Answer:
These lines are from William Bradford's 'Of Plymouth Plantation' aiming to offer a glimpse of the pilgrims' beliefs and their perspective to view the world. The paraphrased version of this excerpt can be:
The problems receded and thus, all the pilgrims were able to continue the journey on a single ship. They settled down again and moved ahead as the wind was buoyant now and it continued for several days. This encouraged them to move ahead, however, many of them started feeling dizzy and nausea due to being in motion constantly.