JFK's inaugural address invokes the use of many rhetorical devices:
1. REPETITION: Many of his paragraphs started with "Let both sides..." I think this demonstrated his purpose to unify the country. Partisian politics are difficult throughout the course of an election and he was trying to bring the nation together after the contest.
2. PARALLEL STRUCTURE: This use of repeating grammatical structures creates a rhythm that envokes our attention:
Let every nation know, whether it wishes us well or ill, that we shall pay any price, bear any burden, meet any hardship, support any friend, oppose any foe, in order to assure the survival and the success of liberty.
These italicized words share the same grammatical format: verb + any + noun.
3. RHETORICAL QUESTION: These questions not meant to be answered allowed are positioned to make the audience think about how they would answer the question. Most speakers hope this create action:
Can we forge against these enemies a grand and global alliance, North and South, East and West, that can assure a more fruitful life for all mankind? Will you join in that historic effort?
4. ALLUSION (reference to something famous, in this case... God): JFK was specifically elected because of his Catholic background. He cites this at least twice:
the belief that the rights of man come not from the generosity of the state, but from the hand of God.
With a good conscience our only sure reward, with history the final judge of our deeds, let us go forth to lead the land we love, asking His blessing and His help, but knowing that here on earth God's work must truly be our own.
The italicized is an additional device: personification.
His rhetorical purpose in addition to unifying the country can be summed up in the statement he used that has certainly outlived his legacy: "And so, my fellow Americans: ask not what your country can do for you—ask what you can do for your country." He wanted to involve the people in the process from here on out.