Which should I use with "neither/nor": "has" or "have"? [duplicate]

There is no reason to pluralize "version" in the second example. So has is the obvious choice, in my opinion.

Regarding your first example, I don't think there's any absolute rule in the sense of one being always right and the other always wrong. For that particular sentence, and in general, the singular has would be more common. But not many people would seriously object to have, even if they wouldn't say it themselves. I don't disagree with what this chap says.

Regarding the second example, I expect someone will say it's ok, but I don't like the pluralising of versions at all. It just seems like a futile attempt to justify have, which is at best somewhat suspect in the first place.

Your first sentence is another way of saying:

The first version of the original, written in Latin (the language of science at the time), has not survived until our time; neither has the second [version].

In this formulation, there is no question but that 'has' is correct. (You could use 'nor' in place of 'neither'; in fact, my first version of this text did, but it didn't survive until the time I hit submit.) On that basis, I think that 'has' is also better for your 'neither/nor' version, though I agree with FumbleFingers that 'have' is not traumatically wrong and few would object to it, even if the strictest of grammarians could object to it.

In your second sentence with 'versions', there is no question that you need 'have'. If you extend the list of cited versions:

Neither the first nor the second, fourth or fifth versions of the original, written in Latin (the language of science at the time) have survived until our time[, but fortunately a battered copy of the third edition shows...]

So, if you use the singular 'version', use 'has'; if you use the plural 'versions', use 'have'.