Origin and history of desperate

Middle English spede, from Old English sped "success, a successful course; prosperity, riches, wealth; luck, good fortune; opportunity, advancement," from Proto-Germanic *spodiz (source also of Old Saxon spod "success," Dutch spoed "haste, speed," Old High German spuot "success," Old Saxon spodian "to cause to succeed," Middle Dutch spoeden, Old High German spuoten "to haste").

This is reconstructed to be from PIE *spo-ti-, from root *spes- or *speh- "prosperity" (source also of Hittite išpai- "get full, be satiated;" Sanskrit sphira "fat," sphayate "increases;" Latin spes "hope," sperare "to hope;" Old Church Slavonic spechu "endeavor," spĕti "to succeed," Russian spet' "to ripen;" Lithuanian spėju, spėti "to have leisure;" Old English spōwan "to prosper").

The meaning "rapidity of movement, quickness, swiftness" emerged in late Old English (at first usually adverbially, in dative plural, as in spedum feran). The meaning "rate of motion or progress" (whether fast or slow) is from mid-14c. The sense of "gear of a machine" is attested from 1866. Slang use in reference to methamphetamine or a related drug is attested by 1967, from its effect on users.

Speed limit "maximum speed" of a vehicle (originally a locomotive), limited either by law or capability, is from 1879; the police officer's speed-trap is from 1908 (trap (n.1) in the police sense is by 1906). Speed bump as a traffic control device is by 1975; the figurative use is by 1990s. Full speed "highest rate of speed" is recorded from late 14c. Speed reading first attested 1965. Speedball "mix of cocaine and morphine or heroin" is recorded from 1909.

in old law, in reference to a debt, "having some likelihood of recovery," 1550s; earlier, of a debtor, "able to pay" (mid-15c.), from Latin speratus, past participle of sperare "to hope, look forward to," denominative of spes "hope" (from PIE root spes- "prosperity," for which see speed (n.)).

General (non-legal) use is by 1808. Etymologically, it is the opposite of desperate. Donne has speratory "resting on hope or expectation."

active word-forming element in English and in many verbs inherited from French and Latin, from Latin de "down, down from, from, off; concerning" (see de), also used as a prefix in Latin, usually meaning "down, off, away, from among, down from," but also "down to the bottom, totally" hence "completely" (intensive or completive), which is its sense in many English words.

As a Latin prefix it also had the function of undoing or reversing a verb's action, and hence it came to be used as a pure privative — "not, do the opposite of, undo" — which is its primary function as a living prefix in English, as in defrost (1895), defuse (1943), de-escalate (1964), etc. In some cases, a reduced form of dis-.