What is the origin of the phrase "cautious optimism" (when/where it
was first said, by whom, and in what contect?)

I've found usage of it in a news artcile as early as 1901 (UK).
Perhaps another researcher may find the answer.
answerfinder-ga

A similar phrase, "cautiously optimistic," was widely publicized
because of its use by former US President Ronald Reagan:

"William Safire, in 'Safire's New Political Dictionary,' (Random
House, New York, 1993) says: 'cautiously optimistic -- having a
guarded sense of well-being; the hopeful politician's straddle. This
phrase restricts the adjective 'optimistic' by modifying it with the
wary adverb 'cautiously.' President Reagan, asked how he felt about
the possibility of approval for his sale of AWACS aircraft to Saudi
Aradia, often answered, 'cautiously optimistic'."

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