In "Ulysses," what lines would encourage someone who needed to go forward despite the temptation to give up the struggle?
"Ulysses" is about a once great warrior trying to come to terms with being an older, less active king. Although this is a poem about Ulysses refusing to accept a more passive lifestyle as an older man, the poem can easily be read more generally as an allegory for making the most of your time, facing obstacles, and refusing to rest on your laurels.
In the first part of the poem, Ulysses expresses his boredom with his slow-paced life. Then, he reminisces about his adventures and knows that his son is more apt for this type of life. Ulysses needs adventure.
From line 44 until the end is basically a motivational speech. This entire final section is filled with encouraging lines. The final part of the poem/speech is the most rousing:
Tho' much is taken, much abides; and tho'
We are not now that strength which in old days
Mov'd earth and heaven, that which we are, we are:
One equal temper of heroic hearts,
Made weak by time and fate, but strong in will,
To strive, to seek, to find, and not to yield. (65-70)
This section can be applied to one individual although, in a modern context, it does sound more like a speech given by a coach to a team or by a sergeant to his/her soldiers.
Some critics have noted that this is a poem about Ulysses being selfish. He doesn't want to sit at home and be with his family. He only wants adventure, for the experience but also for the accolades.
Other interpretations consider the poem as a message of battling through life's hardships to have richer experiences and not to give up. Those hardships and obstacles are described literally and metaphorically in this poem as the forces of nature. These include the seas ("It may be that gulfs wash us down"), weather ("That ever with a frolic welcome took / The thunder and the sunshine"), and time ('Tis not too late to seek a newer world").
Thinking of time, this poem is basically saying "it's not too late; we can still succeed."