I just Googled "CivDOS manual PDF download" and got quite lot of hits, one of which was
right here on CFC.
Although it's not technically the tree, if you didn't mind taking the half an hour or so needed to do it, you could at least use this page to reverse-engineer a hardcopy sketch version, starting from the most advanced techs (Robotics and Fusion, IIRC) and working backwards. Admittedly, the most basic 1st- and 2nd-tier techs (needing 0 or 1 prerequisite) aren't included here, since they're not part of the copy-protection, but most of them appear in the prereqs, and you could fill in the rest from the Civilopedia.
And if you didn't mind taking a little longer to optimise your layout, you could even print out the page, cut out each tech, and then shuffle them around/ stick them back down on a larger sheet (and draw in the arrows afterwards) -- or just use
something like this (NB found using Google string '"flow chart" creator software' -- no product endorsement should be inferred!).
EDIT:
While I was looking for the thread about 'tech hiding' (this is apparently the name of the mechanic) that I mentioned in my previous post, I found
this thread started by CFC user hydraulics, containing his self-made Civ1 tech-tree diagram. It could probably do with some layout optimisation, but it's all there...
EDIT 2: Son of EDIT
Re. tech-hiding:
I was nearly there, but not quite. I still haven't found the definitive CivDOS thread, but if I've understood the various other discussions (mainly with respect to CivII) correctly, each tech is assigned to one of 3 sublists (call them 'List0', 'List1', and 'List2' for the sake of argument), based on its
alphabetical position within the
full list of Civ1 techs
-- so AdvancedFlight might be in List0, Alphabet in List1, Astronomy in List2, AtomicTheory in List0, etc...
Each time the game asks you to pick your next research target, one of the 3 sublists will be unavailable -- which one is excluded depends on how many techs you've already learned (e.g. if you've learned 3n+0 techs, where n≥1, List0 techs might be unavailable to research, 3n+1 known techs would exclude List1 techs, and 3n+2 known techs would exclude List2 techs).
Since lightbulb-cost is
also incremented based on how many techs you already know, knowing which techs are in which sublist and picking your research path carefully can therefore make a
big difference to how fast you progress through the game.
EDIT 3: Return of the Son of EDIT
Or there's
this ready-made tech-tree.