prevent further aggression. (5)
This is the first of two statements clearly implying war. Notice that "going to war" or "declaring war" are nowhere to be seen, which is probably on purpose. In this case, "repel any armed attack" suggests using military force (duh), yet the word choice makes it seem more defensive and less aggressive. However, the "all necessary measures" part clearly suggests using a lot of military force.
Quote #3
[…] the United States is, therefore, prepared, as the President determines, to take all necessary steps, including the use of armed force, to assist any member of protocol state of the Southeast Asia Collective Defense Treaty requesting assistance in defense of its freedom. (6)
The second statement about waging war, this quote specifically references armed force. Most people would probably agree that using armed force at this level means war, but again, the word "war" isn't found anywhere. Notice again the crafty choice of words, as the Congress spins this as a defensive operation, assisting nations who are in harm's way. Being defensive always looks better than being offensive.