speh₁-
“to succeed, to prosper”succeed, prosper, speed
Root for prospering, yielding English speed, Old English spedan, Latin sperare (to hope).
Discussion
The Proto-Indo-European root *speh₁- meant "to succeed, to prosper, to thrive." The Latin reflexes center on spēs, "hope": despair (dēspērāre, to be without hope) and prosper (prōsperāre, to cause to succeed). Latin built both its word for ultimate optimism and its word for ultimate pessimism from the same root. The Germanic branch took a different path. Old English spēd meant "success, prosperity," and modern English speed descends from it — but originally speed had nothing to do with velocity. "God speed you" was a wish for success, not swiftness. The shift from "success" to "quickness" occurred in Middle English, as the culture increasingly associated rapid completion with successful outcome. This semantic drift is itself a small cultural history: a society that once measured prosperity in abundance came to measure it in velocity. Sanskrit sphāyate, "he prospers, he grows fat," preserves the root with particular clarity, emphasizing the physical dimension — to prosper is to grow substantial, to thrive in the visible way that a well-fed body thrives. The root thus moves from bodily thriving through material success to psychological hope and finally to modern velocity.
Notes
Pokorny 983-984. English speed, prosper, despair, esperance.