The underlying problem that leads to "hidden fifths" (or "hidden octaves") comes from the historical performance practice of diminution — "filling in" the spaces between two notes some interval apart.
The idea is explained by Fux:
Josephus [the student]. — What kind of mistake have I made?...
Aloysius [the teacher]. — ... You moved from the third to the fifth in direct motion against the rule: from an imperfect consonance to a perfect consonance1 one must go in contrary motion....
Josephus. — Do you mind explaining to me the reason [for that rule]?...
Aloysius. — ...One may not do it because two fifths follow each other immediately, of which one is apparent or open, the other, however, concealed or hidden, and would stand out by the diminution of the interval [emphasis mine], as I shall show you now in the example:
Below is Fux's example, adapted to use the notes given in the OP above.
T: Hidden Fifths
T: by diminution
V:V2 clef=bass middle=d
[V:V1] F D || F x1/2 E/4 D |]
[V:V2] d G || d c/4 B/4 A/4 G |]
(Johann Joseph Fux, The Study of Counterpoint, revised edition, translated and edited by Alfred Mann [W. W. Norton & Co., 1971], page 32.)
1 Fux defines "perfect consonances" as perfect unisons, fourths, fifths, and octaves. "Imperfect consonances" are major and minor thirds and sixths.