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From Late Middle English pulse, Middle English pous, pouse (“regular beat of arteries, pulse; heartbeat; place on the body where a pulse is detectable; beat (of a musical instrument); energy, vitality”) [and other forms], from Anglo-Norman puls, pous, pus, and Middle French pouls, poulz, pous [and other forms], Old French pous, pulz (“regular beat of arteries; place on the body where a pulse is detectable”) (modern French pouls), and from their etymon Latin pulsus (“beat, impulse, pulse, stroke; regular beat of arteries or the heart”), from pellō (“to drive, impel, propel, push; to banish, eject, expel; to set in motion; to strike”) (ultimately from Proto-Indo-European *pel- (“to beat, strike; to drive; to push, thrust”)) + -sus (a variant of -tus (suffix forming action nouns from verbs)).

From Late Middle English pulse, Middle English pulsen (“to pulse, throb”), from Latin pulsāre, the present active infinitive of pulsō (“to push; to beat, batter, hammer, strike; to knock on; (figuratively) to drive or urge on, impel; to move; to agitate, disquiet, disturb”), the frequentative of pellō (“to drive, impel, propel, push; to banish, eject, expel; to set in motion; to strike”); see further at etymology 1. Doublet of push.

From Middle English puls (“(collectively) seeds of a leguminous plant used as food; leguminous plants collectively; a species of leguminous plant”), Early Middle English pols (in compounds), possibly from Anglo-Norman pus, puz, Middle French pouls, pols, pous, and Old French pous, pou (“gruel, mash, porridge”) (perhaps in the sense of a gruel made from pulses), or directly from their etymon Latin puls (“meal (coarse-ground edible part of various grains); porridge”), probably from Ancient Greek πόλτος (póltos, “porridge made from flour”), from Proto-Indo-European *pel- (“dust; flour”) (perhaps by extension from *pel- (“to beat, strike; to drive; to push, thrust”), in the sense of something beaten).