The Spanish verb 'alentar' (meaning 'to encourage' or 'to breathe') comes from the Vulgar Latin *alenitare, which underwent a sound change called metathesis from an earlier form *anhelitare. This Vulgar Latin form was a frequentative verb (indicating repeated action) derived from the Classical Latin 'anhelare', meaning 'to breathe with difficulty' or 'to pant'.

The semantic development from 'breathing' to 'encouraging' is quite intuitive - when we encourage someone, we're metaphorically breathing life or energy into them. This connection between breath and spirit/encouragement is found in many languages, reflecting how fundamental this association is to human thinking.

A related Spanish word is 'aliento', which means 'breath' or 'encouragement'. You can see how both the literal meaning of breathing and the metaphorical meaning of encouragement are preserved in this noun form. Another related term is 'alentar el fuego' (to fan the fire), which uses the original breath-related meaning quite literally.

While English doesn't have any direct cognates from the Latin 'anhelare', we do have some words that capture a similar connection between breathing and spirit/energy. For example, 'inspire' (from Latin 'inspirare' - to breathe into) has both a literal breathing meaning and the figurative meaning of encouraging or stimulating someone. Similarly, 'aspire' (from Latin 'aspirare' - to breathe upon) shows this same pattern of developing from a breathing-related meaning to a more abstract one.