exult v.

word-forming element, in English meaning usually "out of, from," but also "upwards, completely, deprive of, without," and "former;" from Latin ex "out of, from within; from which time, since; according to; in regard to," from PIE *eghs "out" (source also of Gaulish ex-, Old Irish ess-, Old Church Slavonic izu, Russian iz). In some cases also from Greek cognate ex, ek. PIE *eghs had comparative form *eks-tero and superlative *eks-t(e)r-emo-. Often reduced to e- before -b-, -d-, -g-, consonantal -i-, -l-, -m-, -n-, -v- (as in elude, emerge, evaporate, etc.).

1560s, "leaping," a heraldic term, from Latin salientem (nominative saliens), present participle of salire "to leap," from a PIE root of uncertain form (source also of Sanskrit sisarsi, sisrate "to flow, run, hurry;"Greek hallesthai "to leap," Middle Irish saltraim "I trample," Middle Welsh sathar "trampling").

The meaning "pointing outward" (preserved in military usage) is from 1680s; that of "prominent, striking" first recorded 1840, from salient point (1670s), which refers to the heart of an embryo, which seems to leap, and translates Latin punctum saliens, going back to Aristotle's writings. Hence, the "starting point" of anything.