From Latin 'demonstrare' (to point out), from 'monstrum' (portent) — connecting proof to the ancient act of pointing.
To show clearly by giving proof or evidence; to illustrate and explain by practical example or experiment; to take part in a public protest.
From Latin 'dēmonstrātus,' past participle of 'dēmonstrāre' (to point out, to show, to prove), a compound of 'dē-' (entirely, completely) and 'monstrāre' (to show, to point out). 'Monstrāre' derives from 'monstrum' (a divine portent or warning), which comes from 'monēre' (to warn, to remind, to advise), ultimately from PIE *men- (to think). The chain from 'thinking' to 'warning' to 'showing a sign' to 'proving' traces an extraordinary semantic arc. Key roots: dēmonstrāre (Latin: "to point out, to prove
The word 'demonstrate' is an etymological cousin of 'monster.' Both trace back to Latin 'monēre' (to warn): a 'monstrum' was originally a divine warning sign — a birth defect or natural prodigy that the Romans interpreted as a message from the gods — and 'dēmonstrāre' meant to show or reveal such signs. The creature sense of 'monster' came later, from the idea that these portents were frightening.