The Fountain Jump

From the introduction: It is the year of our lord Fifteen Hundred - The age of exploration is upon us, and the New World and all its mysteries lie ahead. Fortune, Glory, Immortality await those who have the strength to obtain it. But it is also the 2000th year of the Common Era - The Modern Age, just on the cusp of greatness, the world in all its technological wonder awaits brilliant minds willing to work for what they want and dedicated enough to change the future. And yet, it is also the year 2500 - Mankind has achieved immortality, freedom from all disease, and mastered reactionless interstellar travel. You have just jumped into all three of these time periods, as three different versions of yourself.