How did European ideas about the natures of, and the relationships between, science and religion change during the 17th century?17th century ideas
This is a good question. Stating from the Renaissance, people began to question the authority of the church. Within this context, science was beginning to be seen as an alternative authority. We can even see the Protestant Reformation as an outflow of the impulse of the Renaissance. In many ways, the Reformation was an intellectual movement that questioned and protested.
During the 17th century, we see the further growth of science. For example, the great scientist and mathematician Sir Isaac Newton was born in 1642. So, we see the further development of what we would call the scientific method. However, with this said, I am not implying that the church was dying. Isaac Newton was a religious person. Moreover, we see some of the great religious documents created during this time as well, such as the Westminster Confession of faith.
Based on the above observations, we can say that people began to see science and religion as twin authorities. In time, the scales would tip and science would gain the upper-hand, at least in Europe. This period is the beginning of the age of reason or what scholars call the Enlightenment.