Of course the fictional time-traveller had to contend with all sorts of problems. Suppose he accidentally killed his great-grandfather when he was a boy - would he cease to exist and fade-out? But, if he didn't exist, how could he kill anyone? Would he pop in-and-out of reality at 60hz?
In 'The door into Summer' by Robert Heinlein, (1955), as an aside to the main plot of a regular guy getting stitched-up by a wily dame, an American lab-tech. called Leonard Vincent gets lobbed back into the 1400s by a mad-scientist, never to return. Somehow he makes his way to Renaissance Italy, ( who with- the ruddy Vikings? L. da Vinci b.1452-d.1519, so the bulk of his life is before Columbus ), and dreams up lots of doolally machines and dabbles in painting and stuff.....!
Actually, the best parts of this book, from a 21C viewpoint, are the electrics / electronics, which Heinlein visualises quite accurately with robots, CAD design centres and computers. Heinlein had a 'thing' about time travel; in his book 'Job', the main character, ( named after the Old Testament character tested by God), is doomed by some higher being to flick through parallel, but almost identical, universes every 2 weeks or so, with all his cash turned to worthless funny-money, loss of his friends, his possessions etc. The plot is that insignificant chance actions multipy chaos and create multiple futures- so which one is his particular America, and can he get back there?
Alan
