In 1905, you have someone saying in direct quotation in the present tense that he is anxious to see an airplane* and that anxiety is not contingent (again in the present tense) on seeing it in flight. The present tense in do not see is an enduring present. It means that he'd really like to see the airplane on the ground even if subsequent to the observation and thereon into the future he never sees it take off.
When you transpose the whole thing to a past report, the observer was anxious (simple past), but the simple past of did not see covers any time in the past, including the time before the anxiety took hold. This leaves the slightly uncomfortable implication that the airplane might have been airborne and visible to our observer before he became anxious to see it, but he just wasn't observant enough to have noticed it.
In 1905, he was very anxious to see the new apparatus anyway even if he was not to see it fly.
(The fly here is the bare infinitive [to] fly. Exchanging it for the participle flying won't matter since both are non-finite verbs, which do not carry tense.)
*OK, I'm assuming the "apparatus" is not a dirigible.