'Subtract' is Latin for 'draw away from underneath' — from 'sub-' + 'trahere' (to pull).
To take away a part from the whole; in mathematics, to deduct one number or quantity from another.
From Latin 'subtractus,' past participle of 'subtrahere' (to draw away from below, to withdraw, to remove secretly), composed of 'sub-' (from below, under) + 'trahere' (to draw, to pull, to drag), from PIE *tragh- or *dhragh- (to draw, to pull along). The PIE root *dhragh- underlies a wide family of words involving pulling: 'tractor,' 'tract,' 'trail,' 'drag,' and the Germanic forms in German 'ziehen' (to pull) and Dutch 'trekken' (to pull, to trek). The earlier English form was 'subduct' (from the related 'subducere'), which persists in geology
The Latin prefix 'sub-' in 'subtract' originally meant 'from below' — the image being of pulling something away from underneath, like removing a card from the bottom of a deck. This secret, stealthy connotation survives in the related word 'subterfuge' (literally, 'fleeing underneath'), from the same prefix.