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Our latitude in Shawnee is 35 degrees north, and we find Polaris 35 degrees above the northern horizon. Similarly, to sail west at a constant latitude Columbus kept the north star at a constant altitude above the horizon.
[Edit] Greyure's answer contains a serious error: At the northern summer solstice, it's possible to see roughly 11 3/4 degrees further south than at the equinoxes, so that would make the centre of the Southern Cross visible from any point south of 45 degrees north, though obviously it would be just on the horizon..