nisi . . . non . . .

I know what this must be saying (and other translators agree), but a non seems to reverse the meaning.

  • Praeter has duas species argumentandi perfectas aliae sunt imperfectae duae, quae,
    nisi captiosae sint et non in speciem tantum,
    sed vere conficiantur, ad istas semper redigi possunt. (Rudolph Agricola)

must mean

  • Besides these two perfect kinds of argument, there are two other imperfect ones, which
    if they are not captious and not just specious,
    but are constructed truthfully, can always be reduced to these.

Why is the non in there?

If it were not there, would the condition not be

  • unless they are captious and just specious

With the non, doesn’t the condition say

  • unless they are captious and not just specious

the opposite of what it must be saying?

Should nisi . . . non be read as if not this . . . and also not that, rather than unless this . . . and not that?

I suppose si is implicitly supplied from nisi before non. More common is the use of “nisi si” instead of nisi. In both there’s logical slippage, but in opposite directions.

Thanks @mwh. That helps.