"To live" is fine. It indicates that the living took place at the point of reference -- the second half of the 17th century -- when it was exciting, or when it must have been exciting. The point of reference is in the beginning or middle of someone's life, not toward the end of it.

"To have lived" could be used, too. This would indicate that, at the point of reference -- the person's life would be over, or almost over. This would be at the end of the second half of the seventeenth century.

For a previous discussion of a similar subject, see this discussion particularly Marilyn's post at the end.

https://thegrammarexchange.infopop.cc/eve/forums/a/tpc/f...911099123#8911099123

Rachel

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